Zvezda shape

[baldusi]

Module with a diameter greater than 4.1 ок 4.35m have a mass greater than that of Proton can lift into orbit   

That depends on the amount of internal equipment, the might elect to send it "light". And also, on the outer layers. A 4.1m cylinder with some extra .3m of polypropylene can do wonders for radiation shielding. I'm just saying. In any case, the whole issue of bigger fairing was more on Angara's timeframe.

[ace5]

What is the connection between payload fairing diameter and the mass of the payload itself?

[baldusi]

What is the connection between payload fairing diameter and the mass of the payload itself?

Whithin the current topic (i.e. Russian space station modules), there's a certain "density" given the equipment's average weight. And there's also the assumption that it's going to be longer than wider (which seems to be how most of this things are). Thus, wider module -> bigger module -> heavier module.
The fact is that wider cylinders require heavier walls. Thus, it's usually desirable to make the "long". And then there's the actual ergonomics. Make the internal passages bigger than 2m and it's a problem when the astronaut is in the middle and can't reach the walls.
Thus, I assume that a wider module would mean more insulation. Be it because of micrometeorite protection or radiation insulation. There's also the issue of ports. Russian docking ports are "small diameter", at least when compared to the CBM. Since they don't use the ISS Standard Rack either, there's little point for wider interiors. Plus, they already have the 4.1m tooling.
I still believe that a quick and cheap way to make a DSH is to put a nice wall of 0.3m of polypropilene around a stock 4.1m module, cover it in some micrometeorite wall and wrap it into some thermal insulator. That should offer some very useful protection.
But, if they ever want to make use of artificial gravity, they'll need something bigger. I think 6m is the bare minimum internal diameter, but most probably around 15m. But you don't need (or even desire) a 15m wide module. You can just build a ring out of smaller modules. In which case even 2.55m diameter would be desirable.