persistentDataPath for web (facebook) app

I have a game that I intend to run on multiple platforms. For testing, I copy a webplayer build of the project to Parse and link to it as a Facebook app.

When I try to save a save file to the Application.persistentDataPath, nothing happens. Should I use something other than persistentDataPath for the webplayer?

Here's the code in question:

 var saveFile = Application.persistentDataPath+"/storeItems.dat";
         
 BinaryFormatter bf = new BinaryFormatter();
 FileStream fs = File.Create(saveFile);
 bf.Serialize(fs, this); //'this' is a serializable class with a serializable list member
 fs.Close();

When I debug Application.persistentDataPath, it's an empty string.