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# Preface! ✨

It’s your favorite material science & nanotechnology enthusiast! Today, we will cover the mechanisms of hydrophobicity from Young’s Law with a bit of help from surface energy, critical surface tension, and mathematics!

The articles below are fundamental to build the intuition for the equations used in Young’s Law!

## TL;DR → Young’s Law (Part 1)! 🔑

• The main concepts in the article are Young’s Law, Critical Surface Tension of both the solvent and the aerogel, Solvents (Pure & Aqueous), and the overall concentration of the solvents in the solution when it comes into contact with the aerogel!
• In an aerogel, the more of the (concentrated) solvent you add, it can actually decrease the contact angle and reduce hydrophobicity in the aerogel.
• Young’s LawThe contact angle of a liquid or vapor touching the surface of solid material and determines how wet an object can get. The angle is normally measured from the angle between the liquid and the solid.
• Young’s Law (Mechanism)If the contact angle is greater than 90 degrees (90°), the liquid/water in the aerogel will not be able to spread, and the aerogel is impervious/hydrophobic to water. If the contact angle is less than 90 degrees (90°), the liquid/water in the aerogel will spread, and the aerogel is hydrophilic to water, and the water will adsorb until the contact angle is equal to 0 degrees (0°).
• SolventA liquid/dissolving medium where a substance/solid (a.k.a. solute) will dissolve in the liquid to form a solution/homogenous mixture.
• Surface TensionThe strongest intermolecular forces between molecules of a liquid (water) at the surface only. Because the intermolecular forces are the strongest, the water molecules will minimize their surface area.

## TL;DR → Young’s Law (Part 2)! 🔑

• If the surface energy of a solid is low, the contact angle will be greater than 90° (γ(sl) ≥ γ(sv)). The water droplet won’t be able to spread and adsorb on the surface of the aerogel. WHY?
• The bonds at the surface of the aerogel are most likely non-polar bonds (electronegativity is below 0.5 with the presence of Van der Waal Forces).
• If the surface energy of a solid is high, the contact angle will be less than 90° (γ(sv) ≥ γ(sl)). The water droplet will begin to spread and adsorb on the surface of the aerogel completely until the droplet flattens out and the angle is equal to 0°. WHY?
• The bonds at the surface of the aerogel are most likely polar, covalent, ionic, coordinate covalent, hydrogen, or metallic bonds (electronegativity is equal to or greater than 0.5.)
• Surface Energy is the measurement of energy at the surface of a material and the interaction between molecules of the solid material/aerogel.

Authors Note:

This was an overview of the definitions of the fundamental concepts used when calculating the outcome of Young’s Law! If this information still leaves you confused, I highly recommend going back to the articls above and read them completely before coming back! 🙏🏽

Now that we have our overview and explanation, let’s go over the mathematical rabbit holes in Young’s Law via Surface Energy and Critical Surface Tension! 😄

# Surface Energy x Critical Surface Tension! 💡

## Definitions! 🔑

Surface EnergyThe measurement of energy at the surface of a material and the interaction between molecules of the solid material/aerogel.

Young’s LawThe contact angle of a liquid or vapor touching the surface of solid material and determines how wet an object can get. The angle is normally measured from the angle between the liquid and the solid.

Surface TensionThe strongest intermolecular forces between molecules of a liquid (water) at the surface only. Because the intermolecular forces are the strongest, the water molecules will minimize their surface area.

We can calculate surface energy, but it is measured apart from the contact angle (Young’s law), despite the majority of the equations coming from Young’s Law.

## Equations! 🔑

To calculate the surface energy of a solid, we have to use the contact angle (derived from Young’s Law) in our equation.

This is the equation below for the surface energy of a solid:

σ(s) = Surface Energy of the Solid (Aerogel).

σ(sl) = Interface (Intersection) of the tension between the solid (aerogel) and the liquid (solvent or solution).

σ(l) = Surface Tension of the liquid.

cos θ = The angle used to measure the contact angle (to see if the liquid is greater or less than 90° on the solid).

However, the interface of the tension between the solid and the liquid can be calculated using σ(sl).

The equation to calculating the interfacial (adhesive) tension between the liquid and the aerogel is listed below.

S = Spreading parameter/coefficient. The Spreading Coefficient determines and measures how likely a liquid will spread out on the surface of a solid. Wetting of a surface of a solid is positive values only.

Adhesive means the ability to stay or stick to a surface.

Interface means the section where the aerogel and the liquid come into contact (which is the surface, of course!).

## Results! 🔑

To finally plot the calculations of surface energy, we can use Zisman Model, which can help us locate the Critical Surface Tension.

Critical Surface Tension is when the surface energy of the solid (aerogel) is equal to the surface tension of the liquid that equals a contact angle of 0°.

The contact angle is used as cos θ (to see if the liquid is greater or less than 90° on the solid). We can make θ = 0°. This means that the angle of cosine at 0° is equal to 1 (cos 0° = 1). When cos θ =1, the surface tension (of the liquid) is equal to the surface energy of the aerogel (solid).

If the surface tension of the aqueous solvent/liquid (γ) is greater than the surface energy of the aerogel/solid (γc), the aqueous solvent will be able to wet the gel a little bit. 👌🏽

If the surface energy of the aerogel/solid (γc) is greater or equal to the surface tension of the aqueous solvent/liquid (γ), the aqueous solvent will be able to wet the gel completely, and the solvent will undergo adsorption. 💥

# Closing Thoughts! 💭

The Zisman Model only works for non-polar bonds like Van der Waal Forces and non-polar molecules like hydrocarbons.

However, for polar bonds, we need a different model other than the Zisman Model, as it fails to include polar interactions like the polar interactions in water.

Relating to surface tension and surface energy, the maximum concentration of methanol you can achieve without lowering the contact angle below 90° is 39% of pure concentrated methanol in the solvent. The maximum concentration of ethanol you can achieve without lowering the contact angle below 90° is 35% of pure concentrated ethanol in the solvent.

Summary:

You can calculate the surface energy of a solid to see if the surface tension could equal to cos 0°= 1, which means that the surface tension is equal to the surface energy of the aerogel.

The Spreading Coefficient determines and measures how likely a liquid will spread out on the surface of a solid. Wetting of a surface of a solid is positive values only.

Critical Surface Tension is when the surface energy of the solid (aerogel) is equal to the surface tension of the liquid that equals a contact angle of 0°.

See you soon to discuss the final functions of aerogel-based material science in the series! ✌🏽

# Vocabulary! 📓

Young’s LawThe contact angle of a liquid or vapor touching the surface of solid material and determines how wet an object can get. The angle is normally measured from the angle between the liquid and the solid.

Young’s Law (Mechanism)If the contact angle is greater than 90 degrees (90°), the liquid/water in the aerogel will not be able to spread, and the aerogel is impervious/hydrophobic to water. If the contact angle is less than 90 degrees (90°), the liquid/water in the aerogel will spread, and the aerogel is hydrophilic to water, and the water will adsorb until the contact angle is equal to 0 degrees (0°).

Surface TensionThe strongest intermolecular forces between molecules of a liquid (water) at the surface only. Because the intermolecular forces are the strongest, the water molecules will minimize their surface area.

Adhesive The ability to stay or stick to a surface.

Interface → The section where the aerogel and the liquid come into contact (surface of aerogel, which is why we have surface tension and surface energy to explain the interface).

The Spreading Coefficient Determines and measures how likely a liquid will spread out on the surface of a solid. Wetting of a surface of a solid is positive values only; (S).

Surface EnergyThe measurement of energy at the surface of a material and the interaction between molecules of the solid material/aerogel.

Critical Surface TensionThe surface energy of the solid (aerogel) is equal to the surface tension of the liquid that equals a contact angle of 0°.