# Predicting Solubility and Mixing with Solubility Parameters

Key:

The SP value is a parameter related to the cohesive energy between liquid molecules. Solvents with similar SP values mix well, and polymers dissolve well in solvents with SP values close to their own.

1. What is Solubility Parameter, SP

Solvents are needed to dissolve binder resins, and in paints, a combination of different solvents is often used. To determine if a solvent can dissolve high-molecular-weight substances and if solvents can mix well together, the Solubility Parameter (SP) is crucial. Solvents with similar SP values are known to mix well and facilitate dissolution.

2. The definition of the Solubility Parameter (SP value)

The SP value is assigned to each solvent (liquid) and is important for a liquid to stay as a liquid; it needs an attraction between its molecules. Without this attraction, a liquid would turn into a gas. This attracting force comes from what we call cohesion energy (ΔE), usually shown as energy per mole. Because solvents have different molecular weights and densities, it’s hard to compare this cohesion energy directly. To make it work for any solvent, we convert the energy to a per volume basis using the volume of one mole, called molar volume (Vm). This ΔE/Vm is the cohesion energy per unit volume for any solvent, known as the cohesion energy density. The SP value is the square root of this energy density, and the formula looks like this: δ = √(ΔE/Vm). We use the square root to make the amount of energy needed to change from interactions between similar molecules to different molecules match the energy before the change.

3. SP Values and Mixing or Not Mixing

The change in cohesive energy (ΔEmix) during the mixing of two solvents (1 and 2) using SP values is expressed by the following formula. Φ represents the volume fraction during mixing, where Φ1 + Φ2 = 1.

ΔEmix = Φ1Φ2(δ1-δ2)²

In this equation, ΔEmix is always a positive value, resulting in an increase in energy. Therefore, the concept of SP is only applicable to endothermic mixing systems, which is a limitation. However, it works well in many organic solvent systems. Mixing is a phenomenon that increases entropy (disorder) and is advantageous for the system.

On the other hand, an increase in cohesive energy is unfavorable. Therefore, the decision to mix or not is determined by the balance between these factors. To promote mixing, it’s better if ΔEmix is small, which occurs when the term inside the parentheses is small. In other words, the closer the SP values Φ1 and Φ2 of the two solvents are, the smaller ΔEmix is, and you can say, “The closer the SP values, the better the mixing.” While the SP value of polymers cannot be directly measured, it can be estimated based on the solubility in solvents with known SP values.