Heat capacity measurement of organic thermal energy storage materials

Abstract

The heat capacities of tris(hydroxymethyl)aminomethane (TRIS), 2-amino-2-methyl-1,3-propanediol (AMPL), and neopentylglycol (NPG) are measured from (193.15 to 473.15) K by modulated differential scanning calorimetry (MDSC). The heat capacities of the low temperature layered or chain ordered phases, high temperature orientationally disordered phases, and the liquid phases are reported for these compounds. The low temperature heat capacities (193.15 to 280) K of AMPL are reported for the first time. The heat capacities obtained from our MDSC experiments are in good agreement with adiabatic calorimetry measurements.

Introduction

Alcohol and amine derivatives of neopentane [NP: C(CH₃)₄] belong to a special group of compounds that undergo solid–solid phase transition from a layered or chained low temperature structure (tetragonal, monoclinic, etc.) to a high temperature orientationally disordered cubic structure (FCC or BCC). The polyalcohol series of these compounds include pentaerythritol [PE: (CH₂OH)₂C(CH₂OH)₂], pentaglycerine [PG: (CH₃)C(CH₂OH)₃], neopentylglycol [NPG: (CH₃)₂C(CH₂OH)₂], and neopentylalcohol [NPA: (CH₃)₃C(CH₂OH)]. Examples of amine derivatives include 2-amino-2-methyl-1,3-propanediol [AMPL: (NH₂)C(CH₃)(CH₂OH)₂], and tris(hydroxymethyl)aminomethane [TRIS: (NH₂)C(CH₂OH)₃]. The solid–solid phase transition in these organic compounds is characterized by an unusually large enthalpy compared to the enthalpy of fusion from the orientationally disordered structure to the liquid phase. In this paper, we use the nomenclature of phases as suggested by Chandra et al. [1], [2], [3]; ‘α’ or ‘β’ for the low temperature phases and ‘γ’ or ‘γ′’ for the high temperature cubic phases as this nomenclature may be easily extended to binary solid solutions. These organic compounds have been alternately referred to as “Plastic Crystals” due to the plastic nature of the orientationally disordered high temperature phase. The ability of these compounds to reversibly absorb or release a large amount of heat at the phase transition temperature during the solid–solid phase transition makes them attractive as solid state thermal energy storage materials. After the pioneering study of Murrill and Breed [4], numerous researchers have conducted thermodynamic and crystallographic studies on pure as well as binary mixtures to design new thermal energy storage materials (TES) for practical applications. A compilation of the thermodynamic and crystallographic properties of the compounds of interest to this study (AMPL, TRIS, and NPG) are shown in table 1. Additional references can be found in recent experimental and calculated phase diagram studies of (AMPL + NPG) [5], and (PE + AMPL) [6], [7] binary systems.

The focus of experimental thermodynamic studies has been on binary systems, primarily to change the transition temperatures and evaluate the possibility of using binary mixtures as novel thermal energy storage materials. For use in practical applications, such as, development of heat sink materials for electronic devices [8] accurate knowledge of heat capacities for both pure as well as binary mixtures is highly desirable. Also, from a thermodynamic modeling perspective, the knowledge of heat capacity of pure compounds allows us to determine accurate Gibbs free energy expressions [5] and aids in the development of a consistent thermodynamic database of phase diagrams. There are very few reported studies exclusively devoted to the determination of heat capacities of these pure compounds and even fewer for binary mixtures. The earliest known C_p,m determination for TRIS (T_trs = 407.5 K [9], T_fus = 443.4 K [9]) was done by Arvidsson and Westrum [10] in 1972 from (5 to 350) K using adiabatic calorimetry (AC). The temperatures of phase transition are given in parenthesis where T_trs is the temperature of solid–solid transition and T_fus is the temperature of fusion. Zhang and Yang [9] measured the C_p,m of TRIS from (290 to 455) K and Chandra et al. [11] reported the C_p,m from (305 to 447.5) K performed by using conventional differential scanning calorimeter (d.s.c.). A closer examination of temperature range reveals that there are three independent datasets available for the high temperature γ phase, however, here is only one dataset for low temperature C_p,m by Arvidsson and Westrum [10] and one for the liquid phase [9]. Therefore, there is a need for a C_p,m measurement in the low temperature as well as the liquid phase. The C_p,m of AMPL (T_trs = 353.72 K [12], T_fus = 384.08 K [12]) was first measured using AC by Zhang and Yang [12] from (280 to 384.37) K while Chandra et al. [11] reported from (305 to 422.5) K using d.s.c. There are no reports of low temperature C_p,m of AMPL (T < 280 K) and there is only one dataset for the liquid phase. The C_p,m of NPG (T_trs = 314.8 K [13], T_fus = 403.3 K [13]) first reported by Zhang et al. [13] using AC from (270 to 440) K and subsequently by Chandra et al. [11] from (305 to 447.5) K. Recently, Kamae et al. [14] reported low temperature C_p,m of NPG (as well as its deuterated analogues) from (14.9 to 339.89) K. It can be seen that there is a need for further C_p,m measurements in the low temperature and liquid region for AMPL and NPG.

It is well known that adiabatic calorimetry [15] is a more precise method for measurement of heat capacities and was the predominant mode of conducting thermal analysis experiments during the early 1900s. However, it is a specialized and time consuming experimental technique and needs highly experienced scientists for obtaining this data. Thermal analysis using d.s.c. was introduced in the early 1960s [16] and has since been a popular method for determining the enthalpy and temperature of phase transitions for many practical applications. However, there are some inherent disadvantages in conventional d.s.c. experiments which are especially apparent while analyzing complex transitions (glass transitions, amorphous to crystalline transitions, etc.) that involve more than one thermodynamic event. It is also well known that there is trade off between sensitivity and resolution of conventional d.s.c. experiments. To distinguish between phase transitions that are separated by a few degrees (requires high resolution), it is essential to use a lower heating rate with small sample masses. However, this can lead to loss of sensitivity as well as problems associated with baseline heat flow. Chandra et al. [17] have conducted a systematic study of the effect of heating rate and sample mass on the resolution of the d.s.c. thermograms for trimethylolpropane [TRMP: (CH₂OH)₃C(C₂H₅)], an alcohol derivative of neopentane using conventional d.s.c. The heat capacities using d.s.c. may be determined by two different procedures as described below:

(1) The first method is to conduct three experiments at a pre-determined heating rate; measuring the heat flow of empty pan (baseline run), measuring the heat flow of the sample (sample run), and to obtain a calibration of the heat flow with a known calibrant (typically sapphire, calibration run). The molar heat capacity of an unknown sample, C_p,m (J · K⁻¹ · mol⁻¹) can be determined by

$$\begin{array}{cc}\hfill & C_{\mathrm{p}\text{,}\mathrm{m}}=K\left\{(\mathrm{d}H/\mathrm{d}t{)}_{\mathrm{sample}}-(\mathrm{d}H/\mathrm{d}t{)}_{\mathrm{empty}}/m_{\mathrm{sample}}\right\}\text{;}\hfill \\ \hfill & K={\mathit{MW}}_{\mathrm{sample}}\left\{m_{\mathrm{sapphire}}·C_{\mathrm{p}\text{,}\mathrm{m}}^{\mathrm{sapphire}}/(\mathrm{d}H/\mathrm{d}t{)}_{\mathrm{sapphire}}-(\mathrm{d}H/\mathrm{d}t{)}_{\mathrm{empty}}\right\}\text{,}\hfill \end{array}$$

where K is the calibration constant that is determined from the calibration heat flow, m_sapphire and m_sample are the masses of the sapphire standard and the sample, respectively, dH/dt is the rate of change enthalpy (J · mol⁻¹ · min⁻¹), $C_{\mathrm{p}\text{,}\mathrm{m}}^{\mathrm{sapphire}}$ is the known molar heat capacity (J · K⁻¹ · mol⁻¹) of the sapphire standard. The method described in equation (1) is the basis for ASTM E1269 [18].

(2) The second method is to conduct two experiments on the sample at different heating rate and determine the heat capacity as shown below:

$$C_{\mathrm{p}\text{,}\mathrm{m}}=\overline{K}\left[\left\{(\mathrm{d}H/\mathrm{d}t{)}_{\mathrm{sample}}^{{\beta }_1}-(\mathrm{d}H/\mathrm{d}t{)}_{\mathrm{sample}}^{{\beta }_2}\right\}/({\beta }_2-{\beta }_1)\right]\text{,}$$

where $\overline{K}$ is a unitless calibration constant determined by subjecting a sapphire standard to two different heating rates, β₁ (K · min⁻¹) and β₂ (K · min⁻¹), and dH/dt is the rate of change enthalpy (J · mol⁻¹ · min⁻¹). It is apparent that measuring heat capacities using conventional d.s.c. requires conducting multiple experiments and it can also be time consuming if the experiments have to be conducted to exacting requirements such as those prescribed by ASTM E1269 [18]. An advancement over conventional d.s.c. is the temperature modulated d.s.c. (abbreviated henceforth as MDSC, a trademark of TA Instruments [19]; there are many commercial instruments that have the temperature modulation capability) has proven to be useful in thermal analysis over the past decade and is described in the following section.

Temperature modulated d.s.c. was introduced by Reading et al. [20], [21] and has its basis in the multiple heating rate method of measuring heat capacities. In MDSC, the sample is subjected to a temperature regime that is a superposition of a linear heating rate and a sinusoidal modulation. An example of the equivalency between the multiple heating rate conventional d.s.c. and MDSC methods of heat capacity measurement is shown in figure 1. A typical temperature profile, T(t), imposed on a sample is of the following form:

$$T(t)=T_0+\beta t+A\sin (\omega t)\text{,}$$

where T₀ is the initial temperature (K), β is the average heating rate (K · min⁻¹), A and ω are the amplitude (K) and frequency of the modulation, and ω is given by 2π/P where P is the period of modulation (min). A typical heating profile that was used for conducting experiments discussed in this study is shown in figure 2. A discussion on the choice of these experimental parameters is given in section 2.

The rate of total heat flow for a d.s.c experiment is given by the following expression:

$$\mathrm{d}Q/\mathrm{d}t=C_{\mathrm{p}\text{,}\mathrm{m}}\beta +f(T\text{,}t)\text{,}$$

where dQ/dt is the rate of total heat flow (per mole basis), C_p,m is the molar heat capacity, β is the heating rate, and f(T, t) is the heat flow associated with any kinetic process (absolute temperature and time dependent) involved. The instantaneous heating rate (modulated heating rate), total heat flow and modulated heat flow for an MDSC experiment conducted on TRIS is shown in figure 3. The heat capacity of a sample can be determined by comparing the amplitude of the modulated heat flow and the amplitude of the modulated heating rate at a particular frequency to a reference sine wave of the same frequency (using discrete Fourier transformation) as shown in the following equation [23], [24]:

$$C_{\mathrm{p}\text{,}\mathrm{m}}=K_{C_{\mathrm{p}}}(Q_{\mathrm{amp}}/T_{\mathrm{amp}})(P/2\mathrm{\pi })\text{,}$$

where Q_amp is the heat flow amplitude (J · mol⁻¹), T_amp is the temperature amplitude (K), and $K_{C_{\mathrm{p}}}$ is the calibration constant. Further mathematical details regarding the application of discrete Fourier transform (DFT) for data analysis and deconvolution of heat flow and temperature signals can be found in Wunderlich [24]. Due to the imposition of a modulated temperature regime as shown in equation (3), the total heat flow recorded by a single MDSC experiment can be separated into two parts: (1) so-called “reversing heat flow” due to heat capacity component, (2) so-called “non-reversing heat flow” due to kinetic component. As an illustrative example, all the three heat flow components, total heat flow, reversing heat flow, and the nonreversing heat flow of an MDSC experiment on a TRIS sample is shown in figure 4. The nonreversing heat flow is very close to zero during the single-phase region (α, γ, or L) suggesting no kinetic activity while there is a strong kinetic component during phase transitions (an endotherm during the solid–solid transition and an exotherm during melting). The exotherm during melting is typically attributed to the enthalpic relaxation [22].

In an early critique on MDSC (1995), Ozawa and Kanari [25] concluded that due to the linear thermal response (especially during baseline and peak areas), measurement of C_p,m and use of DFT for data analysis is acceptable. Alternate interpretation of signals from MDSC based on linear response theory has also been presented by Schawe and Höhne [26], [27] who identified “real” and “imaginary” parts of a complex C_p,m corresponding to reversible and non-reversible C_p,m interpretation of Reading et al. [20], [21] and Wunderlich [24]. Cao et al. [28], [29] have identified several drawbacks with respect to measurement of heat capacities using MDSC as well as the mathematical theory of interpretation of signals. However, recent theoretical studies by Clarke et al. [30] and MacDonald et al. [31] have clarified that the mathematical basis of MDSC as put forth by Wunderlich [24] is correct. It should be noted that recent reviews have also elucidated that there are still several issues such as heat transfer, sample thermal lag, and other experimental variables that have to be accounted for while using MDSC for thermal analysis [32].

In this study, MDSC has been used to determine heat capacity of organic thermal energy storage materials and the accuracy of the measured heat capacity values is established by comparing with previously reported values by adiabatic calorimetry and also by conducting many experiments to establish reproducibility. The parameters for temperature modulation have been chosen (slow heating rate and long modulation period) to account for expected thermal lags in the sample behavior and careful attention has been given to sample preparation itself. We report the heat capacities of AMPL, TRIS, and NPG here from (193.15 to 280) K for α, γ, and L regions.