Question: What is the difference caused by using “nope” instead of ”no”?

Is it used because “nope” sounds better and not straight like “no”? In some situations, it feels like *nope* is better to use than *no* even though it adds 2 more characters. What is the reason why many use it?

Answer: 
I agree with the person who says that nope is dismissive and slightly rude and I would add that a text nope feels rude to the recipient. It feels like a "final" no.
I think there is a subtle difference between emphatic and dismissive or terminal. And I think that nope is often used in the latter two ways. Think of how the lips must close together and this gives nope its terminal feeling in a physical way. Pursed lips. Can't pry them open. Not going to change.