WO2023158308A1

WO2023158308A1 - Novel method for analyzing dsc data

Info

Publication number: WO2023158308A1
Application number: PCT/NL2023/050077
Authority: WO
Inventors: Stephen James Picken; Elmira GHANBARI
Original assignee: Technische Universiteit Delft
Priority date: 2022-02-18
Filing date: 2023-02-16
Publication date: 2023-08-24

Abstract

The present invention is in the field of investigating or analyzing materials by obtaining their chemical or physical properties, such as by measuring quantity of heat. An example of such measuring is a thermoanalytical method, such as differential scanning calorimetry (DSC), in which the difference in the amount of heat required to increase the temperature of a sample and reference is measured as a function of temperature.

Description

Novel method for analyzing DSC data

FIELD OF THE INVENTION

BACKGROUND OF THE INVENTION

The present invention relates in general to a thermoanalytical method, such as differential scanning calorimetry (DSC). Differential scanning calorimetry (DSC) is a thermoanalytical technique in which a difference in the amount of heat required to increase (or likewise decrease) the temperature of a sample and the amount of heat required to increase the temperature of a known reference is measured as a function of temperature. Ideally the sample and the reference are maintained at the same increased temperature throughout the experiment. Typically the temperature increases linearly as a function of time, except when a phase transition is encountered, such as when melting the sample. The reference sample is often In (Indium), which has well defined characteristics over the temperature range considered, such as a well-defined heat capacity (see e.g. fig. 1). DSC is in particular used in material science, where it is applied to perform quantitative analysis, such as of (rapid) phase transitions, particularly on fast cooling. Various types of DSC exist nowadays, in particular heat-flux DSC, power differential DSC, ultra DSC, and Fastscan DSC, each having advantages in particular cases. Fast-scan DSC is a rather a novel technique that employs micromachined sensors, therewith enabling a fast scan. It provides a relatively ultrahigh scanning rate (e.g. - 100 K/s) and a heat capacity resolution typically better than 1 nJ/K. Fast-scan DSC can be used to obtain thermophysical properties of thermally labile compounds. Quantities like fusion temperature, fusion enthalpy, sublimation, and vaporization pressures, and enthalpies of such molecules became available. Heat-flux DSC obtains changes in heat flow by integrating the ATr_ef-curve over the temperature range or typically part thereof. Often a sample and a reference crucible are placed on a sample holder with integrated temperature sensors for temperature measurement of the crucibles. Thereto often a temperature- controlled oven is used. In Power differential DSC the sample and reference crucible are typically placed in thermally insulated furnaces. They are not next to one and another in the same furnace like in Heat-flux-DSC experiments. Typically the temperature of both chambers is controlled having the same temperature for the sample and reference. Use is made of the electrical power consumption to obtain characteristics of the sample.

In DSC a melt temperature is to some extent obtained rather arbitrary. An operator of a DSC device, with regard to an obtained heat flow versus temperature curve, determines a temperature range to be used, having a lower temperature, and a higher temperature. The lower temperature and the higher temperature are typically chosen relatively close to a peak in the DSC-curve, representing a phase transition (melting or liquid crystal transitions, glass transition). Both are chosen within a few degrees centigrade of the peak. Effectively, therewith a remainder of the DSC curve is neglected, or at least not taken into account. The usual procedure is to associate the melting temperature with the maximum value of the heat of fusion peak. In the current method it is found that for samples with a substantial asymmetry of the melting process it is better to locate the melting point on the declining edge of the latent heat curve, the model provides a useful criterion for this phenomenon.

The DSC method is often used as a tool for convenient thermal analysis of samples, as it provides a relatively fast method to determine melting points, glass transitions, liquid crystal transitions, points of crystallisation (e.g. effect or rate and nucleation). It is frequently possible to use only a small amount of sample e.g. 5 mg which is very useful for new synthesised substances that are often not available on a large scale. It is the de facto standard method to determine this type of thermodynamic parameters, also for quality control, effect of impurities, molar mass of polymers or indeed determining whether a formulated product is on spec. It is worth noting that some types of food (tempered chocolate) and pharmaceutical products often require a specified T' 0 Im •

Nevertheless the DSC method is not without issues, as the thermal phenomena are frequently not very sharply defined. This can be due to impurities in the sample, or a wide range of crystal sizes, internal stress, low thermal conductivity, presence of volatile solvents, and many other. This leads to a certain ambiguity in the determination of ‘the melting temperature’ or ‘the crystallisation temperature’; it also may lead to problems in integrating the heat flow as this requires a baseline correction and the baseline is not known a priori.

Incidentally reference can be made to prior art documents US 2007/128731 Al, EP 1 340 969 Al, and WO 2005/034915 A, which represent typical prior art DSC-methods. US 2007/128731 Alrecites methods for purifying rapamycin are described, as well as methods for measuring particle quality, median particle size, and crystallinity of samples containing rapamycin or a derivative thereof are also provided, comprising analyzing the heat flow signal of a sample comprising a rapamycin compound; and comparing the heat flow signal of said sample to the heat flow signal of a predetermined standard; wherein said particle quality is proportional to the melting temperature of said heat flow signal of said sample. EP 1 340 969 Al recites a system and method for obtaining the contact thermal resistance for a sample and pan without a priori knowledge of the properties of either sample, by measuring the reversing heat capacity of a sample and its pan (or an empty pan on the reference side of the DSC) at a long period and a short period during a quasi-isothermal MDSC experiment and then finding the value of contact thermal resistance that makes the short and long period heat capacities match. Several different methods may be used to find the contact thermal resistance using quasi -isothermal MDSC with a long and a short period. Two methods are direct calculation methods that use the results from an MDSC experiment used with model equations to calculate the contact thermal resistance. A third method is another direct calculation method, based upon the phase angle between the heat flow and temperature signals. A fourth and fifth method use curve fitting of the apparent heat capacity for multiple values of pan contact thermal resistance. WO 2005/034915 A recites a method for generating a correlation between at least one thermal property of a liposomal carrier in the presence of a therapeutic agent and a pharmacokinetic property for the therapeutic agent in the liposomal carrier and using the correlation for predicting the pharmacokinetic property of the liposomal carrier in the presence of any therapeutic agent in a liposomal carrier.

The present invention therefore relates to an improved thermo-analytical method, which solves one or more of the above problems and drawbacks of the prior art, providing more reliable results, without jeopardizing functionality and advantages.

SUMMARY OF THE INVENTION

It is an object of the invention to overcome one or more limitations of the prior art and provide a thermoanalytical method comprising providing a sample to be measured, the sample having a heat capacity, in particular a sample of 10 pg-100 mg, more in particular 0.1-10 mg, such as 1-5 mg, measuring a heat flow to or from the sample over a measuring temperature range with a thermoanalytical device therewith obtaining heat flow versus temperature data, in particular wherein the measuring temperature range comprises at least one phase transition temperature, based on the heat flow versus temperature data obtaining a combination of physical or chemical characteristics of or imposed on the sample, wherein the characteristics is selected from the combination of a size distribution of crystal sizes, an amount of impurities in the sample, a measurement accuracy, based on the heat flow versus temperature data and the combination of physical or chemical characteristics of the sample obtaining thermic characteristics of the sample, wherein the thermic characteristics of the sample is selected from at least one of a melting point of the sample, or latent heat of fusion of a first order phase transition of the sample, a change in heat capacity, a glass transition temperature, a liquid crystal transition, a point of crystallization, a melting temperature range, a speed of melting, a degree of crystallinity, a temperature increase, a temperature decrease, a fusion temperature, a fusion enthalpy, a sublimation temperature or enthalpy, an enthalpy change, a specific heat, a variation of said thermic characteristics as a function of temperature, and a combination thereof. The current method addresses the above issues by obtaining the combination of physical or chemical characteristics of or imposed on the sample based on the heat flow versus temperature data (DSC curve). Thereto a fitting procedure is used which is found to be much more insensitive to coincidental choices of sample mass, thermal history, integration bounds. It provides a best value of Tm° taking the (sometimes asymmetric) peak shape into account. With the present method the melting point can be determined with an about ±1 mK reproducibility, whereas the latent heat of fusion with a better than 1.5% reproducibility. This is substantially more accurate than the prior art methods. The better reproducibility is partly due to the method using all the experimental data points instead of only using a few points in the region of interest in the prior art. It is worth noting that experimental accuracy of the DSC instrument itself will typically be in the 0.1-0.2 C range; this can be due to drift in the temperature of the environment, or whether the machine is used continuously or only occasionally. The reproducibility at a given instant is about 0.01 C. Clearly the low error of the present method will not improve such instrument related systematic errors or indeed calibration errors, but it does provide a highly repeatable and robust method of analysis, with the added advantage that there are no (or less) choices made by the user such as the (shape of) baseline or the integration interval. The present method takes into account characteristics of the sample, such as activated crystal growth and unknown Gaussian broadening due to multiple plausible factors, for obtaining thermic characteristics of the sample. This method appears to be remarkably versatile, although other choices might be more appropriate under certain circumstances. For instance, for characterizing ideal samples (with a very sharp melting transition) a normalized Gaussian might be used, as the measured peak should only contain a (narrow) thermal gradient and (limited) instrumental broadening. In practice many samples are far from ideal, and this is where the present method provides a substantial improvement. It should be noted that other normalized functions may be used to determine reproducible analysis data, although the present method is found to be rather versatile and convenient. An additional feature that could be implemented is to expand the present function to include a (gradual) step in the baseline Cp (specific heat) value, as it is anticipated and indeed visible that there is a small difference when examining the height of the baseline Cp_K and beyond Cp_I the melting transition. This would give rise to the ability to determine the ACp,m, the level of change of the Cp. This factor is hardly studied systematically as the normal DSC analysis methods would not provide a required level of precision in this respect. For the present method, in this respect, a minor change is considered sufficient. The base line becomes Cp_S + ACp,m x AH(T)/ AH, where AH(T) is the already absorbed latent heat up to temperature T and AH is the whole latent heat of fusion.

In a second aspect the present invention relates to a computer program comprising instructions for operating a calorimeter, the instructions causing the calorimeter to carry out the following steps: measuring a heat flow to or from the sample over a temperature range therewith obtaining heat flow versus temperature data, based on the heat flow versus temperature data obtaining a combination of physical or chemical characteristics of or imposed on the sample, wherein the characteristics is selected from a size distribution of crystal sizes, an amount of impurities in the sample, a measurement accuracy, and a combination thereof, based on the heat flow versus temperature data and the combination of physical or chemical characteristics of the sample obtaining thermic characteristics of the sample, wherein the thermic characteristics of the sample is selected from at least one of a melting point of the sample, a latent heat of fusion of a first order phase transition of the sample, a change in heat capacity, a glass transition temperature, a liquid crystal transition, a point of crystallization, a melting temperature range, a speed of melting, a degree of crystallinity, a temperature increase, a temperature decrease, a fusion temperature, a fusion enthalpy, a sublimation temperature or enthalpy, an enthalpy change, a specific heat, a variation of said thermic characteristics as a function of temperature, and a combination thereof.

The present invention is also subject of a scientific article entitled “Analysis for differential scanning calorimetry DSC: Determining the transition temperatures, and enthalpy and heat capacity changes in multicomponent systems by analytical model fitting”, J. Thermal Analysis and Calorimetry, under review, which article and its contents is incorporated by reference. Advantages of the present description are detailed throughout the description.

DETAILED DESCRIPTION OF THE INVENTION

In an exemplary embodiment of the present method the heat flow versus temperature data comprises at least 50% of the measuring temperature range measured, in particular at least 99% of the measuring temperature range measured, more in particular a temperature of OK to a>K, that is, the mathematical integral is taken from T=0K to <»K. Typically a substantially full temperature range (as measured) may be used. In a, what may be considered as a minimalistic, approach a small range could be used, including the transition peak, if present. Leading to better results a wider range or even the full range of the temperature data may be used. As such the step of obtaining the thermal characteristics of the sample becomes even more accurate.

In an exemplary embodiment of the present method the heat flow versus temperature data comprises the transition temperature and a temperature range of ±50K, that is a temperature range of 100K is taken, a lower point of the range being 50K below the transition temperature and a higher point of the range being 50K above the transition temperature.

In an exemplary embodiment of the present method the heat flow versus temperature data comprises >95% of the latent heat, in particular >98% of the latent heat, more in particular >99% of the latent heat. As such the step of obtaining the thermic characteristics of the sample becomes even more accurate.

In an exemplary embodiment of the present method the amount of impurities in the sample is from 0.01-30 wt.%, in particular 0.1-10 wt.%, more in particular 0.2-2 wt.%.

In an exemplary embodiment of the present method the sample comprises molecules with an average molecular weight distribution of 25-10,000,000 Da, in particular 1,000-1,000,000 Da, more in particular 10,000-500,000 Da (such as determined with ISO 16014 for plastics),

In an exemplary embodiment of the present method the sample comprises molecules with a molecular polydispersity is from 1.05-5, in particular 1.2-3, more in particular 1.5-2.0, (such as determined with ISO 13321 or ISO 22412, in particular using light scattering), in particular including molecular impurities.

In an exemplary embodiment of the present method the thermoanalytical method is selected from calorimetric methods, in particular DSC, more in particular heat-flux DSC, power differential DSC, ultra DSC, and Fastscan DSC, and differential thermal analysis, in particular temperature difference versus temperature or time analysis.

In an exemplary embodiment of the present method obtaining the combination of physical or chemical characteristics comprises, for the measuring temperature range, correcting for measurement inaccuracies, in particular n^th-order correcting, wherein n <12, in particular wherein n is from 1-5, in particular wherein n is 1, 2, or 3. High order correcting could in principle work better in terms of mathematically fitting, but the fitting would lack physical/chemical basis. The (lower order) correction is primarily directed for correcting measurement inaccuracies.

In an exemplary embodiment of the present method obtaining the combination of physical or chemical characteristics comprises, using the formula

Table 1/fig. 75 .show's the variables, Junctions, and the parameters of the DSCs(T).

The above model has been tested extensively on experimental data. The table 2 gives experimental data, analyser software, and fit errors (3 samples of the same Benzoic Acid).

Table 2/fig. 16 shows experimental versus fit errors (3 samples of the same Benzoic acid measured under the same condition)

Figure 8 shows DSC thermogram of Indium [as metal calibration sample] during heating from 25°C to 170°C at different scanning rate and DSCN(T) function fitted to the measured curves which were calibrated at the onset for the given rate, the unit of heat flow in each trace is [W/g], The fit (solid lines) overlap very well with the measured data. The dashed horizontal line shows the baseline, the left vertical deashed lines the T_cai, and the right vertical dashed lines the T_m°.

Table 3 shows fit parameters of the DSCN(T) for experimental curves of Indium (7mg) heated at different rates after calibration for the given weight (the error margins are from the nonlinear fitting), *nonlinear least squares error out of the bounds due to indeterminate high a value.

Indium-7mg R=2 [K.min ¹] R=10 [K.min ¹] R=20 [K.min ¹] R=50 [K.min ¹]

Figure 9 shows a DSC thermogram of different weights of Indium during heating from

25°C to 170°C at 2°C/min and DSCN(T) function fitted to the measured curves which were calibrated at the onset for the given weight, the heat flow has been normalized per weight of each sample, the unit of heat flow in each trace is [W/g],

Table 4. Fit parameters of the DSCN(T) for experimental curves of Indium with different weights heated at 2[K.min ] measured after calibration at the onset for the given weight (the error margins are from the nonlinear fitting).

Indium-R=2 [K .min^-1] w=l[mg] w=7[mg] w=54[mg]

AH [J.g ¹] 29.61±0.00 30.27±0.00 29.71±0.00

T_m° [°C] 156.86±0.00 157.24±0.00 157.69±0.00 a [K -¹] 10.25±0.03 4.43±0.01 1.87±0.00 p [K ’²] 98.60±0.27 34.49±0.11 8.34±0.03

AC_p,m [W.g fK -¹] 0.06±0.00 0.01±0.00 0.00±0.00 The present method is also suited for phase transitions in a liquid crystal compound. Three endothermic peaks were detected in the DSC experimental trace of 8OCB (4’ -octyloxy -4- cyanobiphenyl) heated at 2K.min'¹ from 0°C to 100°C (Figure 10).

Figure lOa-d show DSC thermograms of 8OCB and DSCN(T) function fitted to the measured curves for 6mg of 8OCB heated at 2[K.min'¹] after calibration for the given weight and rate, AC_p,t is for different liquid crystal transitions; 10a: K to Sm-A, 10b: Sm-A to N, and 10c: N to I.

Table 5 shows fit parameters of the DSCN(T) for experimental curves of 6mg of 80CB (4’ -octyloxy -4- cyanobiphenyl) heated at 2[K.min-l] after calibration at the onset for the given weight and rate (the error margins are from the nonlinear fitting).

8OCB- 6[mg]- 2[K.min'¹] 1st peak 2nd peak 3rd peak

(K to SmA) (SmA to N) (N to I)

AH [J.g ¹] 97.05±0.00 0.21±0.00 1.74±0.00

T_m° [°C] 55.62±0.00 66.96±0.00 80.16±0.0002 a [K’¹] 2.31±0.00 1.01±0.01 10.36±0.12

P EK’²] 5.72±0.02 36.21±2.16 91.10±1.15

AC_P [W.g-fK’¹] -0.06±0.00 0.01±0.00 -0.01i0.00

wherein T is the temperature (K), in particular an element of the measuring temperature range, wherein A (or Ai’s) is (are) a constants for amplitude(s) of the heat of fusion peak(s), wherein B is a constant for heat flow (or heat capacity) baseline offset, wherein C is a constant for linear slope (n = 1), which constant may be supplemented by further, higher order, terms, such as D for n=2, E for n=3 etc.), wherein T°_m is the actual melting temperature of the sample, wherein a [K‘ ’] is representative for a crystal size distribution, wherein P is representative for measurement inaccuracies, and impurities (sample inaccuracy). One may use the new normalised function and base line starting from B = offset, C= linear, etc.

Table 6. parameter unit Physical attribution a K'¹ the width of the peak in the rising edge of the signal

(due to crystal size distribution)

P K'² The width of the peak in the decaying edge of signal (Due to the

Gaussian broadening of the measurement)

W.gr'hK² the intensity factors for the peak

W.gr'¹ Baseline offset

W.gr'¹ K'¹ Baseline slope D baseline curvature

T_m° Equilibrium melting point

AH= Enthalpy of fusion

DSC

heat flow

In an exemplary embodiment of the present method the sample is in an temperature wise asymmetric behaving sample, in particular a sample comprising molecules with a weight larger than 100,000 Da, or comprising slow melting molecules, or having a melting point depression, or having a temperature spread in melting points, or having >0.5 wt.% impurities, or a combination thereof.

In an exemplary embodiment the present method further comprises calibrating the thermoanalytical device prior to use.

In an exemplary embodiment the present method further comprises measuring a reference sample with the thermoanalytical device and therewith correcting for measurement inaccuracies,

In an exemplary embodiment the present method further comprises prior to the method, removing a sample history by swinging back and forth at least once between an lower and higher measurement temperature.

The invention will hereafter be further elucidated through the following examples which are exemplary and explanatory of nature and are not intended to be considered limiting of the invention. To the person skilled in the art it may be clear that many variants, being obvious or not, may be conceivable falling within the scope of protection, defined by the present claims.

SUMMARY OF THE FIGURES

Figs, la-b, 2a-b, 3, 4a-b, 5-10a-d, 11-13, 14a-d, 15-16 show details of the present invention.

DETAILED DESCRIPTION OF FIGURES AND EXPERIMENTS

The figures are detailed throughout the description, and specifically in the experimental section below.

Figure 1 shows a DSC measurement of an In sample of 6,92 mg. The sample was heated from room temperature to about 180 °C. The heat flow (W/g) was measured. Based on the obtained DSC curve the physical or chemical characteristics were obtained. The following results were found:

DSCN(T) parameters Indium 6mg a 5.197±0.149 [K ]

P 3.168±0.030

A 16570229.96±13168428.44

B 0.338±0.001

C -6.675*10'⁵ ±2.9*10'⁵

R² 0.998

T' 0

1 m 157.5±1 °C

AH 3.22 [kJ/mole]

In conclusion, a perfect match between calibration data and phy si cal/ chemi cal characteristics was obtained. Figure 2 shows a DSC measurement of a benzoic acid sample of 5 mg. The sample was heated from room temperature to about 180 °C. The heat flow (W/g) was measured. Based on the obtained DSC curve the physical or chemical characteristics were obtained. The following results were found: DSCN(T) parameters Benzoic acid 5 mg a 1.701 ± 0.011 p 1.001 ± 0.004

A 2491.0936±188.602

B -0.281 ± 0.001

C 0.0034 ± 2.6*10'⁵

R² 0.996

T_m° 124.613 ±1 °C

AH 42.4352 [kJ/mole]

Figure 3. Single low molecular weight bisamide (BA) gelators with different number of methylene spacers between the amide groups. DSC curves plus fitting DSC and DSCN(T) function fitted to the measured curves of 6mg of odd and even bisamides heated at 2[K.min'¹] after calibration at the onset for the given weight and rate (vertical dashed line is T_m°, note it is not at all near the peak maximum).

It is noted that prior art fitting routines, such as a Gaussian, would not work here very well.

Figure 4. Thermal properties of BA compounds showing odd-even effect, a) melting temperatures were obtained from the peak maximum values of the DSC experiments and calculated from the analytical physical model, b) the enthalpy of fusion was calculated by Pyris software and using the DSCN(T) analytical model from experimental DSC traces

Figure 5. Binary bisamides. This example shows how the model can also be used to determine binary mixture melting points and heats of fusion of the separate components (these can be pure or more likely are the result of an unknown level of demixing A(+B) and B(+A)) . Note the unprecedented quality of the peak fitting “straight out of the box”. The dashed vertical lines are the equilibrium melting points of the demixed components.

Fig. 6 shows details of peak fitting of 6BA - reproducibility of the fitting process, effect of incomplete peak fitting.

Sensitivity of parameters:

Using different seed value for non-linear curve fitting, SSQ interval 120 - 140 °C. Inventors performed multiple fitting and find that the deviations of the parameters are approximately: A T_m° a p AH

0.03% 0.1 mK 0.02% 0.04% 2E-5%

In addition inventors limited the range of the curve fitting space to a narrower window around the melting peak 126 - 136 °C (this means that the contribution of the tails is not fully captured in the non-linear curve fitting), the internal reproducibility of the fitting is still robust: A T_m° a p AH

0.04% 0.1 mK 0.02% 0.01% 4E-3%

This means that the non-linear fitting process itself seems to converge well. Note AH is essence unchanged, the parameter errors compensate each other it seems.

Effect of incomplete peak fitting

Comparing the parameter values obtained for the 120 - 140 °C range and the (too narrow) 126 - 136 °C range we find deviation of the parameters around: A T_m° a p AH

2.86% 1 mK 0.82% 4.42% 1.33%

If inventors propose that the 120 - 140 °C data is correct then we see that even taking a too narrow range for the peak fitting still provides reasonably good values of the primary thermodynamic results. The shift of the T_m° of 1 mK is well within any reasonable experimental accuracy for a DSC machine, which would normally be estimated at about 0.2 °C or 200 mK (the absolute accuracy may further depend on calibration). The latent heat of fusion, which is calculated from the fitted values of A, a and P, changes by only about 1.33 %, which is an exceptionally useful result as it shows that this method of implicit integration of the peak is remarkably insensitive to coincidental (erroneous) choices of the interval of analysis. Phrased differently the parameters of the peak fitting allow the whole latent heat of fusion to be determined implicitly including the contributions that are outside the experimental window. The traditional way of peak integration relies on a (operator dependent) choice of the integration bounds, this is reasonably well established, but can easily cause substantial errors in the value of the latent heat for nominally identical measurements on identical samples. For instance a difference of 20% can easily occur if one chooses a narrow or a wide integration interval, respectively. The present method is rather insensitive to this choice.

In figure 7 crystallization curve fitting is discussed. It shows and analogous expression can be used to fit crystallisation upon cooling, here for the compound 10BA as an example, the quality of fit still appears to be very satisfactory. The determined Tc is somewhat lower than the equilibrium melting point of the same compound T_m° is 142.5 °C and Tc = 135.9 °C. Such a shift is not unusual. However, having a robust way to unambiguously fit the TmO and Tc might prove to be very useful, e.g. to reveal trends in Tc versus cooling rate. Note that as before the best estimate for Tc is by no means located at the minimum of the heat of crystallisation.

In figure 11 DSC experimental traces and DSCN(T) function are fitted to the traces of 6mg of molecularly mixed binary bisamides (5BA and 6BA in different ratios) heated by lOfK.min’¹] after calibration at the onset for the given sample weight and rate.* for the overlapping peaks ACp.m doesn’t converge due to purely mathematical artefact, if the peaks are sufficiently apart with sufficient baseline tail on each side, the cumulative AC_p,_m can be reliably determined via the function.

Table 7. Fit parameters and statistical coefficient of the DSCN(T) function fitted to the experimental DSC trace of 6mg of molecularly mixed binary bisamides (5BA6BA in different ratios) heated at 2[K.min^-1] after calibration at the onset for the given weight and rate, in the case of (5BA)3(6BA)1, only one fitting peak is required due to the peak overlap (the error margins are from the nonlinear fitting), AC_p,_m doesn’t converge (Not available=NA) due to purely mathematical artefact, if the peaks are sufficiently apart with sufficient baseline tail on each side, the cumulative AC_p,_m can be reliably determined via the function. 5BA6BA-

6mg-2[K.mm ¹ 1 (5BA)i(6BA)₇ (5BA)i(6BA)₃ (5BA)i(6BA)i (5BA)₃(6BA)i (5BA)₇(6BA)I

First peak 21.58±0.09 40.94±0.08 81.93±0.14 120.97±0.11 59.56±0.76 130.45±0.04 130.63±0.01 131.54±0.01 131.94±0.00 128.99±0.02 0.18±0.00 0.32±0.01 0.45±0.04 0.49±0.01 0.07±0.00 1.1 H0.19 1.63±0.11 2.50±0.10 1.23±0.19 1.62±0.21

] NA NA NA NA NA

Second peak

AH [Jg ¹] 127.38±0.10 107.76±0.23 23.72±1.07 see first 120.66±0.23 T_m° [°C] 145.46±0.00 142.97±0.01 137.81±0.08 see first 133.62±0.00 a [K ¹] 0.35±0.00 0.27±0.00 0.60±0.24 see first 0.30±0.00 P [K-²] 1.5H0.03 1.88±0.06 0.73±0.09 see first 2.65±0.04 ACp.m [Wg 'K ¹] NA NA NA see first

B [Wg ¹] 0.38±0.00 0.46±0.00 0.47±0.00 0.41±0.02 0.39±0.00 C [Wg ¹] 0.00±0.00 0.00±0.00 0.00±0.00 3.39±0.00 0.00±0.00 D [Wg ^loK’²] 0.00±0.00 0.00±0.00 0.00±0.00 0.00±0.00 0.00±0.00

R² 0.99 0.99 0.99 0.99 0.99

AHtotal [J.g ¹] 148.96±0.10 148.70±0.23 105.65 120.97±0.11 180.22±0.76

Figure 12 shows a phase diagram of binary 5BA6BA, T_m° calculated from the DSCN(T) versus the mole fraction of 6BA in 5BA, the error bars (from the nonlinear fitting) are not visible since they are very small (table 7) The higher ending line represent a high temperature phase. Figure 13 shows Total enthalpy and Enthalpy of individual phases in 5BA6BA at different ratios calculated from the DSCN(T) and plotted versus the mole fraction of 6BA in 5BA, the error bars (from the nonlinear fitting) are not visible since they are very small.

Further examples relate to semi-crystalline polymer (PHBVH) with glass transition, cold crystallization, and melting peaks. Figure 14a-d shows DSC experimental traces and DSCN(T) function fitted to the traces of 6mg of PHBVH heated after calibration at the onset for the given sample weight and rate. For the overlapping peaks, AC_p,_m doesn’t converge (Not available=NA) due to purely mathematical artefact, if the peaks are sufficiently apart with sufficient baseline tail on each side, the cumulative AC_p,_m can be reliably determined via the function.

Table 8. Fit parameter of the DSCN(T) for experimental curves of 6mg of PHBVH after calibration at the onset for the given sample weight and rate (the error margins are from the nonlinear fitting), *nonlinear least squares error out of the bounds due to indeterminate high a value, ACp,m doesn’t converge (Not available=NA) due to purely mathematical artefact, if the peaks are sufficiently apart with sufficient baseline tail on each side, the cumulative ACp,m can be reliably determined via the function. PHBV 1^st peak 2^nd peak 1^st melting peak 2^nd melting peak glass transition (T_g) Crystallization (T_c)

Claims

1. Thermoanalytical method, comprising providing a sample to be measured, the sample having a heat capacity, in particular a sample of 10 pg-100 mg, measuring a heat flow to or from the sample over a measuring temperature range with a thermoanalytical device therewith obtaining heat flow versus temperature data, in particular wherein the measuring temperature range comprises at least one phase transition temperature, based on the heat flow versus temperature data obtaining a combination of physical or chemical characteristics of or imposed on the sample, wherein the characteristics is selected from the combination of a size distribution of crystal sizes, an amount of impurities in the sample, and a measurement accuracy, based on the heat flow versus temperature data and the combination of physical or chemical characteristics of the sample obtaining thermic characteristics of the sample, wherein the thermic characteristics of the sample is selected from at least one of a melting point of the sample, a latent heat of fusion of a first order phase transition of the sample, a change in heat capacity, a glass transition temperature, a liquid crystal transition, a point of crystallization, a melting temperature range, a speed of melting, a degree of crystallinity, a temperature increase, a temperature decrease, a fusion temperature, a fusion enthalpy, a sublimation temperature or enthalpy, an enthalpy change, a specific heat, a variation of said thermic characteristics as a function of temperature, and a combination thereof.

2. Thermoanalytical method according to claim 1, wherein the heat flow versus temperature data comprises at least 50% of the measuring temperature range measured, in particular at least 99% of the measuring temperature range measured, more in particular a temperature of OK to <»K, or wherein the heat flow versus temperature data comprises the transition temperature and a temperature range of ±50K, or wherein the heat flow versus temperature data comprises >95% of the latent heat.

3. Thermoanalytical method according to any of claims 1-2, wherein the amount of impurities in the sample is from 0.01-30 wt.%, in particular 0.1-10 wt.%, more in particular 0.2-2 wt.%.

4. Thermoanalytical method according to claim 3, wherein the sample comprises molecules with an average molecular weight distribution of 25-10,000,000 Da, in particular 1,000-1,000,000 Da, more in particular 10,000-500,000 Da, and/or wherein a molecular poly dispersity is from 1.05-5, in particular 1.2-3, more in particular 1.5-2.0.

5. Thermoanalytical method according to any of claims 1-4, wherein the thermoanalytical method is selected from calorimetric methods, in particular DSC, more in particular heat-flux DSC, power differential DSC, ultra DSC, and Fastscan DSC, and differential thermal analysis.

6. Thermoanalytical method according to any of claims 1-5, wherein obtaining the combination of physical or chemical characteristics comprises, for the measuring temperature range, correcting for measurement inaccuracies, in particular n^th-order correcting, wherein n is from 1- 5, in particular wherein n is 1, 2, or 3.

7. Thermoanalytical method according to any of claims 1-6, wherein obtaining the combination of physical or chemical characteristics comprises, using the formula

or using the formula

wherein T is the temperature (K), in particular an element of the measuring temperature range, wherein A (or Ai’s) is (are) a constants for amplitude(s) of the heat of fusion peak(s), wherein B is a constant for heat flow (or heat capacity) baseline offset, wherein C is a constant for linear slope (n = 1), which constant may be supplemented by further, higher order, terms, such as D for n=2, E for n=3 etc.), wherein T°_m is the actual melting temperature of the sample, wherein a [K‘ ’] is representative for a crystal size distribution, wherein P is representative for measurement inaccuracies, and impurities .

8. Thermoanalytical method according to any of claims 1-7, wherein the sample is in an temperature wise asymmetric behaving sample, in particular a sample comprising molecules with a weight larger than 100,000 Da, or comprising slow melting molecules, or having a melting point depression, or having a temperature spread in melting points, or having >0.5 wt.% impurities, or a combination thereof.

9. Thermoanalytical method according to any of claims 1-8, further comprising calibrating the thermoanalytical device prior to use, and/or measuring a reference sample with the thermoanalytical device and therewith correcting for measurement inaccuracies, and/or prior to the method, removing a sample history by swinging back and forth at least once between an lower and higher measurement temperature.

10. Computer program comprising instructions for operating a calorimeter, the instructions causing the calorimeter to carry out the following steps: measuring a heat flow to or from the sample over a temperature range therewith obtaining heat flow versus temperature data, based on the heat flow versus temperature data obtaining a combination of physical or chemical characteristics of or imposed on the sample, wherein the characteristics is selected from the combination of a size distribution of crystal sizes, an amount of impurities in the sample, and a measurement accuracy, based on the heat flow versus temperature data and the combination of physical or chemical characteristics of the sample obtaining thermic characteristics of the sample, wherein the thermic characteristics of the sample is selected from at least one of a melting point of the sample, a latent heat of fusion of a first order phase transition of the sample, a change in heat capacity, a glass transition temperature, a liquid crystal transition, a point of crystallization, a melting temperature range, a speed of melting, a degree of crystallinity, a temperature increase, a temperature decrease, a fusion temperature, a fusion enthalpy, a sublimation temperature or enthalpy, an enthalpy change, a specific heat, a variation of said thermal characteristics as a function of temperature, and a combination thereof.