The split insulated wall scenario is shown in the figure below under wintertime conditions in a cold climate.
Vapor permeable mineral wool insulation has been placed outboard of the sheathing. This has the effect of warming the stud space and exterior sheathing - the more exterior insulation, the warmer the cavity and sheathing. No interior or exterior vapor barrier material has been used, though a Class II or III vapor retarder may be necessary to prevent condensation or high RH levels from occurring, depending on the thickness of exterior insulation and the vapor pressure gradient (expected interior and exterior conditions). For moderately cold climates and most indoor conditions within commercial buildings, the installation of a few inches of mineral wool outboard of an insulated 6" stud wall is sufficient to ensure good performance when a Class III vapor retarder (latex paint) is used on the interior of the drywall. Good performance can generally be taken to mean maintaining the RH at the sheathing below 80%. For buildings with high interior humidity levels such as pools or museums, a Class I or II vapor barrier would likely still be required.
The vapor pressure difference from interior to exterior within this scenario is the same as the previous cases, and is not affected by the exterior insulation; however, the temperature within the stud cavity is warmer, and consequently the RH at the sheathing does not increase as much. As a result, condensation does not form within the cavity and the vapor passes through the sheathing and vapor permeable insulation without harm. The RH within the cavity behind the sheathing will depend on the insulation ratio and on the rate at which drying occurs through the sheathing. Therefore, the more vapor permeable the sheathing and insulation, the lower the RH within the cavity.
Because the sheathing temperature is increased, the risk of air leakage condensation is reduced which further improves the durability of this wall. With vapor diffusion and air leakage wetting addressed, the only risk to moisture damage is from an external leak. However, because the sheathing is kept warmer by the insulation, it is able to dry out faster, and in this wall assembly moisture will dry both inwards and outwards by vapor diffusion through the relatively vapor permeable materials.