Here, lines 44 - 50.
In Germany and stated in German Wikipedia polyphosphates were used as water softeners because in this regard they are superior to othophosphates. The chelating effects are also used in foods and food processing. This means polyphosphates do not as readily form precipitates with calcium or magnesium as orthophosphates.
Well, if polyphosphates or some of them break down in solution to orthophosphate the products will be a little bit more "conventional" but I think we don't claim anything wrong. I think we have included some other ideas that make the products still a bit special and different from other products. That is all we want.
I have a different interpretation that I believe explains that observation, as opposed to stronger binding to calcium carbonate surfaces by orthophosphate.
The article you post is, I believe, talking about precipitation of calcium phosphate. It is true that calcium phosphate likely forms better crystals for ongoing precipitation of calcium and orthophosphate from calcium and orthophosphate or polyphosphate in the water.
Polyphosphate will chelate calcium and keep it dissolved, while orthophosphate will not. It is also harder to orient every polyphosphate exactly into the right position to form the most highly stable crystals for ongoing precipitation. It's a basic idea that it is hard to form crystals of larger, more floppy molecules, especially if the molecules precipitating potentially come in a variety of actual chain lengths, preventing good crystal formation.
But that is not the scenario that I am concerned about, which is the binding of phosphate or polyphosphate to calcium carbonate surfaces. The potential for crystal formation says nothing about how well these molecules absorb onto existing calcium carbonate surfaces, and, IMO, polyphosphate is likely to bind more strongly, not less so, due to a known effect called polyvalency where the polyphosphate has multiple points of contact with the mineral surface, while orthophosphate does not, enhancing the binding of the polyphosphate.
A series of anionic homopolymers, poly(sodium 2-(acrylamido)-2-methyl-1-propanesulfonate) (PAMPS) and amphiphilic copolymers of AMPS and sodium 11-(acrylamido)undecanoate (AaU), both block (PAMPS75-b-PAaUn), and random (P(AMPSm-co-AaUn)), were synthesized and their antiviral activity against...
www.mdpi.com
"Moreover, polymers exhibit a phenomenon called “polyvalency” when multiple repeating units of the polymer can bind to multiple complementary cell receptors or viral proteins simultaneously. As multiple individual ligand–receptor interactions act synergistically, polyvalent interactions are typically much stronger than monovalent binding"
