Wafer carrier with ultraphobic surfaces

1. A carrier for articles comprising:

a body having a substrate portion with a surface, at least a portion of said surface having a multiplicity of substantially uniformly shaped asperities thereon to form an ultraphobic surface, each asperity having a common asperity rise angle relative to the substrate portion, the asperities positioned so that the ultraphobic surface defines a contact line density measured in meters of contact line per square meter of surface area equal to or greater than a contact line density value “ΛL” determined according to the formula: Λ L = - P γ ⁢   ⁢ cos ⁡ ( θ a , 0 + ω - 90 ∘ )

 where γ is the surface tension of a liquid in contact with the surface in Newtons per meter, θa,0 is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, ω is the asperity rise angle in degrees, and P is a predetermined liquid pressure value in kilograms per meter, wherein the ultraphobic surface exhibits a liquid-solid-gas interface with the liquid at liquid pressures up to and including the predetermined liquid pressure value.

2. The carrier of claim 1, wherein the asperities are projections.

3. The carrier of claim 2, wherein the asperities are polyhedrally shaped.

4. The carrier of claim 2, wherein each asperity has a generally square transverse cross-section.

5. The carrier of claim 2, wherein the asperities are cylindrical or cylindroidally shaped.

6. The carrier of claim 1, wherein the asperities are cavities formed in the substrate.

7. The carrier of claim 1, wherein the asperities are positioned in a substantially uniform array.

8. The carrier of claim 7, wherein the asperities are positioned in a rectangular array.

9. The carrier of claim 1, wherein the asperities have a substantially uniform asperity height relative to the substrate portion, and wherein the asperity height is greater than a critical asperity height value “Zc” in meters determined according to the formula: Z c = d ⁡ ( 1 - cos ⁡ ( θ a , 0 + ω - 180 ∘ ) ) 2 ⁢   ⁢ sin ⁡ ( θ a , 0 + ω - 180 ∘ )

where d is the distance in meters between adjacent asperities, θa,0 is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, and ω is the asperity rise angle in degrees.

10. A process of making a carrier with an ultraphobic surface portion, the process comprising:

providing a carrier including a substrate having an outer surface; and

forming a multiplicity of substantially uniformly shaped asperities on the outer surface of the substrate, each asperity having a common asperity rise angle relative to the substrate portion, the asperities positioned so that the surface has a contact line density measured in meters of contact line per square meter of surface area equal to or greater than a contact line density value “ΛL” determined according to the formula: Λ L = - P γ ⁢   ⁢ cos ⁡ ( θ a , 0 + ω - 90 ∘ )

 where γ is the surface tension of a liquid in contact with the surface in Newtons per meter, θa,0 is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, ω is the asperity rise angle in degrees, and P is a predetermined liquid pressure value in kilograms per meter, wherein the ultraphobic surface exhibits a liquid-solid-gas interface with the liquid at liquid pressures up to and including the predetermined liquid pressure value.

11. The process of claim 10, wherein the asperities are formed by photolithography.

12. The process of claim 10, wherein the asperities are formed by a process selected from the group consisting of nanomachining, microstamping, microcontact printing, self-assembling metal colloid monolayers, atomic force microscopy nanomachining, sol-gel molding, self-assembled monolayer directed patterning, chemical etching, sol-gel stamping, printing with colloidal inks, and disposing a layer of parallel carbon nanotubes on the substrate.

13. A process for producing a carrier having a surface with ultraphobic properties at liquid pressures up to a predetermined pressure value, the process comprising:

selecting an asperity rise angle;

determining a critical contact line density “ΛL” value according to the formula: Λ L = - P γ ⁢   ⁢ cos ⁡ ( θ a , 0 + ω - 90 ∘ )

 where P is the predetermined pressure value, γ is the surface tension of the liquid, θa,0 is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, and ω, is the asperity rise angle;

providing a carrier with a substrate portion; and

forming a multiplicity of projecting asperities on the substrate portion, so that the surface has an actual contact line density equal to or greater than the critical contact line density.

14. The process of claim 13, wherein the asperities are formed using photolithography.

15. The process of claim 13, wherein the asperities are formed using wherein the asperities are formed using nanomachining, microstamping, microcontact printing, self-assembling metal colloid monolayers, atomic force microscopy nanomachining, sol-gel molding, self-assembled monolayer directed patterning, chemical etching, sol-gel stamping, printing with colloidal inks, or by disposing a layer of parallel carbon nanotubes on the substrate.

16. The process of claim 13, further comprising the step of selecting a geometrical shape for the asperities.

17. The process of claim 13, further comprising the step of selecting an array pattern for the asperities.

18. The process of claim 13, further comprising the steps of selecting at least one dimension for the asperities and determining at least one other dimension for the asperities using an equation for contact line density.

19. The process of claim 13, further comprising the step of determining a critical asperity height value “Zc” in meters according to the formula: Z c = d ⁡ ( 1 - cos ⁡ ( θ a , 0 + ω - 180 ∘ ) ) 2 ⁢   ⁢ sin ⁡ ( θ a , 0 + ω - 180 ∘ )

where d is the distance in meters between adjacent asperities, θa,0 is the true advancing contact angle of the liquid on the surface in degrees, and ω is the asperity rise angle in degrees.

20. A carrier for articles comprising:

a body having a substrate and a polymer outer layer on the substrate, the outer layer having a surface with a multiplicity of asperities thereon forming an ultraphobic surface for contacting a liquid, the asperities distributed so that the surface has an average contact line density equal to or greater than a critical contact line density value ΛL determined according to the formula: Λ L = - P γ ⁢   ⁢ cos ⁡ ( θ a , 0 + ω - 90 ∘ )

 where γ is the surface tension of a liquid in contact with the surface in Newtons per meter, θa,0 is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, ω is the asperity rise angle in degrees, and P is a predetermined liquid pressure value in kilograms per meter, and wherein the ultraphobic surface exhibits a liquid-solid-gas interface with the liquid at liquid pressures up to and including the predetermined liquid pressure value.

21. the carrier of claim 20, wherein the polymer outer layer includes a low surface energy material.

22. The carrier of claim 21, wherein the low surface energy material is a fluoropolymer.

23. The carrier of claim 20, wherein the polymer outer layer includes alkylketene dimer.

24. A carrier for articles comprising:

a body having a substrate and a polymer outer layer on the substrate, the outer layer having a surface with a multiplicity of asperities thereon forming an ultraphobic surface for contacting a liquid in the form of a droplet, the asperities distributed so that the surface has an average contact line density equal to or greater than a critical contact line density value Λ determined according to the formula: Λ L = - ρ ⁢   ⁢ g ⁡ ( V ) 1 3 ⁢ ( ( ( 1 - cos ⁢   ⁢ θ a ) sin ⁢   ⁢ θ a ) ⁢ ( 3 + ( ( 1 - cos ⁢   ⁢ θ a ) sin ⁢   ⁢ θ a ) 2 ) ) 2 3 ( 36 ⁢   ⁢ π ) 1 3 ⁢ γ ⁢   ⁢ cos ⁡ ( θ a , 0 + ω - 90 ∘ ) ,

 where V is the volume of the droplet in cubic meters, g is the density (p) of the liquid in kilograms per cubic meter, (g) is the acceleration due to gravity in meters per second squared, (h) is the depth of the liquid in meters, (γ) is the surface tension of the liquid in Newtons per meter, ω is the average rise angle of the side of the asperities relative to the substrate in degrees, θa is the apparent advancing contact angle of the droplet on the surface, and (θa,0) is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees.

25. A process of making a carrier with an ultraphobic surface portion, the process comprising:

providing a carrier including a substrate having an outer surface; and

forming the ultraphobic surface portion by depositing a layer of polymer material on the outer surface using a chemical vapor deposition process, the layer of polymer material having an outer surface with a multiplicity of asperities, the asperities distributed so that the ultraphobic surface has a contact line density measured in meters of contact line per square meter of surface area equal to or greater than a critical contact line density value “ΛL” determined according to the formula: Λ L = - P γ ⁢   ⁢ cos ⁡ ( θ a , 0 + ω - 90 ∘ )

 where γ is the surface tension of a liquid in contact with the surface in Newtons per meter, θa,0 is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, ω is the asperity rise angle in degrees, and P is a predetermined liquid pressure value in kilograms per meter, wherein the ultraphobic surface exhibits a liquid-solid-gas interface with the liquid at liquid pressures up to and including the predetermined liquid pressure value.