CN108137949A - 疏液涂层 - Google Patents
疏液涂层 Download PDFInfo
- Publication number
- CN108137949A CN108137949A CN201680048500.XA CN201680048500A CN108137949A CN 108137949 A CN108137949 A CN 108137949A CN 201680048500 A CN201680048500 A CN 201680048500A CN 108137949 A CN108137949 A CN 108137949A
- Authority
- CN
- China
- Prior art keywords
- angle
- hydroxide
- lyophoby
- transition metal
- coating
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000576 coating method Methods 0.000 title claims abstract description 86
- 239000011248 coating agent Substances 0.000 title claims abstract description 80
- 238000000034 method Methods 0.000 claims abstract description 53
- XLYOFNOQVPJJNP-UHFFFAOYSA-M hydroxide Chemical compound [OH-] XLYOFNOQVPJJNP-UHFFFAOYSA-M 0.000 claims abstract description 42
- 229910000000 metal hydroxide Inorganic materials 0.000 claims abstract description 29
- 229910000314 transition metal oxide Inorganic materials 0.000 claims abstract description 28
- 150000001875 compounds Chemical class 0.000 claims abstract description 27
- 230000003647 oxidation Effects 0.000 claims description 42
- 238000007254 oxidation reaction Methods 0.000 claims description 42
- 239000007788 liquid Substances 0.000 claims description 40
- 239000000758 substrate Substances 0.000 claims description 40
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 claims description 22
- 229910052782 aluminium Inorganic materials 0.000 claims description 22
- 229910021511 zinc hydroxide Inorganic materials 0.000 claims description 22
- 229940007718 zinc hydroxide Drugs 0.000 claims description 22
- -1 fluoroalkyl silanes Chemical class 0.000 claims description 21
- UGZADUVQMDAIAO-UHFFFAOYSA-L zinc hydroxide Chemical compound [OH-].[OH-].[Zn+2] UGZADUVQMDAIAO-UHFFFAOYSA-L 0.000 claims description 21
- 239000004411 aluminium Substances 0.000 claims description 20
- 239000000523 sample Substances 0.000 claims description 18
- 229920001343 polytetrafluoroethylene Polymers 0.000 claims description 15
- 239000004810 polytetrafluoroethylene Substances 0.000 claims description 15
- 229910002001 transition metal nitrate Inorganic materials 0.000 claims description 14
- VKYKSIONXSXAKP-UHFFFAOYSA-N hexamethylenetetramine Chemical compound C1N(C2)CN3CN1CN2C3 VKYKSIONXSXAKP-UHFFFAOYSA-N 0.000 claims description 11
- IPJKJLXEVHOKSE-UHFFFAOYSA-L manganese dihydroxide Chemical compound [OH-].[OH-].[Mn+2] IPJKJLXEVHOKSE-UHFFFAOYSA-L 0.000 claims description 11
- UQSXHKLRYXJYBZ-UHFFFAOYSA-N Iron oxide Chemical compound [Fe]=O UQSXHKLRYXJYBZ-UHFFFAOYSA-N 0.000 claims description 10
- 239000002033 PVDF binder Substances 0.000 claims description 10
- 238000009826 distribution Methods 0.000 claims description 10
- 229920002981 polyvinylidene fluoride Polymers 0.000 claims description 10
- 230000008859 change Effects 0.000 claims description 8
- 238000011049 filling Methods 0.000 claims description 8
- 235000010299 hexamethylene tetramine Nutrition 0.000 claims description 8
- 239000004312 hexamethylene tetramine Substances 0.000 claims description 8
- 239000000126 substance Substances 0.000 claims description 8
- 238000003618 dip coating Methods 0.000 claims description 7
- 239000001301 oxygen Substances 0.000 claims description 7
- 229910052760 oxygen Inorganic materials 0.000 claims description 7
- 238000011282 treatment Methods 0.000 claims description 7
- ONDPHDOFVYQSGI-UHFFFAOYSA-N zinc nitrate Chemical compound [Zn+2].[O-][N+]([O-])=O.[O-][N+]([O-])=O ONDPHDOFVYQSGI-UHFFFAOYSA-N 0.000 claims description 7
- PXHVJJICTQNCMI-UHFFFAOYSA-N Nickel Chemical compound [Ni] PXHVJJICTQNCMI-UHFFFAOYSA-N 0.000 claims description 6
- 238000004140 cleaning Methods 0.000 claims description 6
- 229910052723 transition metal Inorganic materials 0.000 claims description 6
- XEEYBQQBJWHFJM-UHFFFAOYSA-N Iron Chemical compound [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 claims description 5
- 150000001343 alkyl silanes Chemical class 0.000 claims description 5
- 235000014413 iron hydroxide Nutrition 0.000 claims description 5
- QGZKDVFQNNGYKY-UHFFFAOYSA-N Ammonia Chemical compound N QGZKDVFQNNGYKY-UHFFFAOYSA-N 0.000 claims description 4
- 229910021503 Cobalt(II) hydroxide Inorganic materials 0.000 claims description 4
- 150000001768 cations Chemical class 0.000 claims description 4
- ASKVAEGIVYSGNY-UHFFFAOYSA-L cobalt(ii) hydroxide Chemical compound [OH-].[OH-].[Co+2] ASKVAEGIVYSGNY-UHFFFAOYSA-L 0.000 claims description 4
- AEJIMXVJZFYIHN-UHFFFAOYSA-N copper;dihydrate Chemical compound O.O.[Cu] AEJIMXVJZFYIHN-UHFFFAOYSA-N 0.000 claims description 4
- 230000001186 cumulative effect Effects 0.000 claims description 4
- 238000000151 deposition Methods 0.000 claims description 4
- 229910052751 metal Inorganic materials 0.000 claims description 4
- 239000002184 metal Substances 0.000 claims description 4
- 239000000203 mixture Substances 0.000 claims description 4
- 125000002347 octyl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])[H] 0.000 claims description 4
- ZDHXKXAHOVTTAH-UHFFFAOYSA-N trichlorosilane Chemical compound Cl[SiH](Cl)Cl ZDHXKXAHOVTTAH-UHFFFAOYSA-N 0.000 claims description 4
- 239000005052 trichlorosilane Substances 0.000 claims description 4
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 claims description 3
- HCHKCACWOHOZIP-UHFFFAOYSA-N Zinc Chemical compound [Zn] HCHKCACWOHOZIP-UHFFFAOYSA-N 0.000 claims description 3
- 229910017052 cobalt Inorganic materials 0.000 claims description 3
- 239000010941 cobalt Substances 0.000 claims description 3
- GUTLYIVDDKVIGB-UHFFFAOYSA-N cobalt atom Chemical compound [Co] GUTLYIVDDKVIGB-UHFFFAOYSA-N 0.000 claims description 3
- 229910052802 copper Inorganic materials 0.000 claims description 3
- 239000010949 copper Substances 0.000 claims description 3
- 239000007789 gas Substances 0.000 claims description 3
- 238000010438 heat treatment Methods 0.000 claims description 3
- 229910052742 iron Inorganic materials 0.000 claims description 3
- WPBNNNQJVZRUHP-UHFFFAOYSA-L manganese(2+);methyl n-[[2-(methoxycarbonylcarbamothioylamino)phenyl]carbamothioyl]carbamate;n-[2-(sulfidocarbothioylamino)ethyl]carbamodithioate Chemical compound [Mn+2].[S-]C(=S)NCCNC([S-])=S.COC(=O)NC(=S)NC1=CC=CC=C1NC(=S)NC(=O)OC WPBNNNQJVZRUHP-UHFFFAOYSA-L 0.000 claims description 3
- 229910001960 metal nitrate Inorganic materials 0.000 claims description 3
- 229910044991 metal oxide Inorganic materials 0.000 claims description 3
- 150000004706 metal oxides Chemical class 0.000 claims description 3
- 229910052759 nickel Inorganic materials 0.000 claims description 3
- 229920000642 polymer Polymers 0.000 claims description 3
- 150000003624 transition metals Chemical class 0.000 claims description 3
- 229910052725 zinc Inorganic materials 0.000 claims description 3
- 239000011701 zinc Substances 0.000 claims description 3
- PWHULOQIROXLJO-UHFFFAOYSA-N Manganese Chemical compound [Mn] PWHULOQIROXLJO-UHFFFAOYSA-N 0.000 claims description 2
- CBENFWSGALASAD-UHFFFAOYSA-N Ozone Chemical compound [O-][O+]=O CBENFWSGALASAD-UHFFFAOYSA-N 0.000 claims description 2
- GSEJCLTVZPLZKY-UHFFFAOYSA-N Triethanolamine Chemical compound OCCN(CCO)CCO GSEJCLTVZPLZKY-UHFFFAOYSA-N 0.000 claims description 2
- XSQUKJJJFZCRTK-UHFFFAOYSA-N Urea Chemical compound NC(N)=O XSQUKJJJFZCRTK-UHFFFAOYSA-N 0.000 claims description 2
- 229910021529 ammonia Inorganic materials 0.000 claims description 2
- 239000004202 carbamide Substances 0.000 claims description 2
- 238000003851 corona treatment Methods 0.000 claims description 2
- BFDHFSHZJLFAMC-UHFFFAOYSA-L nickel(ii) hydroxide Chemical compound [OH-].[OH-].[Ni+2] BFDHFSHZJLFAMC-UHFFFAOYSA-L 0.000 claims description 2
- AIBQNUOBCRIENU-UHFFFAOYSA-N nickel;dihydrate Chemical compound O.O.[Ni] AIBQNUOBCRIENU-UHFFFAOYSA-N 0.000 claims description 2
- 238000007740 vapor deposition Methods 0.000 claims description 2
- 229960004011 methenamine Drugs 0.000 claims 2
- PRPAGESBURMWTI-UHFFFAOYSA-N [C].[F] Chemical compound [C].[F] PRPAGESBURMWTI-UHFFFAOYSA-N 0.000 claims 1
- 150000001335 aliphatic alkanes Chemical class 0.000 claims 1
- 229920013822 aminosilicone Polymers 0.000 claims 1
- 229910052748 manganese Inorganic materials 0.000 claims 1
- 239000011572 manganese Substances 0.000 claims 1
- BYOBIQOEWYNTMM-UHFFFAOYSA-N manganese;nitric acid Chemical compound [Mn].O[N+]([O-])=O BYOBIQOEWYNTMM-UHFFFAOYSA-N 0.000 claims 1
- FZHAPNGMFPVSLP-UHFFFAOYSA-N silanamine Chemical class [SiH3]N FZHAPNGMFPVSLP-UHFFFAOYSA-N 0.000 claims 1
- BNCXNUWGWUZTCN-UHFFFAOYSA-N trichloro(dodecyl)silane Chemical compound CCCCCCCCCCCC[Si](Cl)(Cl)Cl BNCXNUWGWUZTCN-UHFFFAOYSA-N 0.000 claims 1
- 238000012512 characterization method Methods 0.000 abstract description 6
- 239000002585 base Substances 0.000 description 21
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Substances O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 21
- 239000000463 material Substances 0.000 description 18
- 230000003075 superhydrophobic effect Effects 0.000 description 13
- 239000000243 solution Substances 0.000 description 12
- 238000009736 wetting Methods 0.000 description 11
- 239000010408 film Substances 0.000 description 10
- 238000009833 condensation Methods 0.000 description 9
- 230000005494 condensation Effects 0.000 description 9
- NUJOXMJBOLGQSY-UHFFFAOYSA-N manganese dioxide Chemical compound O=[Mn]=O NUJOXMJBOLGQSY-UHFFFAOYSA-N 0.000 description 8
- 230000002209 hydrophobic effect Effects 0.000 description 7
- 238000012360 testing method Methods 0.000 description 7
- CSCPPACGZOOCGX-UHFFFAOYSA-N Acetone Chemical compound CC(C)=O CSCPPACGZOOCGX-UHFFFAOYSA-N 0.000 description 6
- OKKJLVBELUTLKV-UHFFFAOYSA-N Methanol Chemical compound OC OKKJLVBELUTLKV-UHFFFAOYSA-N 0.000 description 6
- BLRPTPMANUNPDV-UHFFFAOYSA-N Silane Chemical compound [SiH4] BLRPTPMANUNPDV-UHFFFAOYSA-N 0.000 description 6
- XLOMVQKBTHCTTD-UHFFFAOYSA-N Zinc monoxide Chemical compound [Zn]=O XLOMVQKBTHCTTD-UHFFFAOYSA-N 0.000 description 6
- 230000008901 benefit Effects 0.000 description 6
- 230000015572 biosynthetic process Effects 0.000 description 6
- 238000006243 chemical reaction Methods 0.000 description 6
- 238000001259 photo etching Methods 0.000 description 6
- 229910000077 silane Inorganic materials 0.000 description 6
- 239000007787 solid Substances 0.000 description 6
- 230000001788 irregular Effects 0.000 description 5
- 238000004519 manufacturing process Methods 0.000 description 5
- 230000008569 process Effects 0.000 description 5
- 238000001878 scanning electron micrograph Methods 0.000 description 5
- 238000003786 synthesis reaction Methods 0.000 description 5
- SNRUBQQJIBEYMU-UHFFFAOYSA-N Dodecane Natural products CCCCCCCCCCCC SNRUBQQJIBEYMU-UHFFFAOYSA-N 0.000 description 4
- PEDCQBHIVMGVHV-UHFFFAOYSA-N Glycerine Chemical compound OCC(O)CO PEDCQBHIVMGVHV-UHFFFAOYSA-N 0.000 description 4
- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
- 230000006872 improvement Effects 0.000 description 4
- 238000005259 measurement Methods 0.000 description 4
- YFSUTJLHUFNCNZ-UHFFFAOYSA-N perfluorooctane-1-sulfonic acid Chemical compound OS(=O)(=O)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)F YFSUTJLHUFNCNZ-UHFFFAOYSA-N 0.000 description 4
- 229910052710 silicon Inorganic materials 0.000 description 4
- 239000010703 silicon Substances 0.000 description 4
- UHOVQNZJYSORNB-UHFFFAOYSA-N Benzene Chemical compound C1=CC=CC=C1 UHOVQNZJYSORNB-UHFFFAOYSA-N 0.000 description 3
- 239000004809 Teflon Substances 0.000 description 3
- 229920006362 Teflon® Polymers 0.000 description 3
- 239000002253 acid Substances 0.000 description 3
- 238000004378 air conditioning Methods 0.000 description 3
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 description 3
- 239000000919 ceramic Substances 0.000 description 3
- 125000001309 chloro group Chemical group Cl* 0.000 description 3
- 238000001816 cooling Methods 0.000 description 3
- 125000002704 decyl group Chemical group [H]C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])* 0.000 description 3
- MIVBAHRSNUNMPP-UHFFFAOYSA-N manganese(2+);dinitrate Chemical compound [Mn+2].[O-][N+]([O-])=O.[O-][N+]([O-])=O MIVBAHRSNUNMPP-UHFFFAOYSA-N 0.000 description 3
- VLKZOEOYAKHREP-UHFFFAOYSA-N n-Hexane Chemical compound CCCCCC VLKZOEOYAKHREP-UHFFFAOYSA-N 0.000 description 3
- 239000011148 porous material Substances 0.000 description 3
- 230000009466 transformation Effects 0.000 description 3
- 239000011787 zinc oxide Substances 0.000 description 3
- 229910002651 NO3 Inorganic materials 0.000 description 2
- NHNBFGGVMKEFGY-UHFFFAOYSA-N Nitrate Chemical compound [O-][N+]([O-])=O NHNBFGGVMKEFGY-UHFFFAOYSA-N 0.000 description 2
- 230000008021 deposition Effects 0.000 description 2
- 230000006866 deterioration Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 125000003438 dodecyl group Chemical group [H]C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])* 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 230000002708 enhancing effect Effects 0.000 description 2
- 229920002313 fluoropolymer Polymers 0.000 description 2
- 230000014509 gene expression Effects 0.000 description 2
- 235000011187 glycerol Nutrition 0.000 description 2
- 125000004051 hexyl group Chemical group [H]C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])* 0.000 description 2
- 238000007654 immersion Methods 0.000 description 2
- VCJMYUPGQJHHFU-UHFFFAOYSA-N iron(3+);trinitrate Chemical compound [Fe+3].[O-][N+]([O-])=O.[O-][N+]([O-])=O.[O-][N+]([O-])=O VCJMYUPGQJHHFU-UHFFFAOYSA-N 0.000 description 2
- 239000012528 membrane Substances 0.000 description 2
- 239000004005 microsphere Substances 0.000 description 2
- 239000003595 mist Substances 0.000 description 2
- RZJRJXONCZWCBN-UHFFFAOYSA-N octadecane Chemical compound CCCCCCCCCCCCCCCCCC RZJRJXONCZWCBN-UHFFFAOYSA-N 0.000 description 2
- 239000003921 oil Substances 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- 238000009832 plasma treatment Methods 0.000 description 2
- 229920001296 polysiloxane Polymers 0.000 description 2
- 239000002243 precursor Substances 0.000 description 2
- 238000007789 sealing Methods 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 230000002269 spontaneous effect Effects 0.000 description 2
- 238000012546 transfer Methods 0.000 description 2
- 230000007704 transition Effects 0.000 description 2
- QQQSFSZALRVCSZ-UHFFFAOYSA-N triethoxysilane Chemical compound CCO[SiH](OCC)OCC QQQSFSZALRVCSZ-UHFFFAOYSA-N 0.000 description 2
- 235000012431 wafers Nutrition 0.000 description 2
- 238000005406 washing Methods 0.000 description 2
- 241000894006 Bacteria Species 0.000 description 1
- ZAMOUSCENKQFHK-UHFFFAOYSA-N Chlorine atom Chemical compound [Cl] ZAMOUSCENKQFHK-UHFFFAOYSA-N 0.000 description 1
- LFQSCWFLJHTTHZ-UHFFFAOYSA-N Ethanol Chemical compound CCO LFQSCWFLJHTTHZ-UHFFFAOYSA-N 0.000 description 1
- 241000233866 Fungi Species 0.000 description 1
- 239000002202 Polyethylene glycol Substances 0.000 description 1
- 241000669244 Unaspis euonymi Species 0.000 description 1
- 238000005299 abrasion Methods 0.000 description 1
- 230000003213 activating effect Effects 0.000 description 1
- 230000006978 adaptation Effects 0.000 description 1
- 239000000654 additive Substances 0.000 description 1
- 230000000996 additive effect Effects 0.000 description 1
- 239000003513 alkali Substances 0.000 description 1
- WNROFYMDJYEPJX-UHFFFAOYSA-K aluminium hydroxide Chemical compound [OH-].[OH-].[OH-].[Al+3] WNROFYMDJYEPJX-UHFFFAOYSA-K 0.000 description 1
- 229910021502 aluminium hydroxide Inorganic materials 0.000 description 1
- 238000000137 annealing Methods 0.000 description 1
- 239000007864 aqueous solution Substances 0.000 description 1
- 125000000484 butyl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])C([H])([H])[H] 0.000 description 1
- 238000006555 catalytic reaction Methods 0.000 description 1
- 239000003153 chemical reaction reagent Substances 0.000 description 1
- 239000000460 chlorine Substances 0.000 description 1
- 229910052801 chlorine Inorganic materials 0.000 description 1
- 239000002826 coolant Substances 0.000 description 1
- 239000008367 deionised water Substances 0.000 description 1
- 229910021641 deionized water Inorganic materials 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 125000004386 diacrylate group Chemical group 0.000 description 1
- SZXQTJUDPRGNJN-UHFFFAOYSA-N dipropylene glycol Chemical compound OCCCOCCCO SZXQTJUDPRGNJN-UHFFFAOYSA-N 0.000 description 1
- 238000000635 electron micrograph Methods 0.000 description 1
- 238000005265 energy consumption Methods 0.000 description 1
- 238000005530 etching Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000000284 extract Substances 0.000 description 1
- 239000000835 fiber Substances 0.000 description 1
- XUCNUKMRBVNAPB-UHFFFAOYSA-N fluoroethene Chemical compound FC=C XUCNUKMRBVNAPB-UHFFFAOYSA-N 0.000 description 1
- 238000007710 freezing Methods 0.000 description 1
- 230000008014 freezing Effects 0.000 description 1
- 125000003187 heptyl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])[H] 0.000 description 1
- 230000005661 hydrophobic surface Effects 0.000 description 1
- 125000002887 hydroxy group Chemical group [H]O* 0.000 description 1
- 238000009413 insulation Methods 0.000 description 1
- 150000002500 ions Chemical class 0.000 description 1
- 238000001540 jet deposition Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 229910021645 metal ion Inorganic materials 0.000 description 1
- 125000000956 methoxy group Chemical group [H]C([H])([H])O* 0.000 description 1
- ARYZCSRUUPFYMY-UHFFFAOYSA-N methoxysilane Chemical compound CO[SiH3] ARYZCSRUUPFYMY-UHFFFAOYSA-N 0.000 description 1
- 238000002156 mixing Methods 0.000 description 1
- 125000001421 myristyl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])[H] 0.000 description 1
- IJRVLVIFMRWJRQ-UHFFFAOYSA-N nitric acid zinc Chemical compound [Zn].O[N+]([O-])=O IJRVLVIFMRWJRQ-UHFFFAOYSA-N 0.000 description 1
- 125000001400 nonyl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])[H] 0.000 description 1
- 229940038384 octadecane Drugs 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000010422 painting Methods 0.000 description 1
- 125000000913 palmityl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])[H] 0.000 description 1
- 230000000149 penetrating effect Effects 0.000 description 1
- 229920002120 photoresistant polymer Polymers 0.000 description 1
- 229920001223 polyethylene glycol Polymers 0.000 description 1
- 238000001556 precipitation Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 125000001436 propyl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])[H] 0.000 description 1
- 238000005086 pumping Methods 0.000 description 1
- 239000000376 reactant Substances 0.000 description 1
- 238000005057 refrigeration Methods 0.000 description 1
- 230000001846 repelling effect Effects 0.000 description 1
- 238000002791 soaking Methods 0.000 description 1
- 239000002904 solvent Substances 0.000 description 1
- 238000000527 sonication Methods 0.000 description 1
- 238000001330 spinodal decomposition reaction Methods 0.000 description 1
- 239000010935 stainless steel Substances 0.000 description 1
- 229910001220 stainless steel Inorganic materials 0.000 description 1
- 125000004079 stearyl group Chemical group [H]C([*])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])C([H])([H])[H] 0.000 description 1
- 230000003746 surface roughness Effects 0.000 description 1
- 239000000725 suspension Substances 0.000 description 1
- 238000010998 test method Methods 0.000 description 1
- YODZTKMDCQEPHD-UHFFFAOYSA-N thiodiglycol Chemical compound OCCSCCO YODZTKMDCQEPHD-UHFFFAOYSA-N 0.000 description 1
- 229950006389 thiodiglycol Drugs 0.000 description 1
- 238000000844 transformation Methods 0.000 description 1
- ZFUVZJADECZZMS-UHFFFAOYSA-N trichloro(3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,12-henicosafluorododecyl)silane Chemical compound FC(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)CC[Si](Cl)(Cl)Cl ZFUVZJADECZZMS-UHFFFAOYSA-N 0.000 description 1
- MLXDKRSDUJLNAB-UHFFFAOYSA-N triethoxy(3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,10-heptadecafluorodecyl)silane Chemical compound CCO[Si](OCC)(OCC)CCC(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)C(F)(F)F MLXDKRSDUJLNAB-UHFFFAOYSA-N 0.000 description 1
- 238000001291 vacuum drying Methods 0.000 description 1
- 239000002699 waste material Substances 0.000 description 1
Classifications
-
- C—CHEMISTRY; METALLURGY
- C23—COATING METALLIC MATERIAL; COATING MATERIAL WITH METALLIC MATERIAL; CHEMICAL SURFACE TREATMENT; DIFFUSION TREATMENT OF METALLIC MATERIAL; COATING BY VACUUM EVAPORATION, BY SPUTTERING, BY ION IMPLANTATION OR BY CHEMICAL VAPOUR DEPOSITION, IN GENERAL; INHIBITING CORROSION OF METALLIC MATERIAL OR INCRUSTATION IN GENERAL
- C23C—COATING METALLIC MATERIAL; COATING MATERIAL WITH METALLIC MATERIAL; SURFACE TREATMENT OF METALLIC MATERIAL BY DIFFUSION INTO THE SURFACE, BY CHEMICAL CONVERSION OR SUBSTITUTION; COATING BY VACUUM EVAPORATION, BY SPUTTERING, BY ION IMPLANTATION OR BY CHEMICAL VAPOUR DEPOSITION, IN GENERAL
- C23C26/00—Coating not provided for in groups C23C2/00 - C23C24/00
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- C—CHEMISTRY; METALLURGY
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Abstract
本发明一般地涉及疏液涂层,特别是涉及多孔疏液涂层、制备多孔疏液涂层的方法以及表征用于疏液涂层的多孔表面的方法。本发明还涉及多孔疏液涂层,该涂层包括:过渡金属氧化物和/或氢氧化物多孔层;和疏液化合物层,其沉积在过渡金属氧化物和/或氢氧化物多孔层上,其中,过渡金属氧化物和/或氢氧化物多孔层由多个表面孔构成,该多个表面孔具有平均角度为凹角的不同角度。
Description
相关申请的交叉引用
本申请要求2015年8月19日提交的美国临时专利申请No.62/207,109的优先权,其全部内容通过引用结合在本申请中。
技术领域
本发明涉及疏液涂层,特别是涉及多孔疏液涂层、制备多孔疏液涂层的方法以及表征疏液涂层的多孔表面的方法。
背景技术
最近滴状冷凝已被预测并显示出在空气侧热交换器上表现为增强的热传导。为了实现滴状冷凝,需要超疏水表面。
已经提出了很多将表面能降低到超疏水水平的方法。超疏水性可以通过创造一个具有非常大的面积和疏水化学品的表面来实现。在典型的超疏水涂层中,典型地通过使用高价的光致抗蚀剂和相对绝缘的基底对硅晶片自上而下图案化,或者通过容易磨蚀和热降解的喷涂聚合物涂层,来实现大表面积的产生。
相反,大表面积涂层的自下而上的生长有可能比自上而下的光刻技术便宜得多,并且比喷涂涂层更稳固。然而,已证实极少有可行的自下而上的过程,它们都需要相对复杂和/或昂贵的化学品或者不能在最普通的热交换器材料(铝和不锈钢)上生长。因此,对于商用换热器应用而言,价格低廉且足够稳固的涂层非常少。
滴状冷凝具有多种潜在的有益效果:
a.增强了冷却表面的热传导,从而仅需较少的冷却液的冷却,实现空气温度的给定降低量,从而降低能耗;
b.冷却表面(通常是平行金属板或“翅片”的阵列)上没有水膜使得对空气流动的阻抗较小,从而降低了所需的空气泵送功率;
c.由于表面没有积水,因此热交换器内生长真菌或细菌的风险较小。
因此,仍然需要提供用于表面的疏液涂层,以克服或至少减轻上述问题。
发明内容
根据本发明的一个方面,提供了一种多孔疏液涂层。所述涂层可包括过渡金属氧化物和/或氢氧化物多孔层。所述涂层还可包括疏液化合物层,该疏液化合物层沉积在所述过渡金属氧化物和/或氢氧化物多孔层上。过渡金属氧化物和/或氢氧化物多孔层可由多个表面孔形成,该多个表面孔具有平均角度为凹角的不同角度。
在优选的实施方式中,基于多个表面孔的角度的高斯分布模型,所述角度相对于平均凹角角度Ψ0的标准偏差σ0在0和60°之间,优选地,在0和40°之间。
根据本发明的另一个方面,提供了在基底上制备多孔疏液涂层的方法。所述涂层可以包括上述一个方面中的涂层。所述方法可包括:在20℃至100℃的温度范围内,将基底浸泡于过渡金属硝酸盐和弱碱的溶液中,以在基底上形成过渡金属氧化物和/或氢氧化物多孔层。所述方法还可包括:将疏液化合物沉积在所述过渡金属氧化物和/或氢氧化物多孔层上,从而在所述基板上形成多孔疏液涂层。
根据本发明的又一个方面,公开了一种用所述平均凹角角度Ψ0和多个表面孔的角度相对于Ψ0的的标准偏差σ0表征具有多个表面孔的多孔表面的方法。所述方法可包括:
分别测量各自具有不同表面张力的至少四种探针液体的接触角θ0,其中平坦表面上的接触角通过固着液滴法测量;
分别测量所述至少四种探针液体的表观接触角θ*,其中所述多孔表面上的表观接触角通过固着液滴法测量;和
使用最小二乘误差最小化程序来拟合以下等式中的Ψ0、σ0、φT和r:
φF=1-P(θ0) (2)
cosθ*=φTcosθ0+(1-φT)[φFrcosθ0-(1-φF)].(3)
其中:
P(Ψ)是根据具有平均凹角角度Ψ0和标准偏差σ0的高斯分布的角度Ψ的累积分布函数,
ФF是填充孔的占比,
φT是位于孔之间的多孔表面顶端并且总是与液体接触的面积的分数,
(1-φT)是剩余面积,其被划分为在填充孔的占比ФF和存在液-气界面的未填充孔的占比之间;
r是孔的粗糙度,其使得孔的总表面积是一个孔开口的投影面积的r倍。
附图说明
附图不一定是按比例绘制,而是通常着重于说明各种实施例的原理。在以下的说明中,本发明的各种实施例将参考以下附图进行说明。
图1示出了涂覆的铝表面的扫描电子显微照片,其显示了在涂敷涂层期间形成了均匀的多孔网状物。图1中各插图分别是:(a)平衡接触角为172°的水滴;(b)平衡接触角为177°的水滴;(c)在迅速脱落液滴的情况下促进滴状冷凝的涂层的照片;和(d)在高过饱和度和高空气流速的空调模拟器中,促进在平衡状态下淹没表面的冷凝的涂层的照片。这表明在70℃合成的样品(a)和(c)在凝结条件下优于在110℃的较高温度下合成的样品(b)和(d),尽管前者接触角稍小。
图2示出了涂覆的铝表面的扫描电子显微照片,其显示了通过简单地改变反应浴的浓度和温度可以调节表面特性。图中的每个框的宽度是6.5μm。整个阵列的孔径范围从100纳米以下到5微米以上不等。
图3示出了最常用的合成条件下接触角相对于反应条件的变化图。尽管每个反应温度下使用固着液滴法都具有大致相同的接触角,但是冷凝实验显示较低温度合成(70℃)在冷凝和脱落液滴方面优越得多。误差线表示测量中的1个标准偏差。
图4示出了在铝基底存在下,通过使(a)硝酸锰和(b)硝酸锌与六胺(Hexamine)反应而形成的几乎相同的结构。这导致多孔(a)MnO2和(b)ZnO结构的形成。
图5示出了孔几何形状及其变化对液体表观接触角的影响。经典的(a)Wenzel和(b)Cassie-Baxter模型假定具有固定的凹角角度Ψ的完全空间均匀的表面特征几何形状,结果是在θ0<Ψ处完全润湿(a),或在θ0>Ψ处完全不润湿(b)。实际的表面展现出一系列有效的Ψ,使得孔填充的部分将取决于θ0(c)。
图6显示了用PFOS、PFO-POSS和APTES封端的氧化锌/氢氧化物纳米多孔表面的表面润湿性模型的校准。如扫描电子显微照片(a)所示,水热生长的ZnO中的孔具有高度不均匀的尺寸和侧壁角度。图6(b)展示了一组拟合参数准确地描述了具有三种表面封端的该表面几何形状的cosθ*对cosθ0的依赖。误差线对应于基于五个测量值的平均值的±1个标准误差。
图7示出了用于PVDF微球、用牺牲PS微球模板化的多孔PTFE、水热生长的纳米多孔ZnO和规则凹角的SiO2/Si微结构的表面润湿性模型的校准。PVDF微球的扫描电子显微照片(a)示出了具有均匀分布的直径和纳米级表面粗糙度的微球。PTFE膜显示了很大的孔径变化(b)。模型校准(c)表明,PTFE膜的cosθ*随着cosθ0最平缓地增加,这与孔几何形状的大的空间变化一致。用于PTFE、PVDF和ZnO的标志表示五个测量值的平均值。规则凹角结构的数据来自Liu(Liu,T.“Leo”;Kim,C.-J.“CJ.”Turning a Surface Superrepellent Even toCompletely Wetting Liquids.Science 2014,346(6213),1096-1100)。
具体实施方式
以下详细说明引用的附图,以举例方式展示本发明实施的可能具体细节和实施例。所述实施例中描述了足够的细节,以使得本领域技术人员能够实施本发明。还可以利用其他实施例,且可以进行结构、化学和材料上的变化,而不会脱离本发明的范围。各个实施例之间不必要相互排斥,一些实施例可以与一个或多个其他实施例组合来形成新的实施例。
本发明的示例性实施例涉及多孔疏液涂层。该涂层,特别地,是防水的。该涂层可以用于需要控制基底(例如铝)的润湿性的任何应用中。这可以很容易地应用于在冷凝环境中运行的任何换热器的空气侧,所述冷凝环境包括但不限于空调系统、制冷系统和蒸汽发电厂。热水器技术也在推进使用凝结促进系统来回收水汽化的潜热。雾收集器涂层也可以用来潜在地降低从雾中回收水的能量成本。
该涂层还可以用作防止结冰的涂层,例如用在卫星天线和飞机外部。在催化中也具有潜在的用途。
然而,在某些情况下,将多孔疏液涂层施加到用于排斥其它液体的表面上也可能是有用的,所述其它液体例如甘油和甲醇,它们是表面张力低于水的液体。
在本说明书中,术语“多孔”是指由多个表面孔组成的层。这与表面孔几乎不存在的光滑或无孔的层截然不同。换言之,多孔层可以包括纹理化表面。更确切地说,纹理化表面可以由不同程度的孔几何异质性组成。孔可以从表面向内延伸到多孔层的一定深度。孔可以但不一定具有彼此不同的几何形状。
在各种实施例中,可以根据等式(1)中采用的高斯分布模型,用平均凹角角度Ψ0和所述角度相对于该平均凹角角度Ψ0的标准偏差σ0来表征多孔表面。在本内容中,术语“凹角角度”是指底切表面角度(Under-cut surface angle)或孔侧壁角度。
所述涂层可包括过渡金属氧化物和/或氢氧化物多孔层。
合适的过渡金属氧化和/或氢氧化物可包括:氧化/氢氧化锌、氧化/氢氧化镍(II)、氧化/氢氧化镍(III)、氧化/氢氧化锰(II)、氧化/氢氧化锰(III)、氧化/氢氧化锰(IV)、氧化/氢氧化锰(VI)、氧化/氢氧化锰(VII)、氧化/氢氧化铜(I)、氧化/氢氧化铜(II)、氧化/氢氧化钴(II)、氧化/氢氧化钴(III)、氧化/氢氧化铁(II)、或氧化/氢氧化铁(III)。多孔层可以仅包括一种类型的过渡金属氧化物或氢氧化物。或者,多孔层可以包括多于一种类型的过渡金属氧化物或氢氧化物。基底也可以贡献金属离子,在本例中为铝,以形成混合过渡金属和氧化和/或氢氧化铝涂层。因此,本涂层的一个优点是成本低,因为该涂层是基于地球上一些最常见的元素。此外,所有的前驱材料(将在后面的段落中描述)目前都以高可用性使用在现有的商业化学合成中。这使得与现有的商业涂层相比,成本非常低。
在优选的实施例中,过渡金属氧化物/氢氧化物是氧化/氢氧化锌、氧化/氢氧化铁或氧化/氢氧化锰。
涂层还可包括疏液化合物层,该疏液化合物层沉积在过渡金属氧化物/氢氧化物多孔层上。
在本说明书中,术语“疏水(hydrophobic)”是指憎水性材料或排斥水的倾向。定量地定义,疏水性通常是指水接触角大于90°,例如100°、110°或120°。因此,“超疏水性(superhydrophobicity)”和“超疏水(superhydrophobic)”一般是指水接触角约为150°或更大。一般地,通过固着液滴法测量水接触角。
为了简单明了,在本说明书中使用的术语“疏液”应包括术语“疏水”、“超疏水”、“疏油”(即抗油)、“超疏油”和/或“全憎性”等。
过渡金属氧化物/氢氧化物多孔层可由多个表面孔组成,该多个表面孔具有平均角度为凹角的不同角度。该多个角度可以是一致的(即全部相同的角度)或多种多样的(即不同的角度)。而且,并不是所有的孔都需要具有凹角角度。
“多个”意思是多于一个。
换言之,多孔层是不均匀的,因此不是所有的表面孔都具有相同的角度。
在各种实施例中,多个表面孔中的至少一个具有小于90°的凹角角度。例如,凹角角度可以在10°和90°之间,例如15°、20°、25°、30°、35°、40°、45°、以及最高达90°。
在一个实施例中,多个表面孔中的至少一个具有约90°的角度。
在其他实施例中,多个表面孔中的至少一个具有大于90°的角度。例如,该角度可以在90°和160°之间,例如95°、100°、105°、110°、115°、120°、125°、以及最高达160°。
在又一替代性实施例中,多个表面孔可包括至少一个具有小于90°的凹角角度的表面孔,以及至少一个具有大于90°的角度的表面孔。
在一些优选的、基于根据等式(1)的多个表面孔的角度的高斯分布模型的实施例中,所述角度相对于平均凹角角度Ψ0的标准偏差σ0在0~60°之间,例如0°、1°、2°、3°、4°、5°、6°、7°、8°、9°、10°、11°、12°、13°、14°、15°、16°、17°、18°、19°、20°、21°、22°、23°、24°、25°、26°、27°、28°、29°、30°、31°、32°、33°、34°、35°、36°、37°、38°、39°、40°、41°、42°、43°、44°、45°、46°、47°、48°、49°、50°、51°、52°、53°、54°、55°、56°、57°、58°、59°或60°。优选地,所述标准偏差σ0在0和40°之间。标准偏差σ0的值越高,表面越纹理化(或越不均匀),这对于量化表面的疏液性(例如,如果液体是水,就是疏水性)可能是有用的。
在各种实施例中,疏液化合物可以是氟碳聚合物或化合物。优选地,使用低表面能氟碳聚合物或化合物来涂覆过渡金属氧化物/氢氧化物多孔层以使其具有疏液性。
在各种实施例中,疏液化合物可以是氟代烷基硅烷(FAS)或烷基硅烷,例如十八烷基硅烷(ODS)。
在优选的实施例中,疏液化合物可以是:1H,1H,2H,2H-全氟十二烷基三氯硅烷;1H,1H,2H,2H-全氟辛基三氯硅烷(PFOS);1H,1H,2H,2H-全氟癸基三乙氧基硅烷;1H,1H,2H,2H-全氟癸基三氯硅烷、1H,1H,2H,2H-全氟辛基三乙氧基硅烷、十八烷基三氯硅烷、聚偏二氟乙烯(PVDF)、聚四氟乙烯(PTFE)或全氟辛基多面体低聚倍半硅氧烷(PFO-POSS)。进一步地,FAS的变体还可以包括所有乙氧基、甲氧基、氯代基、己基的变体、辛基、癸基和十二烷基变体。对于每个辛基、癸基和十二烷基的组合,这可以是甲氧基,二甲氧基,三甲氧基、氯、二氯、三氯、乙氧基、二乙氧基、三乙氧基。更进一步地,烷基硅烷的变体可以包括相同的甲氧基、氯代基或乙氧基离去基团,其链长包括丙基、丁基、己基、庚基、辛基、壬基、癸基、十二烷基、十四烷基、十六烷基、十八烷基等。
有利地,多个表面孔的孔径可以从小于50纳米变化到大于10微米。这使得涂层可以用于要求稍微不同特性的多种应用。孔径可调的能力可以归因于形成涂层的容易性,这将在下面讨论。
简而言之,可以简单地在没有模板的情况下,在相对较低温度的水浴中通过浸泡基底、洗涤并使其干燥而生长出所述涂层。
因此,根据各种实施例,提供了一种在基底上制备多孔疏液涂层的方法。该涂层可以包括上述方面中的涂层。
该方法可以包括:将基底(便利地为通常用于热交换器中的铝基底)浸泡于温度在20℃到100℃之间的、过渡金属硝酸盐和弱碱的溶液中,以在所述基底上形成过渡金属氧化物和/或氢氧化物多孔层。
优选地,浸泡基底包括将基底浸泡于过渡金属硝酸盐和弱碱的等摩尔溶液中。应该认识到,虽然过渡金属硝酸盐和弱碱的等摩尔溶液被发现是效果最好的,但是也可以使用其它摩尔比的过渡金属盐和弱碱。换言之,可以使用更高摩尔比的过渡金属盐,反之亦然。
在各种实施方式中,过渡金属硝酸盐和弱碱的溶液具有1mM至1M之间的等摩尔浓度,例如25mM。或者,如上所述,过渡金属盐和弱碱的其他摩尔比也可以使用,只要过渡金属硝酸盐和弱碱各自的浓度落入1mM和1M之间的范围内即可。
使用本方法的另一个优点是,与在压力容器中且需要100℃以上的典型水热过程相比,可以使用相对较低的温度来形成过渡金属氧化物和/或氢氧化物多孔层。特别地,可以在20℃和100℃之间,优选20℃和70℃之间的温度范围内,例如70℃,将基底浸泡于过渡金属硝酸盐和弱碱的溶液中。
在一个优选的实施例中,在沉积疏液化合物层之前,可以对过渡金属氧化物和/或氢氧化物多孔层进行清洁处理。将清洁处理包括进来的好处是可以提高疏液涂层的性能。此外,洗涤步骤和使用弱碱的结合允许疏液化合物的无限选择地沉积到过渡金属氧化物和/或氢氧化物多孔层上。
在各种实施例中,清洁处理可以包括等离子体处理、UV/臭氧处理,热处理、化学清洁步骤或其组合。优选地,使用氧等离子体处理。
在优选的实施例中,所述弱碱可以是六亚甲基四胺(HMTA)或六胺、三乙醇胺、氨或尿素。
在各种实施例中,过渡金属硝酸盐可以包括具有+2价态的阳离子。如前所述,对于某些应用,例如基底通常为铝的热交换器,过渡金属可以选自锌、镍、锰、铜、钴、铁及其混合物。
在优选的实施例中,过渡金属硝酸盐可以包括硝酸锌、硝酸铁或硝酸锰(II)。
所述方法还可包括:在过渡金属氧化物和/或氢氧化物多孔层上沉积疏液化合物层,以在所述基底上形成多孔疏液涂层。
便利地,沉积疏液化合物层可以包括:浸涂或气相沉积,这些是复杂程度和成本都最低的普通的沉积技术。疏液氟烷基硅烷(FAS)或烷基硅烷化合物可以在真空干燥器中或浸涂过程中沉积。
或者,可将疏液的全氟辛基多面体低聚倍半硅氧烷(PFO-POSS)化合物浸涂到过渡金属氧化物和/或氢氧化物多孔层上。
优点是,该涂层已被证明可防止下层基底在酸性和碱性条件下被腐蚀。
其他优点包括以下几点:
a)稳固性(Robustness)-该涂层是与基底化学结合的薄陶瓷膜。这导致优异的耐磨性和耐热性。
b)性能-该涂层显示出超过178°的接触角(将在后面的段落中进行描述)。这优于或等于所有商业的超疏水涂层。
c)可转用-许多不同的氧化物和/或氢氧化物,例如氧化/氢氧化锌(ZnO),氧化/氢氧化锰(IV)(MnO2)可以在不同的基底上生长,以将可能的应用扩展到诸如催化的领域中。
以下段落描述了本发明的一个示例性实施例。这样形成的多孔疏液涂层成本低,操作简便,并且可以通过简单地改变化学浴温度和反应物浓度来调节以适应各种应用。在经过涂覆的铝基底上可以观察到高达178°的接触角,这是迄今报道的最高值之一。另外,所提供的涂层的独特之处在于,它与铝基底化学结合,并且是陶瓷基的。亚微米陶瓷膜对铝的化学附着增加了铝的耐磨性而没有明显降低其导热性。成本、性能、可调性和稳固性的结合目前在商业上无可匹敌。此外,该涂层已经被证明可以在酸性和碱性条件下防止铝被腐蚀,而不会产生接触角劣化。
用于制造和表征多孔涂层的所有材料均得自Sigma-Aldrich。
通过将基底浸入温度范围为室温至100℃的水基化学浴中,使超疏水涂层在铝基底上生长。该溶液包括硝酸盐,该硝酸盐具有+2价态阳离子,如锌、镍、锰,铜、钴或铁离子。该溶液还包括弱碱,如六胺。溶液中六胺和硝酸盐的从1mM到1M的等摩尔浓度与温度结合决定了生长膜的多孔性,并因此决定了其性质。然后洗涤、干燥所述膜,并用等离子体、UV/臭氧、热处理或化学处理来处理所述膜以活化表面,接着用全氟硅烷进行二次浸涂以完成涂层。任何氯代基、乙氧基或甲氧基硅烷都会与金属氧化物/氢氧化物表面相结合。在本例中,使用1H,1H,2H,2H-全氟十二烷基三氯硅烷来实现最大的接触角。全氟硅烷涂层也可以通过在真空干燥器中气相沉积来施加。
有利地,本方法使用较温暖且较温和的工艺参数来在铝表面上形成ZnO或MnO2(在室温至100℃、大气压下),其省略了高压釜的使用。而且,通过在该温度范围内形成ZnO或MnO2,孔更大,表面能更高。这使得全氟硅烷与所述表面的结合更具成本效益,并相对于在高压釜条件下合成的样品,本发明可以促进液滴脱落的增强(参见图1)。
具有可控的多孔性的膜根据反应条件产生不同接触角和接触角滞后性。接触角和液滴脱落性能的例子如图1所示。值得注意的是,涂层防止铝被淹没以持续高效并快速地使水滴脱落。
由于用于脱水的很多最佳性能发生在~50℃的中等合成温度和~10mM的低浓度条件下,这是能量和化学品投入低,且反应浪费最小的。另外,可以通过简单地改变浓度和温度而将所述表面调节至孔径的范围为从50nm以下至10μm以上。图2包含一系列高倍放大的扫描电子显微照片,其示出了使用该方法可以在铝表面上生长的各种孔径和形态。图3示出了最常用的反应条件下得到的预期的接触角。尽管对于给定的浓度,每个反应温度具有大致相同的接触角,但是如图1所示,较低温度的样品在冷凝条件下表现出优异的性能。
还通过之前已公开的超疏水耐久性测试方法测试了样品对酸、碱、己烷、丙酮、乙醇、水浸泡、紫外线照射、高温和磨损的抗性。在测量误差内的接触角测量前后,样品容易地超过了这些耐久性标准。为了进一步检查这些涂层的耐磨性,在丙酮和水中对涂层进行超声处理。30秒后具有最小限度的劣化,仍保持超疏水性,但5分钟后,涂层变得无法排开水。这种超声波测试远远超过了现实世界的换热器中发现的任何条件。水射流测试(所述涂层通过了该测试)是对空调蒸发器盘管中会存在的力的更准确的表征。
此外,这种生长已经扩展到了其他材料系统,并在其他基底上进行了测试。在基底材料离子具有3+价并且金属硝酸盐的阳离子具有2+价的条件下,预计所述反应会形成这些多孔结构。图4展示了由硝酸锰和硝酸锌前驱体在铝上生长出的相同结构。这产生了MnO2(a)和ZnO(b)。
以上公开的内容可以扩展到具有不均匀的孔几何形状的表面的润湿性的统计模型。
在以下段落中,描述了对具有不同程度的几何不均匀性的纹理化表面的润湿行为进行建模的新方法。表面被模拟为具有呈高斯分布的侧壁角度和特征壁粗糙度的孔阵列。使用测量得到的表面与至少四种探针液体之间的表观接触角来校准模型。针对三种不均匀的纳米多孔表面来校准该模型,并与规则的光刻产生的结构进行比较。通过使用三种可供选择的疏水性分子对多孔氧化/氢氧化锌进行封端,也证明了单个几何模型可以获取跨越多种表面化学品和液体的行为。
调整表面的微米和纳米结构能够有助于液体在表面上的表观接触角的最大化,使其具有超疏水或超疏油性。凹角或底切的表面几何形状是特别有价值的,因为已经证明它们能够促使获得低的润湿固体分数和大的接触角,即使是对于会润湿几乎任何光滑表面的低表面张力油和氟化液体也是如此。
已经通过光刻和其他晶体蚀刻机制制成了几何上高度规则的疏水和疏油表面。已经使用精细编织网制成了中度规则的表面结构。已经通过浸涂、颗粒和纤维的喷射沉积以及自下而上的生长,产生了具有更多不规则表面结构的各种表面。不规则表面的生产通常比规则的、光刻产生的表面要便宜得多,并且可以更容易地扩展到更大的区域,但是它们的表面特征几何形状的分布以及它们的性能更难以表征。
液体在纹理化表面上的行为通常被模拟为彻底润湿表面(Wenzel模式,图5a)或者全部处在表面的顶部而不渗入任何孔(Cassie-Baxter模式,图5b)。然而,这种二元区分不能代表许多类型表面的真实行为,这些表面的纹理在空间上是不均匀的(异质的),例如具有一系列壁角的多个孔。在这些情况下,根据它们的局部几何形状,某些孔可能会被润湿,而其他孔仍然是空的。
这里引入了一种新的模型来精确表征几何异质表面。该模型考虑了表面结构的平均壁角以及壁角的变化程度和所述结构的平均粗糙度。
新模型的重要作用是引入了能够获取孔几何形状的变异性的参数。因此,它超越了之前为了使针对特别规则的几何形状的Cassie-Baxter模型特殊化而进行的派生和改进。它将一表面模拟为具有很多带侧壁的等体积孔,这些侧壁的靠近其顶端的凹角角度Ψ近似遵循平均凹角角度为Ψ0、标准偏差为σ0的高斯分布(图5c)。令P(Ψ)为Ψ的累积分布函数:
在该模型中,当液体在平坦表面上的接触角θ0小于凹角角度:θ0<Ψ时,孔将瞬间且彻底地被填充。在这种情况下,液体的表面张力会将液体拉入孔中直至填充。相反地,假设当θ0≥ψ时,孔保持全空,且表面张力使液体保持在孔外。假设与表面接触的液滴足够大、能碰到很多孔。对于给定的θ0值,在液滴下被填充的孔的占比φF为:
φF=1-P(θ0).(2)
然后使用广义的Cassie-Baxter模型来模拟所述表面结构上的液体的整体表观接触角θ*,如下所示:
cosθ*=φTcosθ0+(1-φT)[φFr cosθ0-(1-φF)].(3)
该模型假定多孔膜的投影表面积被分成三个部分(图5c)。首先是处于孔之间的材料的顶端、并且总是与液体接触的面积的分数φT。剩余面积,其分数为(1-φT),被划分为在填充孔的占比和存在液-气界面的未填充孔的占比 之间。假设孔具有粗糙度r,这使得孔的总表面积是一个孔开口的投影面积的r倍。只有当孔填充液体时,这种粗糙度才起作用。在等式3指示cosθ*>1的情况下,cosθ*被设置为等于1并且假定发生完全润湿。通过测量具有一系列表面张力的四种或更多种液体的表观接触角θ*,人们可以拟合Ψ0,σ0,和r的估计值,从而表征一个表面。
对角度Ψ的高斯分布的假设是近似的,因为在工程化表面中,Ψ通常被约束在-90°和180°之间;Ψ实际上不能像高斯分布指示的那样向±∞延伸。然而,对于我们拟合用于实际表面的Ψ0和σ0的值,高斯分布的尾部的可忽略部分处于Ψ的实际范围之外。
为了证明模型描述真实表面行为的能力,制造并表征了三种多孔疏液涂层。用于制造和表征这三种多孔涂层的所有材料均得自Sigma-Aldrich。所有的涂覆方法都使用廉价的试剂和简单的设备,因此保证比精确设计的、几何上规则的、图案化的表面更经济实惠。
首先,考虑在铝上水热生长的纳米多孔氧化/氢氧化锌表面。通过在70℃下,将铝扫描电子显微镜(SEM)样品的安装柱浸泡于25mM硝酸锌和六胺的等摩尔水溶液中1小时,以合成多孔氧化/氢氧化锌表面。然后对ZnO/ZnOH涂覆的基底进行氧等离子体处理(60W,200mTorr,2min),以进行清洁,并赋予羟基表面封端。如图6a所示,所得到的氧化锌孔形态是高度不规则的,并且孔被大致垂直于样品表面排列但具有相当大的角度变化的材料薄壁围绕。
以三种方式之一改进氧化锌/氢氧化锌表面以给予疏水性表面化学品。在第一种改进中,立即将基底置于具有100μL的1H,1H,2H,2H-全氟辛基三氯硅烷(PFOS)的真空干燥器中。然后对干燥器进行抽气20分钟以汽化硅烷,然后放置40分钟,再使器腔内通气。移除后,用去离子水洗涤基底以除去未反应的全氟硅烷,干燥,最后在热板上以120℃退火1小时。在第二种改进中,将基底浸泡于VertrelTMXF(Dupont)的3%全氟辛基多面体低聚倍半硅氧烷(PFO-POSS)溶液中3分钟,然后用作涂层。在第三种改进中,将基底浸泡于去离子水中的1%(3-氨基丙基)三乙氧基硅烷(APTES)溶液中10分钟,然后用去离子水洗涤,并在热板上加热至120℃1小时。
使用六种探针液体来表征这些表面,它们按表面张力从大到小的顺序依次为水、甘油、硫二甘醇、摩尔质量为700g的聚乙二醇二丙烯酸酯,双丙二醇和甲醇。每个液固对的θ0值首先通过直接测量平坦表面(在本例中为硅晶片)上的液体接触角来确定,该平坦表面进行了与纹理化表面相同的表面封端处理。(或者,通常也可以从文献中获得针对特定液-固对的θ0值)。对于测试的最大表面张力液体(在本例中为水)和PFO-POSS表面封端,通过考虑θ*来估算的上限值,并且假定在这种情况下没有孔被填充。于是等式3归纳并重新整理为:
的这个值是一个上限值,因为在观察θ*的过程中,可能有一些孔实际上被水填充,以至于并不是所有的液固接触面积都位于结构的顶端内。利用θ0和已确定的的上限值,然后使用最小二乘误差最小化程序来拟合Ψ0,σ0,和r。图6b展示了单组几何参数与所有六种探针液体和所有三种表面终端的数据密切拟合。目前的模型发现,孔处于平均为中等的凹角上,其Ψ0=53°,并具有宽展的孔几何形状:σ0=23°(表1)。cosθ*随着cosθ0的逐渐增加表明,随着探针液体在光滑表面上的接触角减小(即,随着cosθ0增加),被填充的孔的占比逐渐增大。
表1.拟合于三种异质(不均匀)的纳米多孔表面和一个规则的、光刻产生的表面的模型参数的汇总。该拟合参数是:平均凹角角度(Ψ0)、所述角度相对于Ψ0的标准偏差(σ0)、孔内表面粗糙度因子(r)和表面顶端固体分数
*:Wal,P.van der;Steiner,U.Super-Hydrophobic Surfaces Made fromTeflon.Soft Matter 2007,3(4),426–429.
#:Liu,T.“Leo”;Kim,C.-J.“CJ.”Turning a Surface Superrepellent Even toCompletely Wetting Liquids.Science 2014,346(6213),1096–1100.
作为该模型的第二个测试案例,通过从三元溶剂系统中调幅分解来合成由约600nm直径的聚偏二氟乙烯(PVDF)球体组成的膜。
由于沉淀动力学,所得到的PVDF球体尺寸是相当一致的,尽管球体形成簇以产生形状稍微不规则并且比个别微球大许多倍的凹角孔(图7a)。该材料用与氧化/氢氧化锌相同的探针液体表征,并且表现出比氧化/氢氧化锌表面观察到的更明显的非润湿-湿润转变(图7c)。从接触角测量值中,提取了Ψ0=53°的有效平均侧壁角度和σ0=1°的低的孔侧壁角度变异性(表1)。11的高粗糙度是适配的,并且这个结果可以归因于由微球簇产生的微观粗糙度以及在材料的电子显微照片中看到的个别微球的纳米级表面纹理。
作为第三个测试案例,根据van der Wal等人的方法(Wal,P.van der;Steiner,U.Super-Hydrophobic Surfaces Made from Teflon.Soft Matter 2007,3(4),426–429),通过用牺牲聚(苯乙烯-共-二乙烯基苯)(PS)微球体模板化来制造多孔聚四氟乙烯(PTFE)膜。简而言之,将在水中的PTFE和PS胶体悬浮液混合以得到60%的固体体积分数,其中67%的固体体积是牺牲PS。将100μL该悬浮液呈叶片状浇铸到铝SEM柱上并置于120℃的热板上1小时以蒸发水分。进一步在290℃下进行30分钟热板处理以将PTFE颗粒烧结在一起并部分分解牺牲材料。然后通过在丙酮中洗涤而除去PS。
由于所使用的牺牲PS球体直径的广泛分布而使所得到的PTFE结构具有宽泛的孔径分布(图7b):估计这些直径在1μm至10μm的范围内。使用与之前相同的六种探针液体,提取Ψ0=54°和σ0=38°的表面特征,使得这看起来是我们所检查过的八个表面中最异质化的(图7c)。
所有这些趋势都不可能通过完全规则的直立侧壁特征的简单模型来获取;这样的模型只能包含cosθ0的单个临界值,在该值以下,表面假定为Cassie-Baxter模式,在该值以上,假设孔的润湿是自发和完全的。
可以想象得到,不考虑孔-孔变异性,而是通过针对侧壁轮廓开发一定制几何模型,可以再现观察到的cosθ*相对于cosθ0变化图的形状,其中,所述侧壁轮廓的角度随深度变化的方式使得每单个孔以与cosθ0的增加速度相同的速度逐渐填充。然而,需要针对每一种被表征的材料提出一个非常特殊的轮廓,以充分获取如图6和图7所示的从完全不润湿行为到完全湿润行为的各种转变。目前的孔角度变异性模型只有四个拟合参数,这是一个用以解释不规则的表面如何湿润的更实际和更通用的方式。
为了将随机分布的表面几何形状与更规则的几何形状进行对比,使用新模型来解释之前公开的数据,该数据来自由Liu和Kim以光刻方式制作的单一凹角表面结构的高度规则阵列(Liu,T.“Leo”;Kim,C.-J.“CJ.”Turning a Surface Superrepellent Even toCompletely Wetting Liquids.Science 2014,346(6213),1096–1100)。这些结构由直径~20μm的氧化硅盘的方格阵列组成,其由较窄的硅柱支撑并由~150nm的C4F8疏水聚合物涂覆。正如预期的那样,相比于目前三个更多变的多孔表面,这个表面随着cosθ0的增加从非润湿到润湿的转变更加急剧(图7c)。该最小二乘拟合程序提取Ψ0=27°的平均凹角角度(如果氧化硅盘的蚀刻涉及一些侧壁逐渐变细,这似乎是合理的)以及零角度变异性σ0(这与高度可重复的光刻生产一致)。因此,对于这个特定表面,根据所使用的液体,假设盘间区域完全是空的或完全被填充的情况是合理的。因此,尽管目前的模型拟合过程提取了r=1.2的结构之间的粗糙度值,但是这个值没有实际相关性,因为一旦任何内部结构空隙发生填充,则彻底润湿并且cosθ*变为1。
由此表明,本模型可用于表征液体在平坦表面上的接触角和它在一系列多孔或其它随机分布的材料几何形状上的表观接触角之间的关系。该模型预测平坦表面上的接触角θ0和表观接触角之间的一一对应关系。该模型不获取“突破(breakthrough)”的可能影响,所述突破是指,一个负载(例如液滴的拉普拉斯压力或随机发生的惯性力)导致液体表面变形至孔中,接触到孔的底部且润湿几何形状。目前的模型假设随着cosθ0的增加,孔的侧壁逐渐将液体引进孔的增加部分中,使得cosθ*随着cosθ0的增加是平缓并可预测的,并且仅依赖于孔内液体表面张力的作用。
对于这里已说明的ZnO、PVDF和PTFE表面,现在的模型是准确的,因为孔的尺寸大部分是亚微米级的并因此对“突破”非常稳固。根据Chhatre等人的模型(Chhatre,S.S.;Choi,W.;Tuteja,A.;Park,K.-C.(Kenneth);Mabry,J.M.;McKinley,G.H.;Cohen,R.E.Scale Dependence of Omniphobic Mesh Surfaces.Langmuir 2010,26(6),4027–4035),估计当前表面的稳固性(基本上是指所需的突破压力与典型的液滴拉普拉斯压力的比率)大约为1000。换言之,在这些结构中发生自发的从Cassie-Baxter至Wenzel的转变是不太可能的。对于具有相当大的孔的材料,可能有必要将稳固性作为附加因素。此外,目前的模型没有考虑接触角滞后性或孔几何形状与填塞(Pinning)之间的关系。这些考虑事项在某些应用中可能是相关的。
总之,目前的模型快速且简单地校准,只需要进行接触角测量,并为实验量化表面上孔几何形状的变异性提供了一个框架。该方法的关键性优点之一是,一旦表征了特定的表面几何形状(例如多孔氧化/氢氧化锌的表面几何形状),就可以用cosθ0相对于cosθ*的关系来预测改变应用于该几何形状的表面化学品(例如,PFOS或APTES)的影响,只要该表面改变不会使几何形状发生变化即可。因此,该方法可以很容易地应用于筛选多个候选的“全疏性的(omniphobic)”涂层过程以量化其性能。
所谓“包括(comprising)”是指包含但不限于跟随在单词“包括”之后的任何内容。因此,术语“包括”的使用表示所列元素是必须的或强制性的,但其它元素是可选的,并且可以存在或可以不存在。
“由...组成(consisting of)”是指包括且限于跟随在短语“由...组成”之后的任何内容。因此,术语“由...组成”的使用表示所列元素是必须的或强制性的,并且不存在其它元素。
本申请说明性地描述的发明可以适当地在去掉任何一种或多种本申请未具体公开的要素或限定后实施。因此,例如,“包括”,“包含”,“含有”等术语应被宽泛且非限制性地理解。另外,本申请所用的术语和表达是描述性而非限制性的,且使用所述术语和表达无意排除所述和所示的特征的任何等同形式或其部分,但是,应当理解,还可以在所述发明的范围内,对其进行各种改进。因此,应该理解的是,尽管公开了本发明的优选实施例和可选特征,本领域技术人员仍可以对本申请所公开的发明进行改进和变形,且所述改进和变形应当看作是包含在本发明的范围之内。
相对于给定的数值,如温度和时间周期,“约”指的是包括指定值的10%范围内的数值。
本发明在此进行了广泛和一般性的描述。落入一般性公开范围内的每个更窄的种类和亚属分组也构成本发明的一部分。这包括本发明的带有附带条件或从该属中去除任何主题的消极限制的一般描述,无论被去除的材料是否在本文中具体列举。
其他实施例在以下权利要求范围内及非限制性实施例中。此外,当以马库什(Markush)组来描述本发明的特征或方面时,本领域的技术人员能够理解,本发明也由此在马库什组的任何单个成员或成员的亚组中进行了描述。
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Claims (30)
1.一种多孔疏液涂层,包括:
过渡金属氧化物和/或氢氧化物多孔层;和
疏液化合物层,其沉积在所述过渡金属氧化物和/或氢氧化物多孔层上,
其中,过渡金属氧化物和/或氢氧化物多孔层由多个表面孔构成,该多个表面孔具有平均角度为凹角的不同角度。
2.根据权利要求1所述的涂层,其特征在于,所述多个表面孔中的至少一个具有小于90°的凹角角度。
3.根据权利要求1或2所述的涂层,其特征在于,所述多个表面孔中的至少一个具有大于90°的角度。
4.根据权利要求1至3中任一项所述的涂层,其特征在于,所述多个表面孔中的至少一个具有约90°的角度。
5.根据权利要求1至4中任一项所述的涂层,其特征在于,所述多个表面孔包括至少一个具有小于90°的凹角角度的表面孔,以及至少一个具有大于90°的角度的表面孔。
6.根据权利要求1至5中任一项所述的涂层,其特征在于,基于用于多个表面孔的角度的高斯分布模型,所述角度相对于平均凹角角度Ψ0的标准偏差σ0在0和60°之间。
7.根据权利要求6所述的涂层,其特征在于,所述标准偏差σ0在0和40°之间。
8.根据权利要求1至7中任一项所述的涂层,其特征在于,所述多个表面孔中的每一个均具有从50nm以下至10μm以上的尺寸范围。
9.根据权利要求1至8中任一项所述的涂层,其特征在于,所述多孔层的过渡金属氧化物和/或氢氧化物选自:氧化/氢氧化锌,氧化/氢氧化镍(II)、氧化/氢氧化镍(III)、氧化/氢氧化锰(II)、氧化/氢氧化锰(III)、氧化/氢氧化锰(IV)、氧化/氢氧化锰(VI)、氧化/氢氧化锰(VII)、氧化/氢氧化铜(I)、氧化/氢氧化铜(II)、氧化/氢氧化钴(II)、氧化/氢氧化钴(III)、氧化/氢氧化铁(II)、氧化/氢氧化铁(III)及其混合物。
10.根据权利要求9所述的涂层,其特征在于,所述多孔层的过渡金属氧化物和/或氢氧化物为氧化/氢氧化锌或氧化/氢氧化锰(IV)。
11.根据权利要求1至10中任一项所述的涂层,其特征在于,所述疏液化合物为氟碳聚合物或氟碳化合物。
12.根据权利要求11所述的涂层,其特征在于,所述疏液化合物为氟代烷基硅烷(FAS)或烷基硅烷。
13.根据权利要求12所述的涂层,其特征在于,所述疏液化合物为:1H,1H,2H,2H-全氟十二烷基三氯硅烷、1H,1H,2H,2H-全氟辛基三氯硅烷、1H,1H,2H,2H-全氟癸基三甲氧基硅烷、1H,1H,2H,2H-全氟癸基三氯硅烷或十八烷基三氯硅烷。
14.根据权利要求11所述的涂层,其特征在于,所述疏液化合物为:聚偏二氟乙烯(PVDF)、聚四氟乙烯(PTFE)或全氟辛基多面体低聚倍半硅氧烷(PFO-POSS)。
15.根据权利要求1至10中任一项所述的涂层,其特征在于,所述疏液化合物为氨基硅烷聚合物或氨基硅烷化合物。
16.一种在基底上制备多孔疏液涂层的方法,其特征在于,所述涂层包括:
过渡金属氧化物和/或氢氧化物多孔层;和
疏液化合物层,其沉积在所述过渡金属氧化物和/或氢氧化物多孔层上,
其中,所述过渡金属氧化物和/或氢氧化物多孔层由多个表面孔构成,
所述方法包括:
将基底浸泡于温度范围在20℃至100℃之间的过渡金属硝酸盐和弱碱的溶液中,以在所述基底上形成过渡金属氧化物和/或氢氧化物多孔层;和
将疏液化合物层沉积到在所述过渡金属氧化物和/或氢氧化物多孔层上,以在所述基底上形成多孔疏液涂层。
17.根据权利要求16所述的方法,其特征在于,浸泡所述基底包括将所述基底浸泡于过渡金属硝酸盐和弱碱的等摩尔溶液中。
18.根据权利要求16或17所述的方法,其特征在于,所述过渡金属硝酸盐和弱碱的溶液的浓度在1mM和1M之间。
19.根据权利要求16至18中任一项所述的方法,其特征在于,浸泡所述基底包括将所述基底浸泡于温度范围在20℃和70℃之间的所述过渡金属硝酸盐和弱碱的溶液中。
20.根据权利要求16至19中任一项所述的方法,其特征在于,基底的溶解有助于形成过渡金属氧化物和/或氢氧化物多孔层。
21.根据权利要求16至20中任一项所述的方法,其特征在于,还包括:在沉积所述疏液化合物层之前,对所述过渡金属氧化物和/或氢氧化物多孔层进行清洁处理。
22.根据权利要求21所述的方法,其特征在于,所述清洁处理包括:等离子体处理、UV/臭氧处理、热处理、化学清洁步骤或其组合。
23.根据权利要求16至22中任一项所述的方法,其特征在于,所述弱碱包括:六亚甲基四胺(HMTA)或六胺、三乙醇胺、氨或尿素。
24.根据权利要求16至23中任一项所述的方法,其特征在于,所述过渡金属硝酸盐包括具有+2价态的阳离子。
25.根据权利要求24所述的方法,其特征在于,所述基底包括铝,所述过渡金属硝酸盐包括选自锌、镍、锰、铜、钴、铁及其混合物的过渡金属。
26.根据权利要求25所述的方法,其特征在于,所述过渡金属硝酸盐包括硝酸锌或硝酸锰(II)。
27.根据权利要求16至26中任一项所述的方法,其特征在于,沉积所述疏液化合物层包括:浸涂或气相沉积。
28.根据权利要求27所述的方法,其特征在于,沉积所述疏液化合物层包括:在真空干燥器中气相沉积氟代烷基硅烷(FAS)或烷基硅烷化合物。
29.根据权利要求27所述的方法,其特征在于,沉积所述疏液化合物层包括:浸涂全氟辛基多面体低聚倍半硅氧烷(PFO-POSS)。
30.一种多孔表面的表征方法,该多孔表面具有多个表面孔,所述方法用平均凹角角度Ψ0和所述多个表面孔的角度相对于Ψ0的标准偏差σ0来表征所述多孔表面,所述方法包括:
测量各自具有不同表面张力的至少四种探针液体各自的接触角θ0,其中,通过固着液滴法测量在平坦表面上的接触角;
测量所述至少四种探针液体各自的表观接触角θ*,其中,通过固着液滴法测量在所述多孔表面上的表观接触角;和
使用最小二乘误差最小化程序来拟合以下等式中的Ψ0、σ0、φT和r:
φF=1-P(θ0) (2)
cosg*=φTcosθ0+(1-φT)[φFrcosθ0-(1-φF)]. (3)
其中:
P(Ψ)是根据具有平均凹角角度Ψ0和标准偏差σ0的高斯分布的、角度Ψ的累积分布函数,
是填充孔的占比,
φT是位于孔之间的多孔表面顶端、并且总是与液体接触的面积的分数,
(1-φT)是剩余面积,其被划分为在填充孔的占比和存在液-气界面的未填充孔的占比之间;以及
r是孔的粗糙度,其使得孔的总表面积是1个孔开口的投影面积的r倍。
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