It really depends on what you consider to be IR ink.
Definitions are important.
I was using the definition that the stuff I find in my fountain pen or a printer ink cartridge is "ink" ... so "infrared ink" would have similar properties.
Blue ink would be any fluid that let's you write in blue... by analogy...
Then I checked my concepts by finding out what was being marketed and/or researched under the label "infrared ink". It's not exactly a scientific term.
The only model I'm aware of regarding ink and colors is the Subtractive Color Model (
http://en.m.wikipedia.org/wiki/Subtractive_color) which is all about the frequencies which hit the ink, which ones are absorbed and which ones are bounced back.
That model only refers to the visible light ... and there is an "additive color model" that you must surely have heard of also.
http://www.widescreenmuseum.com/oldcolor/additive-subtractive.htm
...better reference than wikipedia:
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/subcol.html
A basic discussion of colors and how they work:
http://www.fi.edu/color/color.html
Basically, everything will absorb some light, reflect or scatter some, and transmit some.
The proportions change with the wavelength.
When the effect is to produce a striking effect to the eye, the substance is said to have a color.
So colors are mostly about visible light. But knowing that visible light is part of the same phenomena as radio waves and gamma rays means we can extend the concept of color to include any electromagnetic wave. But if we do that, then our ideas about what counts as a pigment need to be adjusted too.
A surface has a color if it strongly scatters light in a well defined range of wavelengths.
Common inks scatter a wide range of wavelengths of visible light, but absorb one or more narrow bands in that range. Outside the visible spectrum you can get a wide range of behaviors - but pretty much all common inks are transparent to high wavelengths, absorb infrared well, but are also transparent to radio.
You can get data on the absorbtion spectra of different pigments.