Open cell spray foam consists of cells that do not completely seal themselves. This makes for a softer and less dense final product. Closed cell foam cells are completely sealed and closed compressed together, creating a denser and firmer final product. This also gives closed cell foam a higher R-value (measured unit of thermal resistance). These differences also affect the cost difference between the two types of insulation.
Open cell is that type of foam in which the cells do not close completely. As the open-cell foam uses less number of chemicals, it is less costly. The foam acts as a barrier for, but cannot barricade water vapor. It has a sponge-like an appearance and can be used on the interiors walls of a home or building, as it causes a reduction in sound. The foam is not used for the outdoor applications.
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R-value is the term given to thermal resistance to heat flow. The higher the R-value of an insulation product, the more effective the insulation properties. Spray polyurethane foam comes in a range of densities and cel structure. Low density foams are referred to as Open Cel SPF while higher density foams are referred to as Closed Cel foam. 1.8-2 pound polyurethane foam has the highest R-value of readily available spray foam insulation used in homes and buildings.[4]
The problem was that the installer was doing his first spray foam job ever, and the thickness of the insulation varied from zero (visible roof deck) to about 9". Unfortunately, good average thickness doesn't cut it. The coverage needs to be uniform because a lot of heat will go through the under-insulated areas. (See my article on flat or lumpy insulation performance.)
Note: The practice of foam insulating the attic has raised eyebrows in the building industry because "standard" roofing techniques call for the attic to be ventilated; however, in a vented attic situation it will become approximately 130 degrees in the summer. There's no reason for an air-conditioning and vent-ductwork to have to work in that type of severe conditions. By applying Icynene right on the underside of the roof deck, the severe temperatures no longer exist in the attic. In short, the attic is now a "conditioned" space of the house that is just as comfortable as any other room in the home. This is called a "Compact Roof", which means you can frame right up against it. The one drawback of using expanded foam on the inside of the roof is that this will cause the temperature of the shingles to rise, but how much is not yet known. And how much damage a rise in temperatures could cause is debatable.

Roof Spray Foam Insulation