The standard installation of a plastic vapor barrier is between the studs and the drywall but there are some exceptions to this.
Plastic vapor barrier basement walls.
The cool surface is the sheathing assuming no exterior insulation.
You should then use fiberglass insulation that has a vapor barrier between the studs with the vapor barrier facing in toward the living space.
1 on the interior wall between the heated and unheated portion of the basement i would not use with a vapor barrier.
If you have a framed wall that is adjacent to a concrete foundation wall where the vapor barrier is next to the drywall in front of the studs the fiberglass insulation gets wet and becomes a breeding ground for mold.
If water vapor diffuses or infiltrates into the wall cavity and finds the cool surface moisture problems can occur.
In exterior walls that are below grade like basement walls.
The material is stapled to the frame of a basement wall before it is finished with plaster or drywall.
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When the mold grows it will spread to everything around it studs drywall etc.
In winter the dew point of the interior air is typically about 50 f assuming an air temperature of 70 f and a relative humidity of 50.
Polyurethane sheeting is a typical vapor barrier that contractors use to prevent moisture from penetrating the walls of a basement.
A vapor barrier is also helpful to keeping a basement insulated and warm.
The humid air is indoors.
The main concerns are condensation and drying potential.
Plastic on the outer surface of a wall in cold weather could cause problems.