Shape Memory Polymers: Heating Capacity Background

In order to affect change within a shape memory polymer, its properties above and below the glass transition temperature, Tg, must be know.  For my purposes, I wish to induce change through a heat source, more specifically electrical heat source.  Therefore, specific heat of the polymer needs to be known.  Heat capacity can be measured by adiabatic calorimetry (0-100 K), differential scanning calorimetry (DSC) (above 100 K), and some other techniques.  The heat capacity for any given polymer is a temperature-dependent quantity (1).   Reference 1, also gives a table containing the variation of the heat capacity of several example polymers with temperature.

In order to calculate the required power input to induce shape change, the First Law of Thermodynamics states:

ΔU = ΔQ – ΔW

meaning, the change in internal energy is equal to the heat added to the system minus the work done by the system.  Therefore, the calculate the power, the change in internal energy needs to be known.  (Power, in terms of electrical work at constant time, is given as W = VIΔt.)  For the change in internal energy, heat capacity can be assumed to be constant, giving the following:


where c is the heat capacity, and ΔT is the change in temperature.  In Reference 2, the authors are using a metal layer to induce a change in an SMP material.  Their approach to calculating the power required is by using standard values for heat capacity to calculate the change in internal energy.


(a) Stiffness tunable composite embedded with Field’s metal strip and liquid-phase Galinstan heater. (b) When electrically activated, the composite softens and easily deforms. (c) Illustration of the composite composed of a (top) elastomer sealing layer, (middle) liquid-phase Joule heating element, and (bottom) thermally activated layer of Field’s metal or SMP. (d) Close-up of Galinstan heating element; ruler marks spaced 1 mm apart (2).


1.  Mark, J. E., Ed.Physical Properties of Polymers, 2nd ed., 2007.

2.  Wanliang Shan et al 2013 Smart Mater. Struct. 22 085005


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