Heat capacity of a polydiacetylene single crystal from 3 to 300 K

Abstract

Heat capacities Cp of a polydiacetylene‐bis(toluene sulfonate) single crystal and its monomer have been measured in the temperature range from 3 to 300 K. The temperature dependence of Cp for both monomer and polymer crystals differs from that for monoatomic solids. By applying a chain lattice model for a polymer crystal, the temperature dependence of the heat capacity can be described assuming a phonon density of states given by bending and stretching modes of the polymer backbone. With a combination of one‐dimensional and three‐dimensional elastic continuum approximations, the heat capacity has been calculated and a good fit to the data has been obtained. A small peak in Cp was detected at 161 K for the monomer and at 198 K for the polymer. This may be ascribed to a lower‐temperature phase transition in the polydiacetylene crystals evidenced by previous x‐ray and spectroscopic measurements.

A calorimetric study of pTS (bis-p-toluenesulphonate of 2,4-hexadiyne 1,6-diol) and its phase transitions as a function of polymerization

“…A' further study is in progress. Since completion of this work, measurements of Cp(T) from 3 to 300 K for pure monomer and polymer pTS single crystals have appeared [21]. These data are in good agreement with ours for the corresponding microcrystalline samples.…”

Thermal expansion of a polydiacetylene single crystal

“…These phonon modes have been indentified with the three dimensional phonon spectrum of bending phonons in a continuum approximation which has been applied to describe the specific heat of the PTS crystal in the temperature range 3 to 400 K (15). According to reference (15) there are two frequency regions from 0 < co ~<co3b with g (co) = a. co2 and from co3b < co <~ corb = COrn with g(co)= b. col/2 with a, b, co3b, and cos~ obtained from fitting procedure. Inserting g(co) into equation [4] C inter has been calculated as shown in the lower part of figure 4.…”

Computation of the generalized Debye functions?(x, y) andD(x, y)

“…For b-phonons the 3D-spectrum additionally is divided into two regions 0 < co ~< co3b and o)3b < co ~< 6o3 a. The appropriate power functions of the phonon densities of state for each region are given in reference [12]. The calculation of the heat capacity from the continuum approximation has been described in detail in reference [12], too, yielding (29) and (30) are functions of temperature T and characteristic temperatures Oia, which are related to the cut-off frequencies 0)i~ in the following way:…”

“…Several tables of computer generated 1-, 2-, 3-dimensional Debye functions have been published [14][15][16][17]. On the other hand chain like models of polymers taking stretching and bending vibrations [7,12] into consideration reveal that computations of 6n(x) for the halfintegers n land n --3 = --are of interest, too. Thus 2 2 it seems to be of advantage to compute 6~(x) not only when n is an integer.…”