Does divorce take effect if I swore to my wife that I would not speak to her for a full week if she did not keep quiet, and my intention was only to silence her, but she did not keep quiet, claiming she did not hear me?

You are not bound by anything if you swore by Allah or by divorce upon your wife that she should not speak, and she did not keep silent because she did not hear your oath. This is because the wife's knowledge of the oath is a condition for the occurrence of breaking the oath, if she is mindful of the matter of the oath. This is the view of the Shafi'is and a narration among the Hanbalis chosen by Sheikh al-Islam Ibn Taymiyyah.