  Membrane based nanocalorimeters have been developed for ac calorimetry
experiments. It has allowed highly sensitive measurements of heat capacity from
solid state physics to complex systems like polymers and proteins. In this
article we review what has been developed in ac calorimetry toward the
measurement of very small systems. Firstly, at low temperature ac calorimetry
using silicon membrane permits the measurement of superconducting sample having
geometry down to the nanometer scale. New phase transitions have been found in
these nanosystems illustrated by heat capacity jumps versus the applied
magnetic field. Secondly, a sensor based on ultra-thin polymer membrane will be
presented. It has been devoted to thermal measurements of nanomagnetic systems
at intermediate temperature (20K to 300K). Thirdly, three specific polyimide
membrane based sensors have been designed for room temperature measurements.
One is devoted to phase transitions detection in polymer, the second one to
protein folding/unfolding studies and the third one will be used for the study
of heat release in living cells. The possibility of measuring systems out of
equilibrium will be emphasized.
