A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids

<jats:title>Significance</jats:title> <jats:p> Whether a drop of liquid such as water is repelled from a solid substrate yielding a large angle of intersection <jats:inline-formula> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> </jats:inline-formula> between the drop’s surface and the substrate or is strongly attracted, small <jats:inline-formula> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> </mml:math> </jats:inline-formula> , is key to the function of a host of physical and biological systems. We elucidate the physics of hydrophobic and hydrophilic substrates in terms of wetting and drying surface phase diagrams. These display a surprising variety of forms that depend upon the nature of the substrate–liquid and liquid–liquid attractive forces. Liquids near weakly attractive substrates exhibit critical drying, a phenomenon occurring as <jats:inline-formula> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>θ</mml:mi> <mml:mo>→</mml:mo> <mml:mn>18</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>○</mml:mo> </mml:mrow> </mml:msup> </mml:math> </jats:inline-formula> that is accompanied by divergent density fluctuations. Our findings provide a conceptual framework for tailoring the properties of superhydrophobic and hydrophilic materials. </jats:p>