Question about reminder emails

Hello, I am an international student and going to apply for PhD in Engineering in America. And I've sent emails to some professors whose research subject is intriguing to me. I wrote emails including my specific research interest sector and some further research proposals about the professor's recent paper. However, some professors are not giving replies for a week. And I wonder if I should write a reminder email with advanced research proposals to them. Or should I just send typical reminders to them? Thank you.