There are two things that could be causing the page to crash. Before you go any further I would suggest that you turn on debugging so that you can see errors rather than just getting the WSOD https://codex.wordpress.org/WP_DEBUG.
Your first problem is that DateTime is a class so you need to use
$publish_date_time = new DateTime( get_sub_field('publish_date_time') );
more than likely you’re getting a fatal error that the function DateTime() does not exist.
After that you will need to make sure that your field is returning a date format that is compatible with DateTime() https://www.php.net/manual/en/datetime.formats.php.
