There is a famous disagreement between Rashi and Rabbenu Tam concerning the sequence in which the parchments in the Tefillin should be arranged. Halacha generally accepts Rashi's view, but many people nevertheless wear "Tefillin Rabbenu Tam" after they wear the standard "Tefillin Rashi" in order to ensure that they fulfill this important Misva according to all opinions. Followers of this custom recite the Beracha over Tefillin before donning Tefillin Rashi, and have in mind for the Beracha to relate as well to the Tefillin Rabbenu Tam which they wear later.
An interesting question arose regarding a case where a person mistakenly put on Tefillin Rabbenu Tam first, thinking they were Tefillin Rashi. Naturally, since he assumed he was donning Tefillin Rashi, he recited the Beracha. When he removes the Tefillin Rabbenu Tam after realizing his mistake, and puts on Tefillin Rashi, should he recite a new Beracha, or does the Beracha recited over the Tefillin Rabbenu Tam cover the Tefillin Rashi, as well?
It is clear that if the individual spoke before he removed his Tefillin Rabbenu Tam, such as if he began praying, reciting Shema, or speaking to somebody, then he must certainly recite a new Beracha when he then dons Tefillin Rashi. His speech constitutes a "Hefsek" (interruption) in between the Beracha and the laying of Tefillin Rashi, such that the Beracha cannot extend to the Tefillin Rashi. Hence, a new Beracha is required when the individual puts on Tefillin Rashi.
What is less clear, however, is whether the person must recite a new Beracha if he realizes his mistake and removes the Tefillin Rabbenu Tam immediately, before he spoke. One might argue that since no verbal interruption has been made, the original Beracha recited when the individual donned the Tefillin Rabbenu can apply to the Tefillin Rashi, as well.
The Hid"a (Rav Haim Yosef David Azulai, 1724-1806), however, in Mahazik Beracha as well as in Haim Sha'al (vol. 1, 1:4), ruled that even in such a case one must recite a new Beracha when putting on Tefillin Rashi. This view, which the Hid"a shares with a number of other Halachic authorities, is predicated upon a number of cogent arguments. For one thing, the act of laying Tefillin may in itself constitute a Hefsek. Even if the person did not speak since reciting the Beracha, he did perform the act of wrapping Tefillin around his arm and head, and one might contend that this act suffices as an interruption that does not allow the Beracha to apply to the Tefillin Rashi.
Secondly, the individual clearly had no intention for his Beracha to apply to any other pair of Tefillin Rashi. Since he presumed that the Tefillin he put on were Tefillin Rashi, it did not enter his mind that this Beracha might refer also to another pair of Tefillin Rashi. This might be compared to a situation known in Halachic jargon as "Nimlach," where a person recites a Beracha on a certain food and then decides to partake of more of that food. Since he had originally intended to eat only the initial item, the Beracha does not extend to the additional food that he decides to eat, and he must therefore recite a new Beracha over that additional food. Similarly, since the individual had no intention to wear another pair of Tefillin Rashi, we cannot extend his Beracha to cover the Tefillin Rashi that he puts on after removing his Tefillin Rabbenu Tam.
Nevertheless, Hacham David Yosef, in his work Halacha Berura (Siman 34, p. 10), concludes that one should not recite a Beracha in this case, in light of the principle of "Safek Berachot Le'hakel" – a Beracha should never be recited in situations of uncertainty. Since the Halacha regarding this case is not conclusive, and the aforementioned arguments could be refuted, one should lay the Tefillin Rashi without reciting a Beracha, rather than risk reciting a "Beracha Le'batala" (a "wasted" Beracha).
Summary: If a person mistakenly put on Tefillin Rabbenu Tam thinking that they were Tefillin Rashi, he should remove them and put on his Tefillin Rashi. If he had spoken in the interim, he should recite a new Beracha when donning the Tefillin Rashi; if he had not spoken in the interim, then he does not recite a new Beracha.
