赞同大鹏老师的解答，为了便于网友理解和掌握，我再补充几点我的理解：

the role of + 名词结构中，根据语境的需要或作者的写作习惯，名词前不使用冠词或使用定冠词或不定冠词，都是常见的。总的来讲，区别很小，有时可以忽略。不用冠词，一般更侧重职责，the role of father, 侧重父亲的职责，当然说话人不一定就是父亲。the role of the father,一般两种可能，类指或特指。如大鹏老师提供的字典例句：The role of the mother was played by... 这里是特指电影中的那个母亲的角色。

有时也可以用所有格结构，如a father's role 名词也可以用复数形式。如：role(s) of fathers.

请比较外媒例句的不同用法：

1. The role of a father in the family is incredibly important to their child or children's psychological and physical wellbeing. 

2. Men who assume the role of a father are often relied upon to impart this inner strength, even when the demand of carrying the weight of that responsibility seems too much to bear. 

3. However, the role of the father has been considerably more contentious, and the evidence is more mixed than for mothers. 

4. The role of the father has tremendously diminished in America. In fact, some actually believe and have expressed the view that the role of the father is a disposable one.

5. Knowing the role of father in the traditional Chinese family is crucial for understanding the meaning of the emperor and Chinese authoritarianism in general.

7. He is trying to learn the role of father, just as the woman is trying to learn the role of mother.

8. He then takes on his father's role and casts Falstaff as himself.

10. Given these limitations, the research provides insights into the roles of fathers in childbirth...