Hansen solubility parameter

Hansen solubility parameters were developed by <a href="/facts/Charles_M._Hansen/u3RoKHla">Charles M. Hansen</a> in his Ph.D thesis in 1967 as a way of predicting if one material will <a href="/facts/Solubility/kLE9h3Jb">dissolve</a> in another and form a <a href="/facts/Solution_(chemistry)/MGchhMQV">solution</a>. They are based on the idea that like dissolves like where one <a href="/facts/Molecule/N9ljSfFq">molecule</a> is defined as being 'like' another if it bonds to itself in a similar way.
Specifically, each molecule is given three Hansen parameters, each generally measured in MPa0.5:

<ul><li>
 
 
 
  
 
 δ
 
 d
 
 
 
 
 {\displaystyle \ \delta _{\text{d}}}
 
 The energy from <a href="/facts/London_dispersion_force/zU842d26">dispersion forces</a> between molecules</li>
<li>
 
 
 
  
 
 δ
 
 p
 
 
 
 
 {\displaystyle \ \delta _{\text{p}}}
 
 The energy from dipolar <a href="/facts/Intermolecular_force/xIcFMvL7">intermolecular forces</a> between molecules</li>
<li>
 
 
 
  
 
 δ
 
 h
 
 
 
 
 {\displaystyle \ \delta _{\text{h}}}
 
 The energy from <a href="/facts/Hydrogen_bonds/85V86IIg">hydrogen bonds</a> between molecules.</li></ul>
These three parameters can be treated as co-ordinates for a point in three dimensions also known as the Hansen space. The nearer two molecules are in this three-dimensional space, the more likely they are to dissolve into each other. To determine if the parameters of two molecules (usually a solvent and a polymer) are within range, a value called interaction radius (
 
 
 
 
 R
 
 
 0
 
 
 
 
 
 {\displaystyle R_{\mathrm {0} }}
 
) is given to the substance being dissolved. This value determines the radius of the sphere in Hansen space and its center is the three Hansen parameters. To calculate the distance (
 
 
 
  
 R
 a
 
 
 {\displaystyle \ Ra}
 
) between Hansen parameters in Hansen space the following formula is used:

(
        R
        a
        
          )
          
            2
          
        
        =
        4
        (
        
          δ
          
            d
            2
          
        
        −
        
          δ
          
            d
            1
          
        
        
          )
          
            2
          
        
        +
        (
        
          δ
          
            p
            2
          
        
        −
        
          δ
          
            p
            1
          
        
        
          )
          
            2
          
        
        +
        (
        
          δ
          
            h
            2
          
        
        −
        
          δ
          
            h
            1
          
        
        
          )
          
            2
          
        
      
    
    {\displaystyle \ (Ra)^{2}=4(\delta _{d2}-\delta _{d1})^{2}+(\delta _{p2}-\delta _{p1})^{2}+(\delta _{h2}-\delta _{h1})^{2}}

Combining this with the interaction radius 
 
 
 
 
 R
 
 
 0
 
 
 
 
 
 {\displaystyle R_{\mathrm {0} }}
 
 gives the relative energy difference (RED) of the system:

R
        E
        D
        =
        
          
            
              
                R
                a
              
              
                R
                
                  0
                
              
            
          
        
      
    
    {\displaystyle \ RED=\textstyle {\frac {Ra}{R_{0}}}}

<ul><li>If 
 
 
 
  
 R
 E
 D
 <
 1
 
 
 {\displaystyle \ RED<1}
 
 the molecules are alike and will <a href="/facts/Solvation/JVM6j8R1">dissolve</a></li>
<li>If 
 
 
 
  
 R
 E
 D
 =
 1
 
 
 {\displaystyle \ RED=1}
 
 the system will partially dissolve</li>
<li>If 
 
 
 
  
 R
 E
 D
 >
 1
 
 
 {\displaystyle \ RED>1}
 
 the system will not dissolve</li></ul>

Hansen solubility parameter open-in-new

Hansen solubility parameter