Differential scanning calorimetry and infrared imaging

Abstract

A method of characterising a sample, the method comprising the steps of: performing differential scanning calorimetry (DSC) on the sample; and, while the sample is undergoing DSC, taking infrared images of the sample.

Description

[0001] DIFFERENTIAL SCANNING CALORIMETRY AND INFRARED IMAGING

[0002] Field of the Invention

[0003] The present invention relates to a method of characterising a sample using differential scanning calorimetry (DSC) and infrared imaging. The present invention also relates to apparatus that can be used to characterise a sample using DSC and infrared imaging, and to related products. The present invention enables the entropy (e.g. Shannon entropy) of a sample during heating to be calculated, which can be used to reveal thermal events not visible by DSC alone and to clarify thermal events visible by DSC alone. The present invention can, for example, be used to calculate the change in Gibbs free energy of mixing for a drug when formulated in a polymer-drug solid solution.

[0004] Background of the Invention

[0005] Differential scanning calorimetry (DSC) is a thermal analysis technique in which the amount of heat required to increase the temperature of a sample is measured. Calorimetry is the measurement of heat flows to / from a body. The sample is typically compared to a reference that typically has a well-defined heat capacity over the range of temperatures to be scanned.

[0006] DSC can be used to measure a number of characteristics of a sample, such as fusion and crystallization events, as well as the glass transition temperature. DSC therefore finds application in a variety of industries.

[0007] In the pharmaceutical industry, for example, it is necessary to have well-characterised drug compounds in order to determine pharmaceutical properties and processing parameters.

[0008] Materials can exist as amorphous and / or crystalline forms. The form a material takes can significantly affect its pharmaceutical properties and its use. For instance, an amorphous form of a drug will typically have enhanced solubility compared to a crystalline form of the drug.

[0009] Amorphous forms are thermodynamically less stable than crystalline forms. In certain formulations the amorphous form of a drug will recrystallise into its crystalline, less soluble, form over time. This can decrease the solubility of the drug over time. The recrystallisation of amorphous forms of drugs into the crystalline form can be limited by mixing the drug with one or more suitable polymers to form a “solid solution”, i.e. a homogenous mixture of the components in a single solid phase. It is necessary to select a polymer that is suitable to form the solid solution with the drug in order to effectively limit recrystallisation of the drug. The identification of an optimal polymer to stabilise the amorphous phase of the drug typically involves trial and error through the preparation of different solid solutions using a range of polymers, and exposing these to high temperatures and durations of storage. An amorphous drug is more likely to remain amorphous if it is mixed with one or more polymers that lower the melting point of the drug. The melting point of a sample, and the effect of a polymer on the melting point of a drug, can be measured by differential scanning calorimetry (DSC). Furthermore, Flory-Huggins theory can be used to calculate the change in Gibbs free energy of mixing for a polymer and a drug. This can be used to determine the stability, solid state miscibility and aqueous solubility of polymer-drug solid solutions (Al-Obaidi et al., International Journal of Pharmaceutics, 2011, 419 (1–2), 20-27; Al-Obaidi et al., International Journal of Pharmaceutics, 2013, 443, 95–102; Bhanderi et al., Journal of Drug Delivery Science and Technology, 2021, 64, 102606). The measurement of thermal events, such as melting and polymorphism events, often provides broad peaks due to the size of particles of the sample and thermal conductivity within the sample. Summary of the Invention According to a first aspect the present invention provides a method of characterising a sample. The method comprising performing the steps of: performing differential scanning calorimetry (DSC) on the sample; and, while the sample is undergoing DSC, taking infrared images (e.g. thermal images) of the sample. By taking infrared images of a sample while the sample is undergoing DSC, the present invention allows the user to obtain unprecedented precise identification of thermal events changes such as melting and polymorphism. Specifically, the present invention allows correlations to be determined between calculated (Shannon) entropy and / or temperature gradient values and data measured through DSC. These correlations allow events not detected or clearly resolved by DSC to be detected and resolved. The characteristics determined of the sample may depend on the type of sample being analysed. For example, samples containing one or more polymers may be characterised in terms of their glass transition temperature(s); samples containing two or more components (e.g. a polymer and a drug) may be characterised in terms of their free energy of mixing; crystalline samples may be characterised in terms of the number of polymorphs (and optionally the melting point(s) and / or glass transition temperature(s) of each polymorph) in the sample; samples with a freezing / melting point may be characterised in terms of their freezing / melting point; liquid samples may be characterised in terms of their polymorphic transitions upon freezing; and samples containing amorphous material may be characterised to determine whether any crystalline material is present. The method has been found to enable surprising improvements in the precision of the characterisation of physical properties of samples such as the change in Gibbs free energy of mixing for a polymer and a drug in a polymer-drug solid solution. It has been recognised that one key limitation of DSC is that it only provides an average bulk value of sample temperature; it cannot measure temperature distribution across a sample. Therefore, it cannot measure any variations in temperature across the surface of a sample. DSC is a powerful tool for characterizing the thermal properties of materials. However, it has been recognised that certain inherent limitations can challenge its comprehensive utilization. For instance, DSC might occasionally struggle with sensitivity issues, potentially overlooking minor phase transitions that release or absorb minimal amounts of heat. The time delay between the temperature of a portion of a sample changing and the thermocouple detecting the change in temperature can cause thermogram peaks to be broad. There can also be complications arising from baseline drifts over time, and in situations where multiple transitions occur in close temperature proximity, the deconvolution of overlapping peaks can be difficult, or even impossible. Another point of contention is the strict necessity for precise sample preparation, as the physical state, moisture content, and history of the sample can influence results. Quantitative data, though obtainable, demand rigorous calibration for accuracy. The capturing of infrared images provides “heatmaps” of the sample during DSC analysis. The introduction of heatmaps into this milieu offers a promising way to circumnavigate some of these hurdles. By providing spatial information about temperature distribution, heat maps illuminate the heterogeneities within a sample, bringing to light localized phase transitions or thermal properties that might be overlooked in a DSC curve. The ability to visualize temperature shifts in real-time, combined with the calculation of entropy (e.g. Shannon entropy) values from these maps, introduces an added dimension of analysis. The inventor has surprisingly determined that calculation of entropy using data from infrared images can reveal thermal events that were not visible with data from DSC alone, and can enhance thermal events that were unclear from DSC alone. While a variety of different entropy models have been used successfully, the best results have been attained using Shannon entropy. The inventor has also found that additional detail can also be determined from the thermal gradient of the sample, which is also able to be calculated using data from infrared images, but not from DSC alone. This allows for precise detection of different polymorphs, detection of crystalline material within polymer material, measurement of glass transition temperature, and the analysis of melting and crystallisation processes in samples. This new layer of data, when correlated with parameters like the Flory-Huggins interaction, has also been used to uncover a deeper thermodynamic understanding of intricate systems, such as polymer-drug blends. Thus, the present inventors have found that by integrating DSC with one or more heatmaps, the user is able to achieve a significantly more refined and comprehensive insight into the thermal behaviour of samples, ameliorating some or all of the existing limitations of DSC alone. The inventors have determined that, by combining and / or correlating infrared imaging with DSC for the same sample, it is possible to improve the precision of thermal analysis of the sample. Infrared (thermal) imaging is based on measuring thermal radiation using the principle of emissivity. Hence, when performing the invention, there is no interference with the molecular or material nature of the compound as opposed to other methods used in spectroscopy. Further, infrared imaging allows the temperature of individual points on the surface of the sample to be determined. The present inventors have determined that the combination of the more precise variation and distribution of temperature across the surface of the sample with data obtained by DSC for the sample allows for significant increases in the precision of analysis of various parameters, such as the change in Gibbs free energy of mixing for a drug when formulated in a polymer-drug solid solution, using Flory-Huggins theory. Importantly, performing both measurements simultaneously on the same sample is required in order to provide precise results for the change in Gibbs free energy of mixing for a polymer and a drug in a polymer-drug solid solution. The present invention has also been able to enhance the precision of determination and measurement of thermal events, such as glass transition temperature (Tg) and melting events; allowing the more precise identification of crystalline materials in polymer-drug blends, and allowing the more precise identification of separate polymorphs in crystalline compounds or compositions. The present invention adds another dimension to conventional measurement of these parameters, enabling more precise measurement of the parameters than was previously possible. The present invention improves the resolution of, and avoid noise generated during, sample characterisation. It also overcomes any interference caused by different molecular compositions and materials in spectroscopy methods, including DSC. The data collected by the infrared imaging device provides information on the temperature (and / or temperature variation) of the surface of the sample that cannot be obtained from visible light imaging and / or DSC. US7033840B1 describes a workstation that incidentally includes DSC apparatus and, external to the DSC apparatus, thermal imaging equipment. However, there is no mention of performing infrared imaging during DSC. The present inventors have found that the more precise characterisation of the sample by simultaneously performing DSC and infrared imaging allows for enhanced analysis of the stability of polymer-drug mixtures. Certainly there is no discussion in US7033840B1 of these particular and surprising benefits that the present inventors have found. It is not possible to simultaneously perform DSC on a sample and take infrared images of the sample using entirely conventional apparatus for DSC. Conventional DSC apparatus is not transparent to infrared radiation that would be necessary to take infrared images of the sample while it is being subjected to DSC. The amalgamation of DSC and infrared imaging (i.e. heatmaps) provides revolutionary enhancements to the analysis of thermal events, for example the calculation of the Flory-Huggins energy of mixing, a crucial thermodynamic parameter. This provides significant benefits to a variety of industries. For the pharmaceutical industry, this offers a game-changer. The enhanced ability to characterize and predict the interactions between drugs and polymers leads to better drug delivery systems, ensuring optimal bioavailability and controlled release profiles, for example by detecting different polymorphs and / or determining the presence of crystalline material within a polymer blend. In polymer science, accurate determination of thermal events, such as glass transition temperature and the calculation of the Flory-Huggins energy of mixing, allow for the development of novel polymer blends with tailored properties. This knowledge is invaluable when designing polymers for specific functionalities, be it biodegradable plastics or high- performance composites. Furthermore, the food industry can harness this predictive power to understand how different ingredients will interact at the molecular level. Such insights can lead to innovations in food processing, preservation, and even flavour enhancement. In the burgeoning field of renewable energy, especially in organic photovoltaics, a precise estimation of the energy of mixing can optimize the efficiency of devices by ensuring the right molecular pairings. The aerospace and automotive sectors, too, can capitalize on these insights to develop materials that can withstand a myriad of environmental conditions, with the understanding of their thermal behaviours at the core of such innovations. According to a second aspect the claimed invention provides a method of processing data. The method comprises determining the entropy and / or thermal gradient (e.g. Shannon entropy, which encapsulates the spread or variation of the temperature across a sample at different times or stages) for one or more infrared images of a sample or a section of one or more infrared images of the sample. The method may comprise taking one or more infrared images of the sample. When the entropy and / or the thermal gradient are calculated from the same data as DSC, these data complement each other and allow more subtle changes to be determined. The method of the first aspect may comprise the method of the second aspect, thereby processing the data obtained from the DSC and / or the infrared images (or a section of the images). The method of the second aspect may comprise calculating, for a sample, a Flory-Huggins interaction parameter and / or a free energy of mixing, wherein the calculation uses data obtained from DSC (i.e. a thermogram) and data obtained from one or more (e.g. two or more, or five or more, or ten or more) infrared images (of the sample, or a section of one or more infrared images of the sample). The method may comprise calculating the thermal gradient from data obtained from one or more (e.g. two or more, or five or more, or ten or more) infrared images (of the sample, or a section of one or more infrared images of the sample). The method may comprise: determining the entropy (e.g. Shannon entropy, which encapsulates the spread or variation of the temperature across the sample at different times or stages) for one or more infrared images; determining the traditional Flory-Huggins interaction parameter from the data obtained by DSC; and combining the entropy with the traditional Flory-Huggins interaction parameter to determine a modified Flory-Huggins interaction parameter. The method may comprise calculating the free energy of mixing from the modified Flory-Huggins interaction parameter. Preferably the data from DSC is obtained simultaneously with the one or more infrared images. The temperature determined by the infrared camera is preferably calibrated with the temperature measured by the DSC apparatus. Preferably the free energy of mixing is the Flory-Huggins free energy of mixing. Preferably the heatmaps are taken / used that show the average temperature around (e.g. within ±0.5°C of) the melting point of the sample (e.g. a drug in a polymer / drug blend). Where the sample (e.g. drug) shows a broad melting point peak, the onset of the melting point peak would be used. The method is preferably computer implemented. The calculations may be performed by a computer (e.g. a processor). The entropy (e.g. Shannon entropy) may be calculated from the data from the one or more infrared images (of the sample, or a section of the one or more infrared images of the sample). The entropy may be used to adjust or modify the traditional Flory-Huggins interaction parameter. A proportionality constant may be used to adjust the magnitude of the entropy (e.g. Shannon entropy) being used to adjust the traditional Flory-Huggins interaction parameter. The (modified) Flory-Huggins interaction parameter and / or the (modified) free energy of mixing may be calculated by combining data from DSC (i.e. one or more thermogram) with the entropy. The modified Flory-Huggins interaction parameter may be used to calculate the Flory-Huggins free energy of mixing. Entropy (including Shannon entropy) has been used to detect the changes in surface temperature, determine drug / polymer compatibility, determine small molecule compatibility, and to determine whether components are mixed properly into a formulation. According to a third aspect the claimed invention provides an apparatus for performing differential scanning calorimetry (DSC) on a sample. The apparatus comprises a housing configured to contain the sample during DSC. The apparatus comprises an infrared imaging device (e.g. thermal camera) adapted to receive infrared radiation emitted by the sample during DSC measurement; and / or the housing comprises a window pane made of a material that is transparent to infrared radiation. According to a fourth aspect the claimed invention provides a cover for differential scanning calorimetry (DSC) of a sample, wherein the cover is made of a material that is transparent to infrared radiation. According to a fifth aspect the claimed invention provides a kit comprising a cover according to the fourth aspect and a pan, wherein the kit is for containing a sample during differential scanning calorimetry (DSC). Preferably the material that is transparent to infrared radiation is BaF2, CdTe, GaAs, Ge, thallium bromoiodide (TlBr-TlI), ZnSe, ZnS, infrared plastic, and / or a glass of germanium, arsenic and selenium (e.g. Ge:As:Se 33:12:55 or 28:12:60 by weight). For example, the infrared transparent material may be BaF2, KBr, CsI, KCl, CdTe, GaAs, Ge and / or a glass of germanium, arsenic and selenium (e.g. Ge:As:Se 33:12:55 or 28:12:60 by weight. More preferably the infrared transparent material for the apparatus is zinc selenide. Zinc selenide is not water soluble, and its infrared transparency is stable to variations in temperature. Therefore, zinc selenide allows for accurate infrared imaging even when the sample is heated to high temperatures. US2021 / 285904 A1 describes a thermal analyser that has a transparent window to allow a sample to be irradiated with visible light, and an electromagnetic image is obtained for the sample. However, this document does not describe the use of an infrared-transmissible material such as zinc selenide. This document does not enable users to retrofit existing DSC machines, as is possible with the present invention. There is no mention of the analysis of drug-polymer mixtures. There is no discussion of the analysis of the sample, for example timepoints or sequential measurements, to measure thermal changes. There is no mention of how DSC data is analysed alongside infrared data to enhance the analysis of samples. WO2022 / 250533 A1 describes a method of DSC and an apparatus for power compensation DSC, including determining the temperature at different positions on the sample. However, there is no discussion of the data analysis methodology. There is no discussion of drug-polymer mixtures. US2016 / 371526 A1 describes measuring melting temperatures and recording temperature change of 'thermal barcodes' during heating and cooling phases. This document focuses on fatty acids, which can be used to identify genuine (rather than counterfeit) articles. JP H10332613 A describes using DSC coupled with IR to analyse structural changes to the temperature of the material. However, the details of the analyser are quite different from that used for the present invention, and details of the analysis are not clear. JP2002156345 A describes a method for measuring DSC and DTA, thereby performing heat flow measurements and examining the effect of an applied temperature on the material's properties. However, to enhance ability to measure sample properties obtained by DSC, and does not mention enhancing or expanding data and insights that can be gained from that analysis. No materials are described for the glass infrared window. None of the prior art document describe the specific apparatus defined by the present application, or the specific analysis steps based on entropy as defined by the present application. The disclosure of the present application includes the subject-matter of the following clauses: 1. A method of characterising a sample, the method comprising the steps of: performing differential scanning calorimetry (DSC) on the sample; and, while the sample is undergoing DSC, taking infrared images of the sample. 2. The method of clause 1, wherein the infrared images are thermal images. 3. The method of any preceding clause, wherein the amount of sample is from 1 to 50mg. 4. The method of any preceding clause, wherein the method further comprises a step of preparing the sample. 5. The method of clause 4, wherein preparing the sample comprises the steps of: providing the sample to a pan for DSC, for example weighing the sample into the pan; and providing an infrared transparent cover onto the pan. 6. The method of any preceding clause, wherein the method is performed using an apparatus for performing differential scanning calorimetry (DSC) on the sample, and wherein: the apparatus comprises a housing configured to contain the sample during DSC; and the apparatus comprises an infrared imaging device adapted to receive infrared radiation emitted by the sample during DSC measurement and / or the housing comprises a window pane made of a material that is transparent to infrared radiation. 7. The method of any preceding clause, wherein the temperature within the housing is increased at a rate of from 2°C to 20°C per minute. 8. The method of any preceding clause, wherein the infrared images are taken at least within a temperature range of from 95°C to 100°C. 9. The method of any preceding clause, wherein the infrared images are taken at a rate of 1 or more images per minute. 10. The method of any preceding clause, wherein the method further comprises determining, from the infrared images, the temperature of a plurality of locations on the surface of the sample. 11. The method of any preceding clause, wherein the method further comprises determining, from the infrared images, the temperature of a location on the surface of the surface at a plurality of time points. 12. The method of any preceding clause, wherein the method further comprises determining the free energy change for mixing for the sample, for example using Flory-Huggins theory. 13. The method of any preceding clause, wherein the sample comprises a biologically active agent and one or more polymers. 14. A method of processing data, the method comprising calculating, for a sample, a Flory- Huggins interaction parameter and / or a free energy of mixing, wherein the calculation uses data obtained by DSC and data obtained by one or more infrared images. 15. The method of clause 14, wherein the method comprises: determining the Shannon entropy for one or more heatflow from the data obtained by one or more infrared images; determining the traditional Flory-Huggins interaction parameter from the data obtained by DSC; and combining the Shannon entropy with the traditional Flory-Huggins interaction parameter to determine a modified Flory-Huggins interaction parameter. 16. An apparatus for performing differential scanning calorimetry (DSC) on a sample, wherein the apparatus comprises a housing configured to contain the sample during DSC, and wherein the apparatus comprises an infrared imaging device adapted to receive infrared radiation emitted by the sample during DSC measurement and / or the housing comprises a window pane made of a material that is transparent to infrared radiation. 17. The apparatus of clause 16, wherein the infrared imaging device has a sensor that comprises 100 pixels or more. 18. The apparatus of clause 16 or clause 17, wherein the infrared imaging device is a thermal camera. 19. A cover for differential scanning calorimetry (DSC) of a sample, wherein the cover is made of a material that is transparent to infrared radiation. 20. The cover of clause 19, wherein the cover: is substantially cylindrical, has a diameter of from 2mm to 30mm, and has a thickness of from 0.05mm to 5mm. 21. A kit for containing a sample during differential scanning calorimetry (DSC), the kit comprising: a cover according to clause 19 or clause 20, and a pan. 22. The kit of clause 21, wherein the pan is made of aluminium, alumina, copper, gold, graphite, quartz, stainless steel, titanium, and / or platinum. 23. The cover or the kit of any one of clauses 19 to 22, wherein the cover consists of a material that is transparent to infrared radiation. 24. The apparatus, the cover or the kit of any one of clauses 16 to 23, wherein the material that is transparent to infrared radiation is BaF2, CdTe, GaAs, Ge, thallium bromoiodide, ZnSe, ZnS, infrared plastic, and / or a glass of germanium, arsenic and selenium. 25. The apparatus, the cover or the kit of clause 24, wherein the material is zinc selenide. Brief Description of the Drawings Embodiments of the present invention will now be described by way of example with reference to the accompanying drawings, in which: Figure 1 is a perspective view of the oven of a DSC apparatus; Figure 2 is a perspective view of the underside of an adaptor for holding an infrared transparent window pane above the oven shown in Figure 1; Figure 3 is a perspective view of the adaptor of Figure 2 fitted onto the DSC apparatus of Figure 1; Figure 4 is a plan view of the adaptor of Figure 2 fitted onto the DSC apparatus of Figure 1, showing the infrared transparent window pane; Figure 5 is a view of a DSC apparatus adapted to perform the present invention; Figure 6 is a cross-sectional views of the apparatus of the invention and the kit of the invention when each are in use; Figure 7A shows a zinc selenide lid; Figure 7B shows an aluminium sample pan containing a sample and covered with a zinc selenide lid; Figure 8 is a thermal image of a sample during DSC, presenting the temperature in three different positions on the surface of the sample; Figure 9 is a thermal image of a sample during DSC showing the maximum and minimum temperature on the surface of the sample; Figure 10 shows the temperatures distribution of the image shown in Figure 6; Figure 11 shows infrared images of a sample of a physical mixture of progesterone and hydroxypropylmethylcellulose acetate succinate during DSC analysis; Figure 12A and 12B are two graphs indicating the Shannon entropy and average temperature for each frame during the analysis performed in Figure 10; Figure 13 shows a graph displaying the heat flow (mW) obtained by the DSC heat capacity measurement alone, and a moving average Shannon entropy, calculated according to the invention, for lidocaine; Figure 14 (A and B) shows graphs of a moving average Shannon entropy and thermal gradient, for lidocaine; Figure 15 (A and B) shows graphs of a moving average Shannon entropy and thermal gradient, for griseofulvin; Figure 16 (A and B) shows graphs of heat flow, moving average Shannon entropy and thermal gradient, for hydroxypropyl methylcellulose and polyvinylpyrrolidone; Figure 17 (A to C) shows graphs of heat flow, moving average Shannon entropy and thermal gradient, for polyoxyethylene (10) oleyl ether (Brij® O10); Figure 18 (A and B) shows graphs of heat flow, moving average Shannon entropy and thermal gradient, for a physical mixture of 67wt% griseofulvin / HPMCAS; and Figure 19 (A and B) shows graphs of heat flow, moving average Shannon entropy and thermal gradient, for 5wt% griseofulvin / HPMCAS. Detailed Description of the Invention It will be understood that one thermal image may contain relevant sections (usually showing the sample) and irrelevant sections (usually covering items other than the sample) – the section of the image(s) used for the analysis should show the sample. Preferably the section of the image(s) used for the analysis only show the sample. It will be understood that where a series of images are analysed, each image or section thereof being analysed should show the same portion of the sample. Method of characterising a sample According to the first aspect, the present invention provides a method of characterising a sample. The method comprising performing the steps of: performing differential scanning calorimetry (DSC) on the sample; and, while the sample is undergoing DSC, taking infrared images (e.g. thermal images) of the sample. The sample is preferably a solid (e.g. powder) or a liquid. It will be understood that the temperature of the sample changes during DSC (e.g. by heating and / or cooling the sample). The images of the sample should be taken while the temperature of the sample is changing. The method may be a method of determining the bulk temperature of the sample and temperature of a plurality of points on the surface of the sample, for example as the heat applied to the sample is varied. The method may be a method of analysing the change in bulk temperature of the sample and temperature of a plurality of points on the surface of the sample, for example as the heat applied to the sample is varied. The sample may comprise a biologically active agent (e.g. drug) and one or more polymers, for example a solid solution of a biologically active agent (e.g. drug) and one or more polymers. The sample may comprise a food product, polymer (e.g. a blend of polymers), an organic photovoltaic compound and / or a lubricant. The method may comprise a step of preparing the sample. Preparing the sample may comprise the steps of providing the sample to a pan for DSC, for example weighing the sample into the pan; and providing an infrared transparent cover onto the pan. A cover is particularly beneficial for solid samples as it allows the compaction of the sample into a thin layer. Liquid samples may be analysed without a cover. The amount of sample (e.g. provided to and / or weighed into the pan) may be 0.1mg or more, or 1mg or more, such as 5mg or more, and / or 500mg or less, or 200mg or less, or 50mg or less, such as 10mg or less, for example from 0.1 to 500mg, or from 5 to 10mg. The amount of sample may be 10mg or more. The amount of sample may be 20mg or less, such as from 10 to 20 mg. Preferably the cover is a cover according to the fourth aspect. Preferably the cover and the pan are provided as a kit according to the fifth aspect. Preparing the sample may comprise sealing (e.g. crimping) the cover onto the pan, such that the sample is sealed within the pan. The pan and cover may form an air-tight seal. The sample in the pan (with the cover) is positioned into an apparatus for performing DSC. Preferably the apparatus is according to the third aspect. In particular, the sample in the pan is provided to the housing of the apparatus (i.e. the temperature-controlled DSC cell, or oven). The housing should include an infrared transparent window pane to allow infrared radiation from the sample to be emitted out of the housing. Preferably the method comprises using an apparatus according to the third aspect to perform DSC on the sample. Preferably the apparatus comprises an infrared imaging device and therefore the method comprises using an apparatus according to the third aspect to perform DSC on the sample and, while the sample is undergoing DSC, taking infrared images of the sample. The housing of the apparatus may be closed; this provides the benefit of minimising air currents that could affect the characterisation of the sample. DSC can be performed using heat flux or power differential methods. Under the heat flux method, sample holders for the test sample and the reference are located in the same temperature- controlled housing (oven). Under the power differential method, sample holders for the test sample and the reference are located in separate (thermally insulated) housings (ovens). Each of these methods are compatible with the claimed invention. Performing DSC on the sample can comprise increasing or decreasing the temperature within the housing. The temperature within the housing may be increased or decreased by a rate of 0.01°C per minute or more, such as 0.1°C per minute or more. The temperature within the housing may be increased or decreased by a rate of 2°C per minute or more, such as 4°C per minute or more, or 5°C per minute or more. The rate may be 20°C per minute or less, or 15°C per minute or less, such as 12°C per minute or less, or 10°C per minute or less. The rate may be 1°C per minute or less, such as 0.1°C per minute or less. The rate may be from 0.01°C to 20°C per minute. The rate may be from 2°C to 20°C per minute, such as from 5 to 10°C per minute. Preferably the temperature is increased or decreased at a substantially constant rate. For example, DSC may be performed by weighing 5–10 mg of a test sample into an aluminium pan, optionally crimping the pan closed with a lid, and heating the sample at a rate of 5°C / min to measure the onset of the melting temperature and the enthalpy of fusion. Performing DSC on the sample may comprise measuring the difference in temperature between the test sample and a reference. The reference may be a pan and cover without any sample. Performing DSC on the sample may comprise measuring the heat flux between the test sample and the reference as the temperature within the housing is increased. Performing DSC on the sample may comprise measuring the power required to maintain the temperature of the test sample the same as the temperature of the reference. The method may comprise positioning an infrared imaging device to capture images of the test sample such that the device can capture images of the test sample while the test sample is subjected to DSC. The infrared images are to be taken while the sample is (enclosed) within the housing. The emissivity of organic compounds is often about 0.7-0.9; the emissivity on the infrared camera should be adjusted to account for this, so that the starting temperature matches the temperature recorded by DSC. The infrared images may be taken for the full duration of the DSC step, or for part of the duration of the DSC step. Infrared images may be taken at from when the sample is at a temperature 20°C or lower, such as 30°C or lower, such as 50°C or lower, or 80°C or lower, such as 90°C or lower or 95°C or lower. Infrared images may be taken at least until when the sample is at a temperature of 100°C or more, such as 110°C or more, such as 120°C or more, or 140°C or more, such as 160°C or more, or 200°C or more. The infrared images may be taken at least within a temperature range of from 95°C to 100°C, such as from 80°C to 120°C, or from 50°C to 160°C. The infrared images may be recorded at a rate of one or more image per minute, such as two or more, or 10 or more, such as 60 or more images per minute. The rate may be 5 per second or more, such as 20 per second or more. The images may be recorded at a rate of 100 images per second or less, such as 60 images per second or less, for example at a rate of from one image per minute to 100 images per second. The rate may be from 20 to 60 images per second. The method may comprise taking two or more infrared images while the sample is undergoing DSC, such as five or more, or 10 or more, or 20 or more, such as 50 or more, or 100 or more infrared images while the sample is undergoing DSC. Analysis of data The method of the first aspect may comprise calculating the entropy (e.g Shannon entropy) and / or the temperature gradient of the sample. The method of the first aspect may comprise calculating, for the sample, a (modified) Flory- Huggins interaction parameter and / or a (modified) free energy of mixing, wherein the calculation uses data obtained by the DSC and data obtained by the one or more (e.g. two or more, or five or more, or ten or more) infrared images. The second aspect provides a method of processing data. The method comprises calculating the entropy (e.g. Shannon entropy) of a sample. The method may comprise calculating, for the sample, a (modified) Flory-Huggins interaction parameter and / or a (modified) free energy of mixing, wherein the calculation uses data obtained by DSC and data obtained by one or more (e.g. two or more, or five or more, or ten or more) infrared images. The method of the first aspect may therefore comprise steps associated with the second aspect. Preferably the data from DSC is obtained simultaneously with the one or more infrared images. Preferably the free energy of mixing is the Flory-Huggins free energy of mixing. The method of the second aspect is preferably computer implemented. The calculations may be performed by a computer (e.g. a processor). Calculations performed during the first aspect are preferably computer implemented. The method of the first aspect and / or the method of the second aspect may comprise determining, from the infrared images, the temperature of a plurality of locations on the surface of the sample. The method of the first aspect and / or second aspect may comprise determining, from the infrared images, the temperature of a location on the surface of the surface at a plurality of time points. The method of the first aspect and / or second aspect may comprise determining, from the infrared images, the temperature of a plurality of locations on the surface of the sample at a plurality of time points. The locations on the surface may correspond to pixels of the infrared images. Each thermal image may be considered to comprise a plurality of temperature points or values, usually corresponding to the pixels of a thermal image. The method may comprise rounding the temperature values. This may be used to determine how finely the temperatures are grouped. Typically a rounding value of 0.01°C is used. Rounding values from 0.001°C to 2.0°C may be suitable, preferably from 0.001°C to 1.0°C. The rounding has an impact on the Shannon entropy: if the rounding step is relatively small, or light, the data retains a high level of detail. This means that more unique temperature values are present in the dataset. This can lead to higher Shannon entropy because the dataset contains more distinct values, increasing the uncertainty or randomness. Conversely, if the rounding is large, or heavy, many temperature values are grouped into fewer bins, reducing the number of unique values. This generally decreases Shannon entropy as the dataset becomes more predictable with fewer distinct values. The rounding has an impact on thermal gradient: a smaller rounding step preserves more of the subtle variations in temperature, which can result in a more accurate calculation of the thermal gradient. The gradient magnitude may be more sensitive to small changes in temperature, providing a detailed understanding of temperature variation across the sample. A larger rounding step smooths out the temperature data, potentially reducing noise but also removing finer details. This can lead to a lower thermal gradient magnitude as the temperature variations become less pronounced. To optimise results with a good balance of detail to noise in the data, it may be preferable to start with a smaller rounding step to capture as much detail as possible, and gradually increase the rounding step while monitoring the changes in Shannon entropy and thermal gradient. Too small a rounding step might introduce noise and make the entropy artificially high, while too large a step might oversimplify the data, hiding meaningful variations. The extent of rounding may be determined by a system (e.g. a computer) or be pre-set by a user. The method may comprise calculating the Shannon entropy and / or thermal gradient for a plurality of windows of two or more adjacent temperature points (i.e. values) from a thermal image (or a section thereof). Each window may comprise four or more, such as six or more, or 10 or more adjacent temperature points. Each window may represent adjacent temperature points in a square, rectangular, triangular or hexagonal section of the thermal image (or a section thereof). Each window may comprise from 2 to 100 temperature points, such as from 2 to 40 temperature points, or from 2 to 20 temperature points, for example from 2 to 10 temperature points, or from 2 to 6 temperature points, such as four temperature points. The size of the windows may be determined by a system (e.g. a computer) or be pre-set by a user. Moving averages are preferably applied to smooth out short-term fluctuations and highlight long- term trends in Shannon entropy and thermal gradient data. The window size in moving averages determines the number of data points used to calculate the average at each step in the time series or spatial data. A small window size means that the moving average is calculated over a few data points, preserving more of the original fluctuations in the data. This can be useful when short- term variations are significant and need to be analysed. A larger window size averages over more data points, smoothing out more of the short-term fluctuations and emphasizing long-term trends. This can be beneficial when the focus is on identifying broader patterns rather than detailed fluctuations. To optimise results it may be preferable to start with a smaller window size, to capture detailed fluctuations in the data. Then, if the results appear too noisy or lack clear trends, gradually increase the window size until the desired level of smoothing is achieved. The method may comprise dividing the thermal image(s) (or the section thereof) into a plurality of adjacent windows. The method may comprise, for each window, determining the entropy of the temperature values in the window. The method may comprise taking the mean average of the entropy of the windows in the thermal image (or the section thereof). The method may comprise dividing the thermal image(s) (or the section thereof) into a plurality of adjacent windows. The method may comprise, for each window, taking the mean average of the temperature values in the window. The method may comprise determining the entropy of the mean average temperature values of the windows of the thermal image (or the section thereof). The rounding of data may be performed before or after the averaging across windows. Segmenting the data into smaller samples allows for a more granular analysis of specific periods or regions. Each sample can be analysed independently, providing insights into localised phenomena or time-specific trends. Larger segments may combine multiple conditions or periods, potentially diluting specific effects but providing a broader overview of the dataset. Parallel processing involves splitting the computational workload across multiple processors, allowing for faster analysis of large datasets. Parallel processing is used to handle multiple samples simultaneously. By distributing the workload, parallel processing can significantly reduce the time required to process large datasets, especially when analysing multiple samples with different rounding steps or window sizes. The entropy (e.g. Shannon entropy) may be calculated from the data from the one or more infrared images (or a section thereof), and the Flory-Huggins interaction parameter and / or the free energy of mixing may be calculated by combining data from DSC with the entropy (e.g. Shannon entropy). The DSC data may be a thermogram. The temperature determined by the infrared camera may be calibrated with the temperature measured by the DSC apparatus. The method may be used to characterise the sample at or above the glass transition temperature (Tg) of the polymer, for example from Tg of the polymer to 50°C above Tg of the polymer, or from Tg of the polymer to 20°C above Tg of the polymer, or from Tg of the polymer to 10°C above Tg of the polymer. DSC measures the differential heat flow as a function of temperature or time, given by: ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^^^^^ ^^ Where^^ ^^^^ ^^ ^^ ^^ is the heat flow, m is the mass of the sample, ^^^^is the heat capacity, and is the heating rate. The heat flow relating to (e.g. before, during and / or after) an event (e.g. a physical event) for a sample may be determined. For example, the physical event may be the melting point. A temperature value may be determined for each pixel of the infrared image that covers the sample. The entropy (e.g. Shannon entropy) may be determined as the sum of, for each pixel of one or more heatmaps, the probability that the pixel has a particular heat flow value. The calculation of entropy may involve gathering the unique temperature values; calculating the frequency each unique temperature value is present in the heat map; calculating the probability for each temperature value; and calculating the entropy for the heatmap. The entropy may be determined for one heatmap or averaged over more than one heatmap. The entropy (H) may be calculated as: Where ^^^^is the probability of a specific heat flow value from the DSC data. For example: where: p(xi) is the probability of occurrence of the outcome xi; n is the total number of distinct outcomes; and the logarithm base 2 ( log2) is used because entropy is often measured in base 2. The entropy (e.g. Shannon entropy) may be calculated for one heatmap (i.e. infrared image). Determining the entropy over a number of heatmaps allows for a more precise result to be determined, especially where the frame rate of the images is relatively high (e.g. 1 frame per second or higher). The entropy may be determined for each heatmap in a series of heatmaps (i.e. each frame of an infrared video). The entropy may be determined over more than one heatmap. For example, the entropy may be determined over (e.g. as the average, such as mean, of) two or more, such as 10 or more, or 100 or more, such as 1000 or more heatmaps (infrared images). The entropy (e.g. Shannon entropy) may be determined over one or more heatmaps related to (e.g. before, during or after) an event (e.g. a physical event) of the sample, such as a change of phase of the sample. The entropy (e.g. Shannon entropy) may be used to adjust the traditional Flory-Huggins interaction parameter. A modified Flory-Huggins interaction parameter ^^ (i.e. ^^′) may be calculated via incorporation of Shannon entropy as per the equation: ^^′= ^^ + ^^ ^^ The conventional Flory-Huggins interaction parameter ^^ can be determined from a plot of ^ ^1^T mix ^1T pure polymeragainst which gives a straight^ff line with a slope equal to the traditional interaction parameter ^^. Tfmix is the melting point onsetof the drug in the polymer drug mixture, Tfpure is the melting point onset of the pure drug,∆Hf is the enthalpy of fusion of the pure drug, R is the gas constant, ^^ ^^ ^^ ^^ ^^ is the volumefraction of the drug, ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ is the volume fraction of the polymer, and r is the ratio of themolecular volume of the polymer to the molecular volume of the drug.The proportionality constant, α, serves as a bridge between two different entropy measures. One is the Shannon entropy, determined from the heatmaps, which encapsulates the spread or variation of the temperature across the sample at different times or stages. The other is the configurational entropy, which accounts for the number of ways molecules (or polymer segments and drug molecules) can arrange themselves in space. α is introduced because these two entropies don't naturally operate on the same scale or even represent the same physical phenomena. The Shannon entropy from the heatmap is a measure derived from information theory, usually dimensionless, and gives us a measure of uncertainty or dispersal in the system. On the other hand, the configurational entropy is a thermodynamic quantity with units of energy / temperature and relates to molecular disorder. Conceptually, α can be viewed as a "translation factor" that scales the entropy from the heatmap to a value that makes sense in the context of the Flory-Huggins theory, which deals with molecular configurations and interactions. From the modified Flory-Huggins interaction parameter, the modified Flory-Huggins free energy of mixing may be calculated using the following formula: ∆Gm′ = kT(n1lnϕ1+ n2lnϕ2+ n1ϕ2x′) Where k is Boltzmann’s constant, T is the bulk temperature, ^^^^and ^^^^are the volume fractions of the drug and polymer, respectively, ^^^^and ^^^^are the number of moles of the drug and polymer, respectively, and ^^′ is the modified Flory-Huggins interaction parameter. Thermal gradient is a crucial measure in physical sciences and engineering, as it indicates how quickly or slowly temperature changes across a material or space. The following method determines the gradient for the entire sample data grid and then averages these values to provide a single measure of the gradient's magnitude. For rounding the data, the temperature data is first rounded to a specified precision (determined by the rounding step). This rounding helps to reduce noise and make the patterns in the data more evident. The thermal gradient in this context is the rate of temperature change across a two-dimensional grid (the sample data). The gradient measures how the temperature varies from one point to another in the dataset. mathematically, the thermal gradient magnitude is calculated as: where:|∇ ^^| represents the temperature at a given point in the dataset; and are the partial derivatives of the temperature with respect to the x and y coordinates, respectively. ∂ ^ partial derivatives∂ ^^ The^∂ ^^ ^^ ^^ ^^ ∂ ^^ represents the rate of change of temperature in the horizontal (x-axis) and vertical (y-axis) directions, respectively. These derivatives are calculated using conventional numerical methods, typically by taking the difference between neighbouring temperature values along each axis. The gradient magnitude |∇ ^^| is then computed as the Euclidean norm of these derivatives. This norm is the square root of the sum of the squares of the partial derivatives. It gives the overall rate of temperature change at each point, irrespective of the direction. For a plurality of images (or sections thereof, i.e. heatmaps) entropy and / or thermal gradient may be plotted against the sequence number of each image in the order of the heatmaps taken and / or against the average (mean) temperature across the temperature values on each heatmap. The method may comprise determining the regions of change in gradient (e.g. peaks and troughs) in the or each plot. The or each region of change in gradient corresponds to a thermal event, such as a melting / freezing point or glass transition temperature. The method may comprise, for a plurality of images (or sections thereof, i.e. heatmaps), calculating the rate of change of the entropy and / or thermal gradient in relation to the sequence number of each image in the order of the heatmaps taken and / or the average (mean) temperature across the temperature values on each heatmap. The method may comprise determining the changes in the rate of change of the entropy and / or thermal gradient. The or each change in the rate of change of the entropy and / or thermal gradient corresponds to a thermal event, such as a melting / freezing point or glass transition temperature. Therefore, for a sample containing a plurality of polymorphs, the number of polymorphs may correspond to the number of regions of change in gradient of the or each plot (e.g. the Shannon entropy plot) and the number of changes in the rate of change of the entropy and / or thermal gradient. Apparatus The third aspect provides an apparatus for performing differential scanning calorimetry (DSC) on a sample. The apparatus comprises a housing configured to contain the sample during DSC. The apparatus comprises an infrared imaging device (e.g. thermal camera) adapted to receive infrared radiation emitted by the sample during DSC; and / or the housing comprises a window pane that is transparent to infrared radiation. In one embodiment the apparatus comprises a housing configured to contain the sample during DSC and an infrared imaging device (e.g. thermal camera) adapted to receive infrared radiation emitted by the sample during DSC. This apparatus may also include a window pane that is transparent to infrared radiation. The infrared imaging device that is able to directly capture images from within the housing of the apparatus. In this embodiment, the apparatus may also include a window pane that is transparent to infrared radiation but there is no need for a window pane. The apparatus includes one or more housings (ovens) to contain the sample being analysed during use. The housing allows the environment around the sample to be controlled during measurement, for example insulating the sample to minimise heat loss from the sample, and / or preventing air currents. Such factors could reduce the accuracy or precision of measurement. Housings typically provide a thermally controlled environment for the samples, and are capable of heating and / or cooling the sample. Each housing traditionally includes a base and a lid, wherein the lid is removable to allow samples to be provided to or removed from the housing, for analysis. The lid traditionally allows the housing to be closed, so that the environment around the sample can be controlled. The housing may be configured to completely enclose the sample. The sample may be sealed within the housing. Apparatuses for DSC traditionally include a holder for the sample to be analysed, within each housing of the apparatus. Apparatuses for DSC traditionally include a holder for the reference. Each housing may comprise one or two or more sample holders, which may be made of a thermally insulating material such as a plastics material. A variety of DSC apparatuses may be adapted for the present invention, for example the DSC 7 (Perkin-Elmer, UK). Apparatuses for DSC traditionally include thermocouples configured to determine the temperature of the sample and the temperature of the reference. The apparatus may be operable to obtain a thermogram for a sample. The apparatus may comprise: a sample housing (or cell), a reference housing (or cell), a thermal shield disposed around the sample housing and the reference housing, a heater arranged to heat the sample housing and the reference housing, a thermal sensor arranged to measure a difference in temperature between the sample housing and the reference housing, and a processing system configured to control the heater and receive temperature measurements from the sample housing and reference housing, and to determine a first thermogram comprising estimates of heat capacity at each of a range of temperatures for a test substance in the sample housing, the estimates being responsive to a difference in the amount of heat required to maintain the sample housing and reference housing at the same temperature while the temperature of both the sample housing and reference housing is varied, wherein the processing system comprises a memory for storing a thermogram. The heater may comprise a sample heater for heating the sample housing (e.g. independently of the reference housing) and a reference heater for heating the reference housing (e.g. independently of the sample housing). Preferably the apparatus comprises an infrared imaging device. Preferably the processing system is configured to perform the method of the first aspect and / or the method of the second aspect. Preferably the processing system is configured to calculate, for the sample, a Flory-Huggins interaction parameter and / or a free energy of mixing, wherein the calculation uses data obtained by DSC and data obtained by one or more (e.g. two or more, or five or more, or ten or more) infrared images. In one embodiment the apparatus comprises a housing configured to contain the sample during DSC, wherein the housing comprises a window pane that is transparent to infrared radiation. This apparatus may also include an infrared imaging device (e.g. thermal camera) adapted to receive infrared radiation emitted by the sample during DSC. A traditional DSC apparatus may be adapted for the present invention by replacing the conventional lid with a lid that comprises the window pane. Such a lid comprise a collar to hold the window pane. The window pane may fit closely in the lid. The lid may sit upon the base of the housing. The lid may be adapted to form a close fit with the base. The lid may be formed of a metal such as stainless steel or aluminium. The lid is preferably annular. The lid preferably extends around the circumference of the sample (e.g. in use). The lid preferably extends around the circumference of the sample holder. The window pane is made of a material that is transparent to infrared radiation. In other words, the window pane is transparent to infrared radiation. The window pane may be in the top of the housing when the housing is closed. The window pane may therefore be in a wall of the housing. In use, wall with the window pane may be positioned above the sample. The infrared spectrum is often divided into five regions, although no precise definition of the regions is widely accepted. Near infrared (NIR) band may be defined as 0.74 to 1 µm. The short wavelength infrared (SWIR) band may be defined as 1 to 3 µm. The medium or mid wavelength infrared (MWIR) band may be defined as 3 to 7 µm. The long wavelength infrared (LWIR) band may be defined as 7 to 14 µm. The very long wavelength infrared (VLWIR band may be defined as 14 to 1000 µm. The MWIR band is most useful when inspecting high temperature objects and the LWIR band when working with objects near room temperature. Infrared transparent materials suitable for the window pane and / or the cover include barium fluoride (BaF2, transmission range 0.15-12.5 microns), potassium bromide (KBr, transmission range 0.21-28 microns), caesium iodide (CsI, transmission range 0.25-55 microns), potassium chloride (KCl, transmission range 0.21-21 microns), cadmium telluride (CdTe, transmission range 2-25 microns), sapphire (Al2O3, transmission range 0.17-5.0 microns), silicon (Si, transmission range 1.2-10, 50-100 microns), high resistivity silicon (Si, transmission range 1.2- 10, 50-100 microns), calcium fluoride (CaF2, transmission range 0.15-9.0 microns), gallium arsenide (GaAs, transmission range 1-15 microns), sodium chloride (NaCl, transmission range 0.2-20 microns), germanium (Ge, transmission range 2-17 microns), borosilicate glass (transmission range 0.35-2.0 microns), fused silica (SiO2, transmission range 0.18-3.5 microns), lithium fluoride (LiF, transmission range 0.12-6.5 microns), magnesium fluoride (MgF2, transmission range 0.13-7.0 microns), quartz (SiO2, transmission range 0.15-3.3 microns), thallium bromoiodide (TlBr-TlI, transmission range 0.6-40 microns), zinc selenide (ZnSe, transmission range 0.55-20 microns), zinc sulfide (ZnS, transmission range 0.37-14 microns), infrared plastic (transmission range 8-12 and 15-40 microns) and / or a glass of germanium, arsenic and selenium (e.g. Ge:As:Se 33:12:55 or 28:12:60 by weight, transmission range 0.8-13 microns). Infrared transparent materials suitable for the window pane and / or the cover also include silicon carbide, aluminium nitride, and chalcogenide glass. For analyses that require higher temperatures, for example in the analysis of metals or alloys, materials with high temperature stability may be used, such as silicon carbide, aluminium nitride, silicon and barium fluoride. Preferably the infrared transparent material is BaF2, CdTe, GaAs, Ge, thallium bromoiodide (TlBr-TlI), ZnSe, ZnS, infrared plastic, and / or a glass of germanium, arsenic and selenium (e.g. Ge:As:Se 33:12:55 or 28:12:60 by weight). For example, the infrared transparent material may be BaF2, KBr, CsI, KCl, CdTe, GaAs, Ge and / or a glass of germanium, arsenic and selenium (e.g. Ge:As:Se 33:12:55 or 28:12:60 by weight. More preferably the infrared transparent material for the apparatus is zinc selenide. Zinc selenide is not water soluble, and its infrared transparency is stable to variations in temperature. Therefore, zinc selenide allows for accurate infrared imaging even when the sample is heated to high temperatures. The infrared transparent material may be transparent to all or part of the mid- and / or long- wavelength infrared bands of the electromagnetic spectrum (1 to 20 µm). The infrared transparent material may be transparent to wavelengths from 9 to 14 µm, or from 7 to 14 µm, more preferably from 3 to 14 µm, or from 1 to 14 µm, for example from 3 to 20 µm. The window pane allows infrared radiation emitted by a sample on one side of the window pane to be received by an infrared imaging device on the other side of the window pane, i.e. outside of the housing. The infrared imaging device may be referred to as a camera. The imaging device may be adapted to take still images (i.e. photographs) or a video (i.e. a sequence of photographs taken over a period of time). The imaging device may be referred to as a thermal imaging device or a thermal camera. Taking an infrared image (or video) of the sample may be termed infrared thermography. The imaging device (e.g. camera) may have a macro mode and / or a macro lens. The window pane is preferably positioned (e.g. in the housing, such as in the lid) so that the sample can be imaged by the imaging device through the window pane. Thus, the window pane may be positioned above the sample. For example, the window pane may be positioned at an angle of 20° or less, or 10° or less, such as 5° or less from the axis perpendicular to the plane of the sample holder. This allows a high proportion of the infrared radiation from the sample be pass through the window. The imaging device is preferably positioned so that it can image the sample (e.g. through the window pane). Thus, the imaging device may be positioned above the sample. For example, the imaging device may be positioned at an angle of 20° or less, or 10° or less, such as 5° or less from the axis perpendicular to the plane of the sample holder. This can allow the imaging device to view a high proportion of the sample through the window pane. The imaging device may be configured to detect radiation in the mid- and / or long- wavelength infrared bands of the electromagnetic spectrum (e.g. 1 µm or longer, such as 1 to 20 µm, or 3 to 20 µm, preferably 1 to 14 µm or 3 to 14 µm, more preferably 7 to 14 µm, or 9 to 14 µm). Images produced by the imaging device may be termed thermograms. The imaging device may be configured to not image / detect visible wavelengths of light (400-700nm) and / or other wavelengths outside of the desired infrared ranges. The imaging device may comprise a staring array (also known as staring-plane array or focal plane array). These arrays respond to longer wavelengths (e.g. mid- and long-wavelength infrared) of radiation. The imaging device may comprise an array (e.g. focal plane array) that is based on InSb, InGaAs, PbSe, PtSi, HgCdTe, a Quantum Well Infrared Photodetectors (QWIP, e.g. made of GaAs), or microbolometers (e.g. with detector materials of amorphous silicon and / or vanadium oxide). Detectors / sensors for focal plane arrays may be made of amorphous silicon (a-Si), vanadium(V) oxide (Vox), lanthanum barium manganite (LBMO), lead zirconate titanate (PZT), lanthanum doped lead zirconate titanate (PLZT), lead scandium tantalate (PST), lead lanthanum titanate (PLT), lead titanate (PT), lead zinc niobate (PZN), lead strontium titanate (PSrT), barium strontium titanate (BST), barium titanate (BT), antimony sulfoiodide (SbSI), or polyvinylidene difluoride (PVDF). The sensor may have a resolution of 160 x 120 pixels or higher, such as 320 x 240 pixels or higher, or 640 x 480 or higher, for example 1280 x 720 or higher, such as 1280 x 1024 pixels. The sensor may comprise 100 pixels or more, such as 10,000 pixels or more, or 100,000 pixels or more. The sensor may comprise 100 million pixels or less, such as 10 million pixels or less, such as 1 million pixels or less. The sensor may comprise from 100 to 100 million pixels. Preferably the apparatus comprises a recording unit configured to record DSC measurements and / or infrared images of the sample. The apparatus may comprise a lens to focus the infrared radiation to be imaged. The lens may be made of an infrared transparent material. The apparatus may comprise a processor and / or memory. A sample to be analysed by DSC is typically placed in a pan that has a cover. The cover is useful to control the atmosphere around the sample and prevent baseline fluctuations in the measurements. Furthermore, the cover can be used to compact the sample into a thin layer, causing the heat flow to stabilise. Separate pans and covers are used for the sample and the reference. A pan and a cover may be sealed (e.g. by crimping), particularly where volatile samples are being studied. Pans and covers are traditionally made of aluminium, alumina, copper, gold, graphite, quartz, stainless steel, titanium, or platinum. The fourth aspect provides a cover for DSC of a sample, wherein the cover is made of (i.e. comprises, consists essentially of, or consists of) a material that is transparent to infrared radiation. The material that is transparent to infrared radiation may be one of those described above (e.g. ZnSe). The cover is preferably substantially cylindrical. The cover may be substantially circular in cross-section. The cover may have a diameter of 2mm or more, such as 5mm or more, or 10mm or more, for example 14mm or more. The diameter may be 30mm or less, such as 25mm or less, or 20mm or less, for example 16mm or less. The diameter may be from 2mm to 30mm, such as from 10mm to 20mm, for example about 15mnm. In other embodiments, the cover may have a diameter from 2 to 5mm, such as from 2 to 4mm, or from 2.5 to 3.5mm, for example about 3mm. The cover may have a thickness of 0.05mm or more, such as 0.1mm or more, or 0.2mm or more, for example 0.3mm or more, or 0.4mm or more, such as 0.5mm or more. The thickness may be 5mm or less, such as 2mm or less, or 1mm or less, for example 0.8mm or less, or 0.7mm or less, or 0.6mm or less. The thickness may be from 0.05mm to 5mm, such as from 0.1mm to 1mm, or from 0.3mm to 0.7mm. The cover may be substantially cylindrical, have a diameter of 2mm or more, and have a thickness of 0.05mm or more. The cover may be substantially cylindrical, have a diameter of 30mm or less (e.g. from 2mm to 30mm), and have a thickness of 5mm or less (e.g. from 0.05mm to 5mm). The fifth aspect provides a kit for containing a sample during DSC, the kit comprising a cover according to the fourth aspect and a pan. The pan may be made of a traditional material for a DSC pan, as described above. A DSC pan is usually cylindrical, with an annular wall joining a closed end with an open end, and defining a central hollow. The volume of the central hollow of a DSC pan is typically from 2 to 200 µL, for example from 10 to 100µL. A DSC pan usually has a diameter of from 2 to 10mm, such as from 2 to 8 mm, such as from 2 to 5mm, e.g. from 2.5 to 3.5mm (e.g. about 3mm), or from 4 to 8mm, such as from 5 to 7mm, for example from 6 to 7mm.A DSC pan usually has a height of from 0.5mm to 10mm, such as from 1mm to 5mm, or from 1mm to 4mm, such as from 1.5mm to 3mm. A DSC pan may include a flange around the open end that may be configured to seal with a lid. Detailed Description of the Drawings Figure 1 of the accompanying drawings shows an apparatus 10 for performing DSC, which is shown without its conventional lid. Figure 1 shows base 12 of the housing and, within the housing, sample holders 14, 16 – one for the test sample and the other for the reference sample. Figure 2 of the accompanying drawings shows a lid 20 adapted to sit, and tightly fit with base 12 of Figure 1. Lid 20 is annular and made of stainless steel. Figure 3 of the accompanying drawings shows lid 20 of Figure 2 fitted onto apparatus 10 of Figure 1. Figure 3 shows central cavity 22 within annular lid 20. An infrared transparent window pane (not shown) can be placed within central cavity 22. Figure 4 of the accompanying drawings shows a top-down view into central cavity 22. This shows infrared transparent window pane 30 positioned within central cavity 22. Through window pane 30, base 12 can be seen. Figure 5 of the accompanying drawings shows a full view of apparatus 10. Figure 6A of the accompanying drawings shows a cross-sectional view through an embodiment of the apparatus 10 of the invention. The apparatus 10 includes housing base 12, sample holders 14,16, annular lid 20, test sample pan / cover unit 40 and reference pan / cover unit 42. Figure 6B of the accompanying drawings shows a cross-sectional view through test sample pan / cover unit 40, revealing pan 44, zinc selenide lid 46 and sample 48. Figure 7A of the accompanying drawings shows a zinc selenide lid 46, which is cylindrical. Figure 7B of the accompanying drawings shows aluminium DSC sample pan 44 and zinc selenide lid 46. The dimensions of the lid are 7mm in diameter by 0.5mm thickness. Figures 8 and 9 of the accompanying drawings show infrared images gathered from a thermal camera used to analyse a test sample during DSC, using apparatus according to the invention. The images shown in Figures 8 and 9 were captured using a FLIR T530 thermal imaging camera, a high resolution thermal camera with macro mode that enables the capture of highly detailed temperature distribution maps from small samples (e.g. 640 x 480 pixels resolution, equivalent to 307200 pixels, where each pixel is a temperature point measured). Figure 8 shows the temperature of three specific locations on the surface of the sample. Figure 9 shows the temperature range across the surface of the sample. Figures 8 and 9 show that that it is possible to record small variations in temperature across a sample using thermal imaging, while simultaneously collecting DSC data, by comparing the temperature of specific locations on the surface of a sample. The temperature distribution across a sample can be presented graphically, as shown in Figure 10 of the accompanying drawings, which shows the temperature (°C) for each pixel of the image in the region of the sample. In the evaluation of drug-polymer compatibility, the temperature distribution allows a “heatmap” to be created whilst simultaneously using DSC to measure the amount of heat released or absorbed by the sample. This map of temperature distribution will differ depending on the type of the polymer used to prepare the solid solution. Simultaneous generation of a temperature distribution map alongside the measurement of the heat absorbed or released from a sample can overcome any interference caused by different molecular compositions and materials in spectroscopy methods, including conventional DSC. Ultimately, the simultaneous generation of a temperature distribution map alongside the measurement of the heat absorbed or released from a sample can enable the more precise calculation of the thermodynamics of mixing based on Flory-Huggins modified model. An infrared / thermal image of a sample may be referred to as a heatmap. In DSC, the variation in heat flow arising from phase transitions, molecular interactions, or other processes / events, is captured visually using heatmaps. Each pixel on this heatmap corresponds to a value of forming a matrix representation of the data. DSC is renowned in material science for its ability to unveil complex thermal interactions. In its analytical milieu, the innovative use of heatmaps provides not just visual cues, but quantitative metrics, particularly through entropy (e.g. Shannon entropy) calculations. This synergy elevates the analysis, particularly in polymer blends, to a fusion of thermodynamics, information theory, and data visualization. This treatise underscores the profound intersection of DSC, Shannon entropy, and heatmaps. The skilled person will understand that the apparatus and system embodiments described herein are exemplary. The modules, systems and method steps described herein may be implemented in software executed by a processor, hardware or a combination of the two. In some embodiments, the modules, systems and method steps described herein may be implemented by one or more computing devices. Such a computing device may include one or more processors, input / output interfaces and memory. The processors may be provided as part of a processing unit which may be provided with one or more Intel®X86 processors such as an I5, I7 processor or the like. The memory may include computer or machine readable memory forming a computer / machine readable medium. The skilled person will appreciate that the memory may be provided by a variety of components including a volatile memory, a hard drive, a non-volatile memory, etc. The memory may store a set of computer readable instructions, data structures, program modules or other data. The computer-readable media may not include temporary computer readable media (transitory media), such as a modulated data signal and a carrier wave. In one aspect, there is provided a machine / computer readable medium or computer program product containing instructions which, when read by a machine or computer, cause any of the methods, or parts thereof, described or claimed herein to be performed. The machine readable medium may be any of the following: a CD-ROM; a DVD-ROM / RAM (including -R / -RW or +R / +RW); a hard drive; a memory (including a USB drive; an SD card; a compact flash card or the like); a transmitted signal (including an Internet download, ftp file transfer of the like); a wire; etc. The machine readable medium may be a non-transitory computer readable medium. Various modifications will be apparent to the skilled person without departing form the scope of the claims. The embodiments described above should be understood as exemplary only. Any feature of any of the aspects or embodiments of the disclosure may be employed separately or in combination with any other feature of the same or different aspect or embodiment of the disclosure and the disclosure includes any feature or combination of features disclosed herein. Examples Example 1: Calculation of Flory-Huggins free energy of mixing - mixture of progesterone and HPMCAS To exemplify the present invention, heatmaps were generated for a physical mixture of progesterone and hydroxypropylmethylcellulose acetate succinate (HPMCAS). The temperature determined by the thermal imaging camera was calibrated with the temperature measured by the DSC apparatus. The heatmaps were recorded as video during DSC analysis, and a section of the frames of the video were extracted as images for further analysis. The heatmaps were cropped to show only the region detecting emissions from the sample. Only the cropped region was analysed. Figure 11 of the accompanying drawings shows representative cropped infrared (thermal) images, which were used as heatmaps. The heatmaps show the variation in temperature across the surface of the sample in unprecedented detail. The data show another dimension in detecting temperature changes that is not possible to observe using DSC alone. DSC measures the differential heat flow as a function of temperature or time, given by: ^^ ^^ ^^ ^^ = ^^ ^^ ^^ ^^^^^^ ^^ Where^^ ^^is the heat flow, m is the mass of the sample, ^^ ^^ ^^ ^^is the heat capacity, and is the heating rate. Shannon entropy, a concept borrowed from information theory, quantifies the amount of uncertainty or randomness associated with a set of data. The entropy (e.g. Shannon entropy) can be determined from heatmaps. When applied to DSC heatmaps, entropy (e.g. Shannon entropy) provides a measure of the randomness or disorder in the heat interactions. The entropy (e.g. Shannon entropy) for one or more given heatmaps (i.e. infrared images) with a set of probabilities (where each probability corresponds to the occurrence of a specific heat flow value) is calculated as: Where ^^^^is the probability of a specific heat flow value from the DSC data. For each frame of the video generated in the experiment described in relation to Figure 11, a Shannon entropy value was calculated and plotted alongside the average surface temperature. Figures 12A and 12B of the accompanying drawings show graphs illustrating the correlation between Shannon entropy and average surface temperature (°C) for each frame of the experiment illustrated in Figure 11. Figure 12A shows the initial phase of the experiment, where the average temperature ranged from about 25°C to about 55°C; Figure 12B shows a later phase of the experiment, where the average temperature ranged from about 90°C to about 125°C. The Flory-Huggins interaction parameter ^^ quantifies the energetics of mixing. It is conventionally derived from entropic and enthalpic considerations. However, integrating entropy (e.g. Shannon entropy) into ^^ is an unconventional modification. Entropy (e.g. Shannon entropy) from heatmaps can be integrated into a modified Flory-Huggins interaction parameter ^^′: ^^′= ^^ + ^^ ^^ Traditional methods of calculating the Flory-Huggins interaction parameter ^^ for drug-polymer blends do not incorporate entropy data derived from heatmaps. This invention introduces a method to integrate this valuable data source. The proportionality constant, α, serves as a bridge between two different entropy measures. One is the Shannon entropy, determined from the heatmaps, which encapsulates the spread or variation of the temperature across the sample at different times or stages. The other is the configurational entropy, which accounts for the number of ways molecules (or polymer segments and drug molecules) can arrange themselves in space. α is introduced because these two entropies don't naturally operate on the same scale or even represent the same physical phenomena. The Shannon entropy from the heatmap is a measure derived from information theory, usually dimensionless, and gives us a measure of uncertainty or dispersal in the system. On the other hand, the configurational entropy is a thermodynamic quantity with units of energy / temperature and relates to molecular disorder. Conceptually, α can be viewed as a "translation factor" that scales the entropy from the heatmap to a value that makes sense in the context of the Flory-Huggins theory, which deals with molecular configurations and interactions. The traditional Flory-Huggins interaction parameter ^^ can be calculated using the temperature of the melting point depression of the physical mixture of the drug and polymer. Upon heating the physical mixture above the glass transition temperature (Tg) of the polymer, the polymer will be in the rubbery state hence it can act as a solvent for the drug. The drug will be dissolved to a certain extent depending on its affinity towards the polymer. The crystalline drug will turn into amorphous as the polymer continues to dissolve it. Once the melting point of the drug is reached the crystalline part of the drug, which has not been dissolved by the polymer, a melting peak can be seen. An ideal solvent (polymer) will dissolve the drug and no melting peak would be detected. The interaction parameter can be estimated from the enthalpy of fusion: A plotagainst therefore gives a straight line with a slope equal to the traditional interaction parameter ^^. Tfmixis the melting point onset of the drug in the polymer drug mixture, Tfpure is the melting pointonset of the pure drug, ∆Hfis the enthalpy of fusion of the pure drug, R is the gas constant,^^ ^^ ^^ ^^ ^^ is the volume fraction of the drug, ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ is the volume fraction of the polymer, andr is the ratio of the molecular volume of the polymer to the molecular volume of the drug.The Flory-Huggins free energy of mixing is calculated using the following formula: ∆Gm= kT(n1lnϕ1+ n2lnϕ2+ n1ϕ2x′) Where k is Boltzmann’s constant, T is the bulk temperature, ^^^^and ^^^^are the volume fractions of the drug and polymer, respectively, ^^^^and ^^^^are the number of moles of the drug and polymer, respectively. The equation above describes the modified Flory-Huggins expression for the free energy of mixing – replacing x’ for x would describe the traditional Flory-Huggins expression for the free energy of mixing for a binary system. The Shannon entropy (as shown in Figure 12) was used to calculate the Flory-Huggins interaction parameter, as described above. This was then used to determine the Flory-Huggins free energy of mixing, as described above. The method enabled surprising improvements in the precision of the characterisation of the change in Gibbs free energy of mixing for a polymer and a drug in a polymer-drug solid solution. The method of the present invention provided unprecedentedly precise identification of thermal events changes such as melting and polymorphism in the sample. Example 2: Calculation of entropy An exemplary 3x3 heatmap of temperature values is used to illustrate calculations of Shannon entropy and thermal gradient. The 3x3 heatmap provides 9 temperature values as shown here: x=0 x=1 x=2 y=0 20.0°C 21.0°C 22.0°C y=1 21.0°C 22.0°C 21.0°C y=2 22.0°C 23.0°C 22.0°C values. The dataset includes the following four unique temperature values: T = [20.0, 21.0, 22.0, 23.0] Step 2: Calculate the frequency of each unique temperature value: 20.0°C appears 1 time; 21.0°C appears 3 times; 22.0°C appears 4 times; 23.0°C appears 1 time. Step 3: Calculate the probability of each value: ^^(20.0° ^^)0.111 ^^(21.0° ^^) 0.333 Calculating each term: ^^(20.0° ^^)log2( ^^(20.0° ^^)) = 0.111 × log2(0.111)≈ 0.111 ×(−3.17)≈ −0.352 ^^(21.0° ^^) log2( ^^(21.0° ^^)) = 0.333 × log2(0.333) ≈ 0.333 × (−1.585) ≈ −0.528][^^(22.0° ^^) log2( ^^(22.0° ^^)) = 0.444 × log2(0.444) ≈ 0.444 × (−1.174) ≈ −0.522 ^^(23.0° ^^) log2(^^(23.0° ^^))= 0.111 × log2(0.111) ≈ 0.111 × (−3.17) ≈ −0.352 Summing these values: ^^(^^)= −(−0.352 − 0.528 − 0.522 − 0.352)= 1.75 So, the Shannon entropy for this heatmap is 1.75. Thermal gradient measures how quickly the temperature changes across neighbouring points. This was calculated for the exemplary 3x3 heatmap described in Example 2. Step 1: Compute the gradient in the x and y directions We calculate the gradient by taking the difference between neighbouring points: Horizontal gradient (x-direction) - for each point (x, y), we compute: ∂ ^^ = ^^( ^^ + 1, ^^) − ^^( ^^, ^^) ∂ ^^ Calculating each term: −^^ ^^(^^ = 0, ^^ = 0): (∂ ^^= 21.0° ^^ − 20.0° ^^ = 1.0° ^^) ∂ ^^ −^^ ^^( ^^ = 1, ^^ = 0): (∂ ^^= 22.0° ^^ − 21.0° ^^ = 1.0° ^^) ∂ ^^ −^^ ^^(^^ = 0, ^^ = 1): (∂ ^^= 22.0° ^^ − 21.0° ^^ = 1.0° ^^) ∂ ^^ The same calculation is performed for the rest of the points. Vertical gradient (y-direction) - for each point (x, y), we compute: ∂ ^^ = ^^( ^^, ^^ + 1) − ^^( ^^, ^^) ∂ ^^ Calculating each term: −^^ ^^( ^^ = 0, ^^ = 0): (∂ ^^= 21.0° ^^ − 20.0° ^^ = 1.0° ^^) ∂ ^^ −^^ ^^( ^^ = 1, ^^ = 0): (∂ ^^= 22.0° ^^ − 21.0° ^^ = 1.0° ^^) ∂ ^^ The same calculation is performed for the rest of the points. Step 2: Compute the total gradient magnitude For each point, the total gradient is calculated using: Calculating each term: For example, at (x=0, y=0), we have: The same calculation is performed for the rest of the points. Step 3: We take the average of the gradient magnitude From the gradient for all points, the average gradient magnitude is computed. For this example: Average gradient = 1.32° ^^ rounding and window size Rounding and window size can be used in Shannon entropy calculations. Rounding controls the precision of the temperature values. Smaller rounding steps retain more detail, while larger steps smooth the data by grouping similar values. The window size affects how much smoothing is applied in moving averages. Larger window sizes reduce the influence of sharp changes by considering more points at once. The combined effect of rounding and window size allows fine-tuning how much detail we wish to retain in the heatmaps versus how smooth or generalized the data should appear. Applying rounding to the heatmap An exemplary 3x3 heatmap of temperature values is used to illustrate calculations using rounding and window size. The 3x3 heatmap provides 9 temperature values as shown here: x=0 x=1 x=2 y=0 20.1°C 21.3°C 22.7°C y=1 21.2°C 22.4°C 21.1°C y=2 22.8°C 23.0°C 22.2°C Rounding Step of 0.5°C When we apply a rounding step of 0.5°C, each temperature value is rounded to the nearest 0.5°C multiple: x=0 x=1 x=2 y=0 20.0°C 21.5°C 22.5°C y=1 21.0°C 22.5°C 21.0°C y=2 23.0°C 23.0°C 22.0°C Rounding Step of 1.0°C When we apply a rounding step of 1.0°C, each temperature value is rounded to the nearest 1.0°C multiple: x=0 x=1 x=2 y=0 20.0°C 21.0°C 23.0°C y=1 21.0°C 22.0°C 21.0°C y=2 23.0°C 23.0°C 22.0°C Applying window size to the heatmap: The heatmap with 1.0°C rounding is broken into 2x2 windows: Window 1: 20.0°C 21.0°C 21.0°C 22.0°C ^ Unique temperature values: [20.0, 21.0, 22.0] ^ Frequency of each value:^Shannon entropy for window 1 ^^(^^1): Window 2 (taken from a section of the heatmap not shown): 21.0°C 22.0°C 22.0°C 21.0°C ^ Unique temperature values: [21.0, 22.0] ^ Frequency of each value: ^ Shannon entropy for window 2 [ ^^( ^^2)2log224)] [ ^^( ^^2) = 0.5 × (−1))] [ ^^( ^^2) = 1.0] Window 3 (taken from a section of the heatmap not shown): 22.0°C 21.0°C 21.0°C 22.0°C ^ Unique temperature values: [21.0, 22.0] ^ Frequency of each value: ^ Shannon entropy )] [ ^^(^^2)= 1.0] The mean average of the three windows was then calculated. - Lidocaine The method of the present invention was used to detect and separate the two polymorphs of lidocaine. A 15mg sample was added to an aluminium pan and compressed under a zinc selenide lid. The sample was heated from room temperature to about 80°C. DSC data and infrared images of the sample were taken. Figure 13 of the accompanying drawings shows the heat flow (mW) obtained by the DSC heat capacity measurement alone (comparative). The DSC data (blue curve) shows two peaks but it is not clear whether they belong to two polymorphs. The data was analysed according to the invention, thereby calculating the Shannon entropy. A fixed rounding value of 0.01 was applied to the data. The Shannon entropy and the thermal gradient were each determined for each frame taken by the infrared camera. A moving average was used to smooth out each of the Shannon entropy data and the thermal gradient data by combining the data from separate frames within a moving window. Figure 13 also shows the moving average Shannon entropy, calculated according to the invention. The x-axis of the graph in Figure 13 represents the average temperature ^̅^: Figure 14 of the accompanying drawings shows graphs of Shannon entropy (left) and of thermal gradient (right), each against average temperature. Figures 14A and 14B show graphs produced using different moving averages to calculate the Shannon entropy and the thermal gradient. Figure 14A uses a smaller moving average window than Figure 14B. Figure 14A showed a broad peak that could be the result of two individual peaks merging. With the greater moving average used in Figure 14B, the data still shows a low level of noise relative to the data, but resolves two polymorph peaks 131. The data showed separation of the two polymorphs. This is not possible to be achieved via the DSC. Example 6: Detection of polymorphs - Griseofulvin Griseofulvin was analysed in accordance with the procedure described for Example 2. Figure 15 of the accompanying drawings shows graphs of Shannon entropy (left) and of thermal gradient (right), each against average temperature. Figures 15A and 15B show graphs produced using different moving averages to calculate the Shannon entropy and the thermal gradient. Figure 15A uses a smaller moving average window than Figure 15B. Figure 15A showed a broad peak that could be the result of two individual peaks merging. With the greater moving average used in Figure 15B, the data still shows a low level of noise relative to the data, but resolves two polymorph peaks 141. The data showed separation of the two polymorphs. This is not possible to be achieved via the DSC. Example 7: measurement of glass transition temperature The present invention may be used to measure the glass transition temperature (Tg) in a polymer or a blend of polymers. Tg of a 1:1 blend (by weight) of hydroxypropyl methylcellulose (HPMC) and polyvinylpyrrolidone (PVP) was determined in accordance with the procedure described for Example 2. Figure 16 of the accompanying drawings shows the results of this analysis. Specifically, Figure 16A shows the heat flow (mW) obtained by the DSC heat capacity measurement alone (comparative, exo down). Figure 16A shows a substantially constant curve with a very faint event 151 occurring at about 175°C. Figure 16B shows graphs of Shannon entropy (left) and of thermal gradient (right), each against average temperature. In contrast to the DSC graph, the Tg of HPMC is shown as a strong peak 152a, 153 in both the Shannon entropy and thermal gradient graphs. The thermal gradient could detect the major thermal change but the entropy graph could detect the smaller event 152b that belongs to the Tg of PVP. As can be seen in the DSC heat flow, there is no evidence of water exothermic peak in the Shannon entropy or thermal gradient graphs. This rules out that the event is due to water loss. Similar observations were made in the analysis of PVP alone and in the analysis of HPMC alone. For each of PVP and HPMC alone, the DSC heat flow shows very faint event but the Shannon entropy and temperature gradient graphs showed clear peaks. The same analysis was performed on hydroxypropylmethylcellulose acetate succinate (HPMCAS), which has a Tg that is known to be more difficult to detect, possibly due to the higher branch chain diversity compared to HPMC or PVP. While DSC alone showed no peak for Tg, the Shannon entropy and temperature gradient graphs prepared according to the invention both showed peaks for Tg. Therefore, the present invention can enhance peaks that are difficult to see and / or interpret using DSC alone, and can reveal peaks that are unable to be seen from DSC alone. 8: liquid samples The detection of melting and crystallization of liquid samples using the present invention and comparing this to DSC alone was analysed. Polyoxyethylene (10) oleyl ether (Brij® O10) was analysed by DSC alone and by the methods of the invention, as described for Example 2. The cycle started by holding isothermal at 70ºC and then cooling to -20ºC. The sample was then heated to 90°C. Figure 17A of the accompanying drawings shows the DSC data. The exothermic peak 161 can be seen at around 10ºC, corresponding to the freezing of the Brij®. Four endothermic peaks 162 can be seen at around 10ºC, corresponding to the melting of the Brij®. Figures 17B and 17C of the accompanying drawings shows the Shannon entropy and temperature gradient data for the cooling and heating phases respectively. Figure 17B shows three peaks 162. Figure 17C shows four peaks 163. The major peak corresponds to the freezing / melting of the Brij®. The minor peaks are likely to correspond to polymorphic transitions. Because the calculations are based on detecting changes, any phase transitions (exothermic or endothermic) will have the same direction as opposed to DSC measurements where exothermic events show as downward peaks and endothermic events show as upward peaks. 9: detection of crystalline content in blends The use of the present invention to detect traces of crystalline material in the griseofulvin / HPMCAS physical mixture. When the blend is heated and above Tg of the polymer, HPMCAS goes through a rubbery state, which, upon further heating, leads to the drug's solubilisation in the amorphous polymer matrix, leading to the drug's lower crystalline content being transformed to the amorphous form. Blends of grisefulvin in HPMCAS ranging from 75 wt% griseofulvin to 5 wt% griseofulvin were prepared and subjected to analysis by DSC alone and according to the methods of the invention. Figure 18A of the accompanying drawings shows the DSC analysis (exo down) for 67% griseofulvin. This shows one peak 171. Figure 18B of the accompanying drawings shows the Shannon entropy (left) and temperature gradient (right) for 67% griseofulvin, prepared according to the invention. This shows two peaks 172. When increasing the temperature, HPMCAS passes through it Tg to act as a solvent for griseofulvin. The Tg for HPMCAS 172a and the melting of griseofulvin 172b are indicated on the graph. Figure 19A of the accompanying drawings shows the DSC analysis (exo down) for 5% griseofulvin. This shows no peaks. Figure 19B of the accompanying drawings shows the Shannon entropy (left) and temperature gradient (right) for 5% griseofulvin, prepared according to the invention. This shows two peaks 182. While DSC is not able to detect the events at such low levels of crystalline material, the more sensitive methods of the present invention are still able to detect these events. Similar experiments were performed with mixtures of progesterone in microcrystalline cellulose (MCC) at concentrations of progesterone from 0.5wt% to 20wt%. The drug and polymer do not interact as the melting point of the polymer is over 200ºC. MCC is a crystalline polymer so change upon heating will only reflect in higher heat provided towards melting of the crystalline drug, as the drug showed melting endotherm. At concentrations of progesterone of 1% or less, no change could be seen in DSC signal. However, the invention showed a strong peak at concentrations of 1% or lower, likely caused by the melting of progesterone. Therefore, the present invention allows correlations to be determined between calculated (Shannon) entropy and / or temperature gradient values and data measured through DSC. These correlations allow events not detected or clearly resolved by DSC to be detected and resolved.

Claims

CLAIMS 1. A method of characterising a sample, the method comprising the steps of: - performing differential scanning calorimetry (DSC) on the sample; and - while the sample is undergoing DSC, taking infrared images of the sample.

2. The method of claim 1, wherein the method is performed using an apparatus for performing differential scanning calorimetry (DSC) on the sample, and wherein: - the apparatus comprises a housing configured to contain the sample during DSC; and - the apparatus comprises an infrared imaging device adapted to receive infrared radiation emitted by the sample during DSC measurement and / or the housing comprises a window pane made of a material that is transparent to infrared radiation.

3. The method of claim 1 or claim 2, wherein the method further comprises using the images and data obtained by the DSC to calculate the entropy of each thermal image, or a section thereof, using the following formula:wherein: H is the entropy; and ^^^^is the probability of a specific heat flow value from the DSC.

4. The method of claim 3, wherein the entropy is determined according to the formula:where: H is the entropy; p(xi) is the probability of occurrence of the outcome xi; and n is the total number of distinct outcomes.

5. The method of any preceding claim, wherein the method further comprises calculating the thermal gradient using the following formula:wherein:|∇ ^^| represents the temperature at a given point in the dataset; andare the partial derivatives of the temperature with respect to the x and y coordinates, respectively.

6. The method of claim 3 or any one of claims 4 and 5 as dependent upon claim 3, wherein the method further comprises determining the free energy change for mixing for the sample, for example using Flory-Huggins theory.

7. The method of claim 6, wherein the free energy change for mixing for the sample is determined using the following formula: ^^′= ^^ + ^^ ^^ wherein: x’ is the Flory-Huggins interaction parameter; x is the Flory-Huggins interaction parameter; α is the proportionality constant; and H is the entropy.

8. The method of claim 7, wherein the Flory-Huggins interaction parameter ^^ is determined from the slope of a plot of :against Φ2polymer, wherein:Tfmix is the melting point onset of the drug in the polymer drug mixture,Tfpure is the melting point onset of the pure drug,∆Hf is the enthalpy of fusion of the pure drug,Ris the gas constant,^^^^ ^^ ^^ ^^is the volume fraction of the drug, ^^^^ ^^ ^^ ^^ ^^ ^^ ^^is the volume fraction of the polymer, andr is the ratio of the molecular volume of the polymer to the molecularvolume of the drug.

9. The method of claim 7 or claim 8, wherein the modified Flory-Huggins free energy of mixing is calculated using the following formula: ∆Gm′ = kT(n1lnϕ1+ n2lnϕ2+ n1ϕ2x′) wherein: ∆Gm′ is the modified Flory-Huggins free energy of mixing, k is Boltzmann’s constant, T is the bulk temperature, ^^^^and ^^^^are the volume fractions of the drug and polymer, respectively, ^^^^and ^^^^are the number of moles of the drug and polymer, respectively, and ^^′ is the modified Flory-Huggins interaction parameter.

10. The method of claim 3 or any one of claims 4 to 9 as dependent upon claim 3, wherein the thermal image, or the section thereof, comprises a plurality of temperature points, and wherein the method comprises rounding each temperature point to the nearest value at a given spacing of from 0.001°C to 2.0°C.

11. The method of claim 3 or any one of claims 4 to 10 as dependent upon claim 3, wherein the thermal image, or the section thereof, comprises a plurality of temperature points, and wherein the method comprises calculating the Shannon entropy for a plurality of windows of two or more adjacent temperature points from a thermal image or the section thereof, and calculating the mean average of the Shannon entropy of the windows of the thermal image or the section thereof.

12. The method of claim 11, wherein each window comprises four or more adjacent temperature points.

13. The method of any preceding claim, wherein the sample comprises a biologically active agent and one or more polymers.

14. A method of processing data, the method comprising calculating, for a sample, entropy and / or the thermal gradient, wherein the calculation uses data obtained from one or more infrared images or a section of one or more infrared images of the sample.

15. The method of claim 14, wherein the method comprises: - determining the Shannon entropy from the one or more infrared images or the section thereof; - determining the traditional Flory-Huggins interaction parameter from the data obtained by DSC; and - combining the Shannon entropy with the traditional Flory-Huggins interaction parameter to determine a modified Flory-Huggins interaction parameter.

16. An apparatus for performing differential scanning calorimetry (DSC) on a sample, wherein the apparatus comprises a housing configured to contain the sample during DSC, and wherein the apparatus comprises an infrared imaging device adapted to receive infrared radiation emitted by the sample during DSC measurement and / or the housing comprises a window pane made of a material that is transparent to infrared radiation.

17. The apparatus of claim 16, wherein the infrared imaging device has a sensor that comprises 100 pixels or more.

18. The apparatus of claim 16 or claim 17, wherein the infrared imaging device is a thermal camera.

19. A cover for differential scanning calorimetry (DSC) of a sample, wherein the cover is made of a material that is transparent to infrared radiation.

20. The cover of claim 19, wherein the cover: - is substantially cylindrical, - has a diameter of from 2mm to 30mm, and - has a thickness of from 0.05mm to 5mm.

21. A kit for containing a sample during differential scanning calorimetry (DSC), the kit comprising: - a cover according to claim 19 or claim 20, and - a pan.

22. The kit of claim 21, wherein the pan is made of aluminium, alumina, copper, gold, graphite, quartz, stainless steel, titanium, and / or platinum.

23. The cover or the kit of any one of claims 19 to 22, wherein the cover consists of a material that is transparent to infrared radiation.

24. The apparatus, the cover or the kit of any one of claims 16 to 23, wherein the material that is transparent to infrared radiation is BaF2, CdTe, GaAs, Ge, thallium bromoiodide, ZnSe, ZnS, infrared plastic, and / or a glass of germanium, arsenic and selenium.

25. The apparatus, the cover or the kit of claim 24, wherein the material is zinc selenide.

Images