# How is charge density a useful measure of polarising power and polarisability?

How do you use charge density ($Z/r$) as a measurement of polarising power and polarisability, and hence hard/soft acid character?

So far I've been looking at different polarising power and polarisability and how that affects a substance in whether it is a hard or soft acid/base, but I don't understand how charge density comes into play, and how we can use it to understand the characteristics.

What does higher charge density of a cation means? It means that the positive charge on a cation is concentrated in a small volume. Small, concentrated charge can cause greater distortion in the anion and therefore they have greater polarising power, or greater power to cause attract the negative electron cloud of the anion and hence greater distortion. The greater the positive charge on a cation, the larger the charge density will be (it is directly proportional to $Z$). Greater positive charge will cause greater distortion in the electron cloud of anion.
What about the anion? When the electron cloud of the anion is small, it is closer to the nucleus and experiences a greater attraction from the nucleus, therefore it is not easy to distort it. But, if the electron cloud is large, the inward force experienced by it from the nucleus is less, hence it can be polarised much easily. The inference is that the greater the radius, the larger the polarisability of the anion will be. What does greater radius mean? The greater the radius, the smaller the charge density will be (it's inversely proportional to $r$, or proportional to $1/r$).