IN the course of exploring the phase diagram of the polymer poly(4-methyl-pentene-l) as a function of temperature and pressure by in situ X-ray diffraction, we have discovered some unusual phase behaviour. The polymer, crystalline under ambient conditions, becomes amorphous reversibly on increasing pressure in two widely separated temperature regimes (∼20°C and ∼200°C), the transformation occurring via a liquid-crystalline state. This suggests the possibility of 're-entrant' liquid-crystal and amorphous phases as pressure or temperature are varied. In the higher-temperature regime, the melting point shows a maximum as a function of pressure. The lower-temperature amorphous phase becomes crystalline on heating, and reverts to the glassy, disordered phase on cooling. Whereas pressure-induced amorphization has been observed previously in other systems, such as ice, silica and A1PO4, we know of no precedent for the disordering on cooling that we observe. © 1991 Nature Publishing Group.