Dynamics of reversible melting revealed from frequency dependent heat capacity

Abstract

Heat capacity of semi-crystalline polymers shows frequency dependence not only in the glass transition range. Also above glass transition and below melting temperature a frequency dependent heat capacity can be observed. The asymptotic value of heat capacity at high frequencies equals base-line heat capacity while the asymptotic value at low frequencies yield information about reversing melting. For polycarbonate (PC), poly(3-hydroxybutyrate) (PHB) and syndiotactic polypropylene (sPP) the asymptotic value at high frequencies can be measured by temperature-modulated DSC (TMDSC). For polycaprolactone (PCL) and sPP the frequency dependence of heat capacity can be studied in quasi-isothermal TMDSC experiments. The heat capacity spectra were obtained from single measurements applying multi-frequency perturbations (spikes in heating rate) like in StepScan™ DSC or rectangular temperature–time profiles. Actually, the dynamic range of commercial TMDSC apparatuses is limited and only a small part of the heat capacity spectrum can be measured by TMDSC. Nevertheless, comparison of measured base-line heat capacity with expected values from mixing rules for semi-crystalline polymers yield information about the formation (vitrification) and disappearance (devitrification) of the rigid amorphous fraction (RAF). For PC and PHB the RAF is established during isothermal crystallization while for sPP only a part of the RAF is vitrified during crystallization. Devitrification of the RAF seems to be related to the lowest endotherm.

Introduction

From glass transition, it is well known and generally accepted to describe heat capacity by complex numbers. The typical frequency dependence as known from other dynamic measurements is observed—a sigmoid step in real and a peak in imaginary part of heat capacity [1], [2], [3]. Recent measurements also indicate a frequency dependence of heat capacity of semi-crystalline polymers outside the glass transition range [4], [5]. These observations are related to the occurrence of an excess heat capacity that can be observed in a rather wide temperature range between glass transition and melting temperature. The origin of this excess heat capacity and its frequency dependence is not yet understood. Probably the molecular processes involved are related to the surface of the polymer crystallites and often the term reversing melting [6] is used. For polymers showing a sliding diffusion in the crystallites (α-relaxation in case of polyethylene), large contributions to reversing melting are due to surface melting [7]. For other semi-crystalline polymers we do not know which surfaces, growth or fold, are responsible for the process of reversing melting and the corresponding excess heat capacity.

In order to obtain information about the characteristic time scale of the molecular process related to excess heat capacity we have studied the frequency dependence of complex heat capacity during quasi-isothermal crystallization. To extend the frequency range available with temperature-modulated DSC (TMDSC) (10⁻⁵ to 10⁻¹ Hz) ac calorimetric measurements were performed at frequency 1 Hz [8]. For polycaprolactone (PCL), a mean relaxation time in the order of seconds can be estimated for the process at 328 K. The frequency range available is still not broad enough for a detailed discussion of the curve shape, see Fig. 1. But from the curve one expects to measure base-line heat capacity without contributions due to reversing melting for frequencies higher than about 100 Hz. Base-line heat capacity corresponds to the heat necessary to increase the temperature of the sample without changing crystallinity. In other words, it is the heat capacity without any contribution from latent heats. On the other hand, at low frequencies, below 10⁻⁵ Hz in Fig. 1, the asymptotic value of heat capacity yields information about the total amount of material taking part in the process of reversing melting.

If base-line heat capacity is available in the temperature range between conventional glass transition and melting, it is possible to study vitrification and devitrification of the rigid amorphous fraction (RAF) of semi-crystalline polymers. There are two possible paths to reach this goal. To extend the frequency range of heat capacity measurements to the necessary high frequencies or to study polymers with very slow dynamics of the reversing melting so that the high frequency limit is reached at standard frequencies of TMDSC. For PCL, as an example, frequencies above 100 Hz are necessary to measure base-line heat capacity, see Fig. 1. This is far above the TMDSC high frequency limit of 0.1 Hz. We used the second approach and have studied bisphenol-A polycarbonate (PC) and poly(3-hydroxybutyrate) (PHB). PC was chosen for this study because of its very slow crystallization behavior [9]. Why PHB does not show reversing melting in the temperature range where it can be crystallized is not known. PHB is able to crystallize relatively fast and, for polymers, high degrees of crystallinity (0.6–0.8) can be easily reached. We compare the measured base-line heat capacities of PC and PHB with estimated heat capacities from mixing rules [10], [11] to detect vitrification and devitrification of the RAF, for details, see [12]. In this paper we present frequency dependent heat capacity for semi-crystalline PC, PHB and syndiotactic polypropylene (sPP).