As CodeGnome pointed out in the comments, enforcing the roles and responsibilities of Scrum will go a long way to increasing collaboration between the team.
Although this isn't an answer to your question, first, if you're being asked to "manage" the team, then by Scrum's definition you are not the ScrumMaster. The ScrumMaster's role is to teach the Scrum Team (Product Owner and Development Team) the correct way to do Scrum and facilitate all of the meetings while leaving leading the meetings up to the team.
When it comes to team structure and who collaborates with the product owner, Scrum says that every Development Team should have all of the skills necessary to produce a working product increment. Therefore, a UX/UI designer could collaborate easier with the Product Owner and those writing the code if he/she is working on the Development Team. Moreover, the UX/UI designer, as well as any member of the Development Team, should be talking directly to the Product Owner, without go-betweens.
It sounds like the problem may be that the Product Owner is too busy. As ScrumMaster, it's your job to help this person find out what tasks are important to being an effective Product Owner and then finding ways to delegate work that isn't related to the product to others. As a key member of the Scrum Team, the Product Owner should be available to the team to clarify requirements, such as what the UI should look like, and to answer questions the Development Team has about the forecasted work.
For more information, see the "The Overworked Product Owner" section of "Common Product Owner Traps" by Roman Pichler.
To avoid an overworked product owner, try the following: First, free the individual from all other responsibilities. Start with the assumption that being a product owner is a full-time job, and that one product owner can look after only one product and one team. Second, ensure that the team makes time in every sprint to collaborate with the product owner. Scrum allocates up to 10% of the team’s capacity in every sprint for supporting the product owner (Schwaber 2007).