Novel　macrostructures　built　up　by　carbon　nanotubes　(CNTs),　such　as　super-graphene　(SG)　similar　to　a　single　graphite　layer　and　super　carbon　nanotube　(SCNT)　analogous　to　a　single-walled　CNT　(SWCNT),　have　been　developed　to　extend　the　superior　mechanical　properties　of　the　CNTs.　This　paper　describes　cohesive　laws　for　the　interfacial　interactions　of　SG/polymer　and　SCNT/polymer　composites　induced　by　the　weak　van　der　Waals　force.　By　denoting　the　volume　density　function　of　the　SG　in　terms　of　the　length　and　area　density　of　the　CNT,　the　van　der　Waals　force　and　the　cohesive　energy　are　obtained　for　infinite　SG/graphene　at　first.　Then　the　tensile　cohesive　strength　and　cohesive　energy　between　the　SCNT　and　the　polymer　matrix　are　given　in　terms　of　the　volume　density　of　the　SCNT　and　volume　density　of　the　polymer.　It　is　shown　that　for　a　SCNT　embedded　in　finite　polymer　matrix,　the　tensile　cohesive　stress　depends　only　on　the　opening　displacement　of　the　interface,　while　the　shear　stress　depends　on　both　opening　displacement　and　sliding　displacements　of　the　interface.　(C)　2016　Elsevier　Ltd.　All　rights　reserved.