Elsevier

Polymer

Volume 126, 22 September 2017, Pages 240-247
Polymer

Heat of fusion of polymer crystals by fast scanning calorimetry

https://doi.org/10.1016/j.polymer.2017.08.042Get rights and content

Highlights

  • A method for determining the heat of fusion of polymer crystals, Δhf0, is proposed.

  • The method plots endotherm area vs. (mass x crystallinity). Δhf0 is the slope.

  • Fast scanning calorimetry is used to demonstrate the method on polyethylene, PE.

  • We find Δhf0 = (281 ± 6) J/g for PE, and is within 2% of its literature value.

  • For the biopolymer, silk fibroin, containing beta sheet crystals, Δhf0 = (137 ± 7) J/g.

Abstract

Knowledge of the specific equilibrium heat of fusion of polymer crystals, Δhf0 [J/g], is an essential thermal property of polymers which permits the degree of crystallinity to be obtained from thermal measurements. We describe an approach to evaluate Δhf0(Tm) and implement this method using fast scanning calorimetry (FSC). Our method uses the measured enthalpy of melting plotted against the product of the sample mass times its crystallinity for samples with variable masses and/or crystallinities. Then, Δhf0 is obtained from the slope of the entire data set, reducing errors in the measurement. To demonstrate the method and give proof of principle, we measure Δhf0(Tm) of samples of a narrow fraction of linear polyethylene (PE) with a weight average molecular weight of 60,700 g/mol, whose thermal properties are already known in the literature. For PE, we obtain Δhf0(PE) = (281 ± 6) J/g at Tm = 136 °C, in close agreement with literature values. Then, we apply the method to determine Δhf0(Tm) of silk fibroin, a fibrous protein, yielding a first estimate of the heat of fusion of silk crystals, Δhf0(Silk) ∼ (137 ± 7) J/g. Advantages include: reduction of error, applicability to all types of polymers, copolymers, and blends regardless of degree of crystallinity, and applicability to biomaterials which may require fast scanning rates of FSC to prevent degradation.

Introduction

The specific heat of fusion of polymer crystals, Δhf0(T) [J/g], is the energy needed to convert one gram of 100% crystalline solid into molten liquid at a temperature T. Commonly Δhf0(Tf0) is provided for the equilibrium melting temperature Tf0. The crystals to which Δhf0 applies are crystals close to thermodynamic equilibrium in which the surface properties can be ignored compared to the bulk properties. For polymeric materials, examples of crystals to which the heat of fusion could approximately apply include solution grown single lamellae and extended chain crystals. But it is more generally the case that polymers crystallized from the melt do not form such perfect structures. Melt crystallized polymers typically form multi-crystalline aggregates (such as spherulites, axialites, or dendrites) whose fractional degree of crystallinity, ϕc, is less than unity. For such types of semicrystalline polymer structures, the measured heat of fusion, Δhfmeas, provides a means by which the degree of crystallinity can be assessed using calorimetric measurements, such as differential scanning calorimetry (DSC). A heating scan of semicrystalline polymer often yields a nearly symmetric melting endotherm with peak at Tm whose measured heat of fusion, Δhfmeas [J/g], is related to Δhf0 to a good approximation [1], [2] through the simple relationship:ϕc=Δhfmeas(Tm)/Δhf0(Tm)

Thus, knowledge of Δhf0(Tm) is an essential thermal property of polymers which permits the degree of crystallinity to be obtained from thermal measurements.

Such measurements of Δhf0 have been made for many polymers using extrapolative methods based on equation (1) [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17] including: polypropylene [3], [4], [5], poly(ethylene terephthalate) [6], poly(trimethylene terephthalate) [7], poly(lactic acid) [8], [15], poly(phenylene sulfide) [10], and nylons [11], [12], inter alia. A series of samples is made in which the crystalline fraction is controllably varied, and a heating scan conducted to give different values for Δhfmeas. Then, a physical property known to scale linearly with the crystallinity is measured for each sample. The results of two such measurements are shown in Fig. 1a,b for data on poly(phenylene sulfide) [10] and poly(lactic acid) [8], respectively. Through the data points, a line of best fit is drawn and extrapolated to the point where ϕc = 1. However, some polymers, like polyamide 11, crystallize to limited extent (meaning ϕc is small), and the range of extrapolation is therefore large [12]. In the case of using X-ray scattering (as in Fig. 1a), the crystallinity is determined from the ratio of the area under the crystalline diffraction peaks to the total area of the scattering curve. This measurement can have a large uncertainly, especially if the sample scatters weakly or gives indistinct crystalline peaks. Use of specific volume measurements, as suggested by Fig. 1b, relies on knowledge of the polymer's amorphous and crystalline densities [6], [10]. Some polymers, like polyethylene and polytetrafluoroethylene, however, are not readily obtainable in the 100% amorphous state for this type of measurement. Other polymers, like poly(phenylene oxide) [18] and poly(ethylene terephthalate) [19], form large fractions of the rigid amorphous phase, and the bulk density is therefore not indicative of the crystalline content. Other interfacial effects can result in curvature in the plot of enthalpy vs. specific volume [3], [20]. In some cases, only a single measurement is taken [15], [16] which could lead to larger errors of extrapolation.

In the present work, we offer another approach to evaluate the equilibrium heat of fusion, and implement this approach using fast scanning calorimetry (FSC) [21], [22], [23]. This work was motivated by our earlier thermal studies of silk fibroin protein, and the desire to determine Δhf0 for this biomaterial. Using DSC or its temperature modulated variant, TMDSC, it was not possible to obtain Δhfmeas for silk fibroin because of interference from the degradation process [24]. The slow scanning rates, β, available in DSC, which commonly range from about 0.17 K/s (1 K/min) to 0.5 K/s (30 K/min), do not allow heating of milligram-size samples fast enough to avoid degradation. To circumvent this difficulty, we took advantage of the very fast heating rates of FSC (β ≥ 100 K/s) to study silk fibroin protein. With this technique we were able to heat nanogram-size samples fast enough to observe the melting endotherm of silk [24].

Here, we propose an approach for using FSC to determine Δhf0(Tm), where Tm is the measured melting peak temperature. A set of samples having different masses and the same (or different) crystallinities is used to obtain endotherm areas, Δhfmeas [J], from heat flow rate vs. temperature in FSC. Heat flow rate is then converted to heat capacity [J/K] and the sample mass is estimated in the way described previously [25]. The value of Δhf0 is then found from the slope of a plot of Δhfmeas vs. the product mass*crystallinity. Advantages include: reduction of error in the measurement; ability to use a single DSC scan to obtain the crystallinity for comparison to the FSC; applicability to all types of polymers, copolymers, and blends regardless of degree of crystallinity; and of particular interest in this work, applicability to biomaterials which may require fast scanning rates of FSC to prevent degradation.

As in the case of DSC thermal measurement, to implement the FSC approach, some prior knowledge of thermal properties is required. Viz., the solid state or liquid state specific heat capacity, cpsolid(T) or cpliquid(T) [J/(gK)], must be known from literature. The degree of crystallinity should be known by using another experiment. The FSC method is outlined in the following section, and then applied to polyethylene (PE) to demonstrate proof of principle using a polymer whose solid and liquid state heat capacities are available in the ATHAS data bank [26]. The temperature dependent enthalpy of fusion, Δhf0(T), for polyethylene is also known [16], [27] allowing direct comparison of this value to the one obtained from FSC as a check. Then the method is applied to silk fibroin, yielding a first estimate of the equilibrium heat of fusion of silk crystals, Δhf0(silk) ∼ (137 ± 7) J/g.

Section snippets

Materials

A narrow fraction of linear polyethylene (PE) with a weight average molecular weight of 60,700 g/mol and polydispersity index of 1.13 was purchased from the Société Nationale des Pétroles d’ Aquitaine (SNPA), France. For DSC tests, a compression molded film (∼100 μm thick) of the polyethylene was used. For FSC tests, the as-received PE granules were solvated at 2 wt% concentration in xylene at the reflux temperature, then spin coated using a Headway research grade spin caster. To obtain samples

Heat flow rate and heat capacity for PE and silk

Fig. 2a,b show a comparison of heat flow rate, or power, vs. T for polyethylene obtained using DSC and FSC, respectively. In DSC, the entire scan was conducted at β = 0.5 K/s (30 K/min) and this results in a peak area of 196.0 J/g on the first cooling and on the reheating. The degree of crystallinity of PE following this treatment is found from Eqn. (1) by using the average heat of fusion corrected for undercooling to the melting point. For DSC, Tm DSC= 406.6 K (133.4 °C), Δhf0(TmDSC

Conclusions

  • 1.

    The equilibrium heat of fusion of polymer crystals, Δhf0 [J/g], may be obtained successfully from fast scanning calorimetric data. The approach involves obtaining FSC scans of samples of different mass and/or different crystallinity. The value of Δhf0(Tm) is determined from the slope of ΔhfmeasFSC vs. mass*crystallinity, rather than from an extrapolation. The same approach can be used in conventional DSC, if the sample mass and crystallinity can be varied over a wide range.

  • 2.

    The method should be

Acknowledgements

Funding for this work was provided by the National Science Foundation, through the Polymers Program of the Division of Materials Research, grants DMR-1206010 and DMR-1608125. PC thanks Tufts University for partial support of her sabbatical stay at the University of Rostock. Tufts undergraduate, Mr. Jonathan Minoff, is acknowledged for assistance with PE thin film sample preparation.

References (38)

  • E. Zhuravlev et al.

    Fast scanning power compensated differential scanning nano-calorimeter: 2. heat capacity analysis

    Thermochim. Acta

    (2010)
  • P. Cebe et al.

    Silk I and Silk II studied by fast scanning calorimetry

    Acta Biomater.

    (2017)
  • A. Toda et al.

    Melting behaviors of polyethylene crystals: an application of fast-scan DSC

    Polymer

    (2014)
  • V.B.F. Mathot

    Ch. 5-Thermal characterization of states of matter

  • J.R. Isasi et al.

    The degree of crystallinity of monoclinic isotactic poly(propylene)

    J. Polym. Sci. Part B Polym. Phys.

    (1999)
  • A. Mehta et al.

    Equilibrium melting parameters of poly(ethylene terephthalate)

    J. Polym. Sci. Polym. Phys. Ed.

    (1978)
  • W.-T. Chung et al.

    Melting behavior of poly(trimethylene terephthalate)

    J. Appl. Polym. Sci.

    (2002)
  • D. Sawai et al.

    Crystal density and heat of fusion for a stereo-complex of poly(L-lactic acid) and poly(D-lactic acid)

    J. Polym. Sci. Part B Polym. Phys.

    (2007)
  • R. Loffler et al.

    DSC and x-ray studies of a thermotropic four-monomer copolyester

    Macromolecules

    (1992)
  • Cited by (42)

    • Chip-Based Fast Scanning Calorimetry

      2023, Handbook of Differential Scanning Calorimetry: Techniques, Instrumentation, Inorganic, Organic and Pharmaceutical Substances
    View all citing articles on Scopus
    View full text