Much is known about the structure and order-disorder transitions of linear block copolymers.1-3 Detailed information about the kinds of microphase domain morphologies that can be found in block polymers, the composition of copolymer that display each structure, and the conditions for the transitions between these morphologies, as well as into a disordered state, is available. For graft polymers, there has been only one theoretical treatment

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Diblock copolymers show a menagerie of morphologies1 as a function of the relative lengths of the blocks and the temperature (or the magnitude of x-N, where x is the Flory interaction parameter and N the degree of polymerization). These structures range from spheres to hexagonally ordered cylinders and lamellae, corresponding to decreasing mean curvature of the interphase boundary. More recently2 a three-dimensionally ordered structure called the ordered bicontinuous double diamond (OBDD) phase is found at styrene compositions 4>s between 0.62 and 0.66 for polystyrene-6-polyisoprene diblock copolymers. When a homopolymer is mixed with a diblock copolymer, the occurrence of macrophase separation adds a new dimension to the possible morphological variations that can be realized, and the phase diagrams of such blends exhibit fascinating complexities.3,4 Even when the amount of added homopolymer is below its solubility limits so that a single macroscopic phase is realized, a range of structure,

The absolute binding energies of Pt on the stoichiometric and reduced TiO 2 ͑110͒ surfaces should be lower by 0.48 eV compared to the values reported in our paper. This results in a uniform shift of the energy scale in Fig. 2͑a͒ and Fig. 3͑a͒. The new Fig. 2͑a͒ and 3͑a͒ with the updated energy scale are shown below. The correct binding energies of Pt to the stoichiometric and reduced surfaces at the most favorable sites should be 2.03 eV ͑2.14 eV for 3 ϫ 2 cells͒ and 3.80 eV ͑3.55 eV for 4 ϫ 2 cells͒, respectively. This does not change the main conclusions of the paper, since the conclusions involve relative binding energies of Pt, which remain the same, and the Pt-Au binding energy differences are still large, ϳ1.5 eV. FIG. 2a. ͑Color online͒ The potential energy profile for Pt on the stoichiometric TiO 2 ͑110͒ surface. The profile is doubled along the ͓001͔ direction ͑compared to the chosen rectangular grid mentioned in the original paper͒ to have the same size as the profiles in Fig. 3͑a͒. FIG. 3a. ͑Color online͒ The potential energy profiles for Pt on the reduced TiO 2 ͑110͒ surface. PHYSICAL REVIEW B 73, 039902͑E͒ ͑2006͒

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