Heat flow rate determination for single sample differential scanning calorimeter

Abstract

A method and calorimeter system for reducing error in a measured sample heat flow rate due to interpan heat exchange is described. The method includes sensing a heat flow rate to or from a sample container placed on a sample calorimeter cell in a single sample differential scanning calorimeter sensor and sensing a reference heat flow rate to or from a reference container placed on a reference calorimeter cell in the single sample differential scanning calorimeter sensor. The temperature of the sample container and the temperature of the reference container are also sensed. An interpan heat exchange between the sample container and the reference container is determined. A sample heat flow rate with reduced error is determined based on the sensed heat flow rate from the sample container and the determined interpan heat exchange rate.

Description

[0001] Related applications

[0002] This application claims the benefit of an earlier filing date, U.S. Provisional Patent Application Serial No. 62 / 951,352, entitled “Heat Flow Rate Determination for a Single Sample Differential Scanning Calorimeter,” filed on December 20, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The following content relates to calorimetry, and more specifically to implementation schemes for heat flow measurement methods used with a single-sample differential scanning calorimeter. Background Technology

[0004] Differential scanning calorimetry (DSC) is a dynamic calorimetry method in which the temperatures of the sample and reference under study are programmed to change relative to time in a predetermined manner. Changes in sample temperature result in heat flowing into or out of the sample. Conventional DSC instruments, such as dual calorimeters, consist of two essentially identical calorimeters (i.e., a sample calorimeter and a reference calorimeter) housed in the same temperature-controlled calorimeter housing for measuring the heat flowing into and out of the sample. The sample to be analyzed is placed in a sample container mounted on the sample calorimeter, and an inert reference sample is placed in a reference container mounted on the reference calorimeter. In most cases, the reference container is empty. The heat flow rates of the sample and sample container are measured by the sample calorimeter, and the heat flow rates of the reference sample (if used) and reference container are measured by the reference calorimeter. The heat flow rate of the sample is obtained by subtracting the heat flow rate measured by the reference calorimeter from the heat flow rate measured by the sample calorimeter.

[0005] Conventional DSC instruments do not measure the heat exchanged between the sample container and the calorimeter housing because this heat does not pass through the sample calorimeter. Furthermore, the measured sample heat flow rate includes noise caused by unavoidable temperature fluctuations in the calorimeter housing. Considering that the sample, sample container, and sample calorimeter are nearly identical to the reference sample, reference container, and reference calorimeter, the heat exchanged between each sample container and the reference container and calorimeter housing will be approximately the same, and the noise in both the measured sample heat flow rate and the reference heat flow rate will be approximately the same. Therefore, when the measured reference heat flow rate is subtracted from the measured sample heat flow rate, the heat exchanged between the sample container and the calorimeter housing, as well as the noise, is almost completely eliminated.

[0006] Most conventional DSC instruments measure the sample heat flow rate by measuring the difference between the sample calorimeter temperature and the reference calorimeter temperature and dividing that temperature difference by a temperature dependent thermal resistance, which is shown by the following equation: q = -(Ts - Tr) / R(Ts), where q is the sample heat flow rate, Ts is the sample calorimeter temperature, Tr is the reference calorimeter temperature, and R(Ts) is the temperature dependent thermal resistance. The sample heat flow rate equation q = -(Ts - Tr) / R(Ts) is based on assumptions and simplifications that are often violated during implementation, and therefore, the measured heat flow rate does not correspond to the true sample heat flow rate. SUMMARY

[0007] In one aspect, a method for reducing errors in measured sample heat flow rates due to interpan heat exchange includes sensing a heat flow rate to or from a sample container placed on a sample calorimeter cell in a single sample DSC sensor and sensing a reference heat flow rate to or from a reference container placed on a reference calorimeter cell in the single sample DSC sensor. The temperature of the sample container and the temperature of the reference container are also sensed. An interpan heat exchange between the sample container and the reference container is determined. A sample heat flow rate with reduced error is determined and is based on the sensed heat flow rate from the sample container and the determined interpan heat exchange rate.

[0008] The interpan heat exchange can be determined according to:

[0009]

[0010] where T pr is the reference container temperature, T ps is the sample container temperature, R sr is the interpan thermal resistance defined between the reference container and the sample container, and is the interpan heat exchange rate. Additionally, the sample heat flow rate with reduced error can be determined according to:

[0011]

[0012] where is the heat flow rate measured by the sample calorimeter cell, is the heat flow rate measured by the reference calorimeter cell, m ps is the mass of the sample container, m pr is the mass of the reference container, is the derivative of the temperature of the sample container with respect to time, is the derivative of the temperature of the reference container with respect to time, and is the determined sample heat flow rate.

[0013] Determining the interpan heat exchange between the sample container and the reference container can include calculating the interpan heat exchange based on the sensed heat flow rate out of the sample container and the reference container and the sensed temperatures of the sample container and the reference container.

[0014] The method can further include heating a base of the single-sample DSC sensor, where the sample calorimeter cell and the reference calorimeter cell are disposed on the base. The temperature of the sample calorimeter cell is sensed using at least one thermocouple formed by an electrical junction between the platform and the detector of the sample calorimeter cell, and the temperature of the reference calorimeter cell is sensed using at least one thermocouple formed by an electrical junction between the platform and the detector of the reference calorimeter cell.

[0015] The interpan heat exchange can be achieved by at least one of conduction through a gas within a calorimeter housing of the single-sample DSC sensor, convection of the gas, and radiation between a surface of the sample container and a surface of the reference container.

[0016] In another aspect, a calorimeter system includes a DSC sensor and a computing system. The DSC sensor includes a base, a single-sample calorimeter cell attached to the base and configured to receive a sample container, and a reference calorimeter cell attached to the base and configured to receive a reference container. The computing system is in communication with the DSC sensor and is configured to determine an interpan heat exchange between the sample container and the reference container and determine a sample heat flow rate with reduced error based on a sensed heat flow rate out of the sample container and the interpan heat exchange.

[0017] The computing system can be configured to determine the interpan heat exchange according to:

[0018]

[0019] where T pr is the reference container temperature, T ps is the sample container temperature, R sr is an interpan thermal resistance defined between the reference container and the sample container, and is an interpan heat exchange rate. The computing system can be further configured to determine the sample heat flow rate with reduced error according to:

[0020]

[0021] where is a heat flow rate measured by the sample calorimeter cell, is a heat flow rate measured by the reference calorimeter cell, m ps is a mass of the sample container, m pr is a mass of the reference container, is the derivative of the temperature of the sample container with respect to time, is the derivative of the temperature of the reference container with respect to time, and is the measured sample heat flow rate.

[0022] The inter-pan heat exchange between the sample container and the reference container can be determined from the sensed heat flow rate out of the sample container, the sensed heat flow rate out of the reference container, the sensed temperature of the sample container, and the sensed temperature of the reference container.

[0023] The DSC sensor can also include a sample region thermocouple for measuring the temperature difference between the single-sample calorimeter cell and the base, and the sample region thermocouple can be formed by a detector connected to the underside of the platform of the single-sample calorimeter cell.

[0024] The DSC sensor can also include a reference region thermocouple for measuring the temperature difference between the reference calorimeter cell and the base, and the reference region thermocouple can be formed by a detector connected to the underside of the platform of the reference calorimeter cell. BRIEF DESCRIPTION OF DRAWINGS

[0025] The above advantages of the present application and other advantages not described herein can be better understood by reference to the following description taken in conjunction with the accompanying drawings, in which like reference numerals refer to the same elements and features in the various figures. Letters can be appended to reference numerals to distinguish between like features of similar elements and to indicate a correspondence in structure, usage or appearance between the like features of different figures. Not every element of the figures is labeled, for clarity. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the application.

[0026] Figure 1 is a schematic diagram of an embodiment of a multiple-sample DSC sensor.

[0027] Figure 2 is a schematic diagram of a DSC sensor of Figure 1

[0028] Figure 3 is a thermal network model of a DSC sensor of Figure 1

[0029] Figure 4 is a functional block diagram of a DSC heat flow rate measurement system.

[0030] Figure 5 is a graphical illustration of heat flow rate versus Figure 1 temperature of the base of a DSC sensor of

[0031] Figure 6 is a graphical illustration of a comparison of heat flow rate measurement methods from Figure 5 examples of​​

[0032] Figure 7 is a graphical illustration of heat flow rate versus temperature of a base of a DSC sensor according to another example. Figure 1

[0033] Figure 8 is a graphical illustration of a comparison of heat flow rate measurement methods from examples Figure 7

[0034] Figure 9 is a graphical illustration of results of a three-sample DSC experiment performed in a calorimeter DSC sensor according to another example Figure 1

[0035] Figure 10 is a schematic diagram of an embodiment of a single-sample DSC sensor

[0036] Figure 11 is a graphical illustration of heat flow rate versus time for an indium melt for a single-sample DSC sensor

[0037] Figure 12 is a graphical illustration of heat flow rate versus temperature of a sample pan of a single-sample DSC sensor as shown in Figure 11 DETAILED DESCRIPTION

[0038] Reference to "one embodiment" or "an embodiment" within this specification

[0039] ​​​​In a conventional dual sample DSC sensor (i.e., two sample calorimeters and one reference calorimeter), the calorimeter cells are positioned symmetrically at the vertices of an equilateral triangle within the calorimeter housing, which means that the distance between each sample container placed on top of the calorimeter cells is the same. When the heat flow from the reference calorimeter is subtracted from the heat flow to either sample calorimeter, the heat exchanged between any pair of sample containers in this symmetric arrangement is compensated. When additional calorimeter cells are added in a conventional dual sample DSC sensor to form a DSC sensor to analyze three or more samples, the symmetry between all sample containers is lost. As a result, cross-talk can appear in the measured sample heat flow rate. To reduce or eliminate such cross-talk, the heat flow rate signals from the multiple sample calorimeter cells and the reference calorimeter cell are used to determine the sample heat flow rate using a heat balance equation, which includes the heat transfer between the multiple sample containers and the reference container. U.S. Patent Application No. 16 / 454,951, filed June 27, 2019, and entitled “Multiple Sample Differential Scanning Calorimeter,” describes how the reduction and / or elimination of cross-talk is achieved by calculating the heat exchange between the multiple sample containers and the reference container placed on the multiple sample calorimeter cells and the reference calorimeter cell, respectively, and then using the calculated heat exchange between the multiple sample containers and the reference container to determine the heat flow rate of the sample within the sample container.

[0040] “Cross-talk” is described as a feature that appears on the DSC curve of one sample calorimeter that is caused by a thermal transition that occurs at another sample calorimeter. Cross-talk occurs through two different and independent heat transfer paths. The first heat transfer path is achieved through thermal conduction via the calorimetric sensor, and the second heat transfer path is the heat exchange between the sample container and the reference container by conduction and convection through the gas within the calorimeter housing and by radiation between the surface of the sample container and the surface of the reference container. While the first heat transfer path through the calorimetric sensor is typically of more concern, the second heat transfer path of cross-talk directly between the one or more sample containers and the reference container becomes significant because the cross-talk via the first heat transfer path is made sufficiently small by the conventional DSC sensor design and construction. Some embodiments disclosed herein relate to a single sample DSC that does not experience cross-talk due to the absence of additional samples. Such embodiments account for the inter-pan heat exchange between the single sample container and the reference container. The heat flow rate determined for the sample includes a term that accounts for the inter-pan heat exchange.

[0041] The existing heat flow measurement method is employed in some embodiments of the multi-sample DSC sensor to determine the heat flow rate between the calorimeter cells. One example of the existing heat flow measurement method (hereinafter referred to as the "conventional method" or "conventional heat flow measurement method") is disclosed in U.S. Patent No. 6,431,747 to Danley, which is hereby incorporated by reference. In the conventional heat flow measurement method, which is different from the existing heat flow measurement discussed in the Background section above, the single temperature (the temperature of the base of the DSC sensor) is measured, as well as two temperature differences: AT, the difference between the sample calorimeter temperature and the reference calorimeter temperature; and AT0, the difference between the base temperature and the sample calorimeter temperature. The heat flow rate of the sample calorimeter is measured using the conventional method according to the following equation:

[0042] ( Equation 1 ) and the reference heat flow rate is measured using the conventional method according to the following equation:

[0043] ( Equation 2 ) where Rs, Rr, Cs, and Cr are the thermal resistances and heat capacities of the sample and reference calorimeters, and Ts, Tr, and To are the temperatures of the sample and reference calorimeter cells and the base, respectively.

[0044] The thermal resistances and heat capacities of the sample and reference calorimeters are determined by a two-step calibration procedure (detailed in the '747 patent to Danley), in which the DSC instrument performs two identical calibration experiments, comprising a low temperature isothermal segment followed by a constant heating rate segment followed by a high temperature isothermal segment, where the temperature range of the calibration experiments is equal to or greater than the temperature range of subsequent experiments. The first experiment is performed with the calorimeters empty (e.g., no sample or reference, and no sample or reference containers). The second experiment is performed with only a calibration sample, with no sample containers on the sample and reference calorimeters, where the calibration sample is inert and its heat capacity is accurately known and its mass is accurately known. Typically, the calibration sample is a sapphire disc with a mass of about 100 mg.

[0045] Further, the sample heat flow rate is determined by taking the difference between the sample calorimeter heat flow rate and the reference calorimeter heat flow rate measured using (Equation 1) and (Equation 2), giving four heat flow rate equations:

[0046] ( Equation 3 ) Now, the thermal equilibrium is performed on the sample and reference containers, and eliminating the specific heat capacity of the sample container from the sample container thermal equilibrium equation gives a new heat flow rate measurement method that includes the difference in heating rates between the sample and reference containers in the measured sample heat flow rate according to the following equation:

[0047] ( Equation 4 ) where, mps and m pr is the mass of the sample container and the reference container, and and is the derivative of the temperature of the sample container and the reference container with respect to time. The temperature of the sample container and the reference container is determined using the following equations:

[0048] (Equation 5)

[0049] (Equation 6) where Rpsand Rprare the contact thermal resistances between the sample container and the sample calorimeter and between the reference container and the reference calorimeter. The temperatures of the sample calorimeter and the reference calorimeter are derived from the equations that define AT and AT0:

[0050] (Equation 7) Ts= To - AT0

[0051] (Equation 8) Tr= Ts- AT

[0052] While To, AT, and AT0are used in the preferred embodiment, any of the following three possible temperatures can be used for the temperature measurement: To, Ts, and Tr, and any of the following three possible temperature differences can be used for the two temperature difference measurements: Ts-Tr, To-Ts, and To-Tr. Thus, there are at least nine possible combinations of one temperature and two temperature differences that can be used.

[0053] Additionally, additional calorimeters can be added to the DSC sensor by extending the area of the base and adding additional calorimeter units. New heat flow measurement methods can be applied to the additional calorimeter units to account for heat exchange between the sample container and the reference container, reducing cross-talk.

[0054] The present teachings will now be described in more detail with reference to embodiments of the present teachings as illustrated in the accompanying drawings. While the present teachings are described in conjunction with various embodiments and examples, it should be understood that the present teachings are not limited to such embodiments. Rather, the present teachings cover various alternatives, modifications, and equivalents, as would be appreciated by one of ordinary skill in the art. One of ordinary skill in the art having access to the teachings herein will recognize additional specific implementations, modifications, and embodiments within the scope of the present disclosure, as well as other uses thereof.

[0055] Figure 1is a schematic diagram of an embodiment of a multi-sample DSC sensor 100. The sensor 100 includes four calorimeter cells 2, 3, 4, 5 arranged on a base 1 for analysis of three samples and a single reference. Calorimeter cells 3, 4, and 5 are sample calorimeter cells that receive sample containers, and calorimeter cell 2 is a reference calorimeter cell that receives a reference container. The calorimeter cells 2, 3, 4, 5 are positioned symmetrically with respect to the center of the base 1. However, each calorimeter cell is asymmetric with respect to at least two other calorimeter cells. For example, calorimeter cell 3 is farther from calorimeter cell 5 than calorimeter cell 4. The different distances between the sample containers placed on the calorimeter cells 2, 3, 4, 5 result in cross-talk due to heat exchange between the sample containers placed on the calorimeter cells 2, 3, 4, 5.

[0056] The structural configuration of the calorimeter cells is described herein with reference to calorimeter cell 5, which is shown in a cutaway view to illustrate features of the calorimeter cell; calorimeter cells 2, 3, 4 have the same structural configuration as calorimeter cell 5 and can be manufactured in the same way, so that the thermal properties of the calorimeter cells 2, 3, 4, 5 are well matched. In some embodiments, there are slight differences between the calorimeter cells 2, 3, 4, 5 due to inaccuracies in the manufacturing process. The calibration method described above takes these differences into account. Calorimeter cell 5 includes a tube 11 having a thickness of between 0.002 inches and 0.010 inches that is contiguous with (e.g., structurally integral with) the base 1. In a preferred embodiment, the thickness of the tube 11 is 0.005 inches. The tube 11 includes a platform 12 that forms the top surface of the tube 11. The platform 12 is a flat disc that is contiguous with (e.g., structurally integral with) the tube 11 and has a flat surface 13 that receives a sample container. The tube 11 provides thermal resistance to the flow of heat through the calorimeter cell 5, which creates a temperature difference that is measured during an experiment.

[0057] In addition, the calorimeter 5 includes a sample area temperature detector 14 that is connected to the platform 12. The detector 14 is a disc that is attached concentrically to the underside of the platform 12 that is opposite the flat surface 13 of the platform 12 that receives a sample container. The detector 14 is composed of E+ type nichrome alloy that has an opposite polarity to the thermocouple material that makes up the platform 12, the tube 11, and the base 1. The base 1, the tube 11, and the platform 12 are made of E type constantan thermocouple alloy and form the negative element of a differential temperature thermocouple. The contact between the detector 14 and the platform 12 forms a sample area thermocouple for measuring the temperature difference between the sample calorimeter cell and the base 1.

[0058] A lead 16, constructed of the same thermocouple material as the detector 14, is welded to the detector 14. As shown, the lead 16 is welded to a central portion 15 of the detector 14 that is concentric with the detector 14 and protrudes from the disc 14 in a direction opposite the platform 12. The detector 14 is welded to the underside of the platform 12 at sixteen equally spaced locations in a circular pattern concentric with the detector 14 and the platform 12, thereby forming sixteen thermocouple junctions in parallel between the platform 12 and the detector 14.

[0059] A reference zone temperature detector (not shown) is attached to the platform of the calorimeter cell 2 (i.e., the reference calorimeter cell). Like the detector 14, the reference zone temperature detector is a disc that is concentrically attached to the underside of the platform associated with the calorimeter cell 2; the detector is made of E+ type nickel-chromium alloy and has an opposite polarity to the thermocouple material that makes up the platform, tubes, and base 1. The contact between the reference zone detector and the platform 12 forms a reference zone thermocouple for measuring the temperature difference between the reference calorimeter cell and the base 1. A lead constructed of the same thermocouple material is welded to the reference zone temperature detector in the same manner as the detector 14. The reference zone temperature detector is welded to the underside of the platform at sixteen equally spaced locations in a circular pattern, thereby forming sixteen thermocouple junctions in parallel between the platform and the reference zone temperature detector. Thus, the DSC sensor 100 includes three sample zone thermocouples and a reference zone thermocouple for temperature measurements.

[0060] Furthermore, the base 1 is a heat source or sink for the flow of heat to or from the calorimeter cells 2, 3, 4, 5. For example, when the DSC sensor 100 is heated, almost all of the heat that flows to the calorimeter cells 2, 3, 4, 5 flows from the base 1, which is at a higher temperature than the calorimeter cells. Conversely, when the DSC sensor 100 is cooled, almost all of the heat that flows from the calorimeter cells 2, 3, 4, 5 flows to the base 1, which is at a lower temperature than the calorimeter cells 2, 3, 4, 5. Thus, the base 1 forms a thermodynamic barrier between the calorimeter cells 2, 3, 4, 5 to prevent the flow of heat by thermal conduction through the DSC sensor 100. The base 1 includes a top surface 6a and a bottom surface 6b. The bottom surface 6b is a flat surface that facilitates mounting of the DSC sensor 100 to Figure 1 The calorimeter housing encloses the calorimeter cells 2, 3, 4, 5 within the same temperature environment. The DSC sensor 100 is mounted to the calorimeter housing by brazing. The brazing of the DSC sensor 100 to the calorimeter housing ensures that the heat exchange between the calorimeter cells 2, 3, 4, 5 and other internal components and the calorimeter housing is uniform and repeatable, and also ensures that the temperature of the base 1 is close to the temperature of the calorimeter housing.

[0061] The DSC sensor 100 also includes mounting elements 7, 8. The mounting elements 7, 8 are provided at a central location on the base 1 to facilitate mounting of positive 9 and negative 10 thermocouple wires forming a base thermocouple for measuring the temperature To of the base 1. The mounting elements 7, 8 are each a disc-shaped element having a generally axial opening therethrough to allow a portion of the wires 9, 10 to pass therethrough. One of the thermocouple wires 9, 10 forms one leg of a temperature difference measurement, as described in more detail in Figure 2 .

[0062] Figure 2 is Figure 1 a schematic diagram of the thermocouples of the DSC sensor 100. The calorimeter units 2, 3, 4, 5 are additionally labeled R, A, B, and C to indicate the three sample calorimeter units (i.e., A, B, C) and the reference calorimeter unit (i.e., R). The letters A, B, C, and R appended to the reference numerals distinguish the numbers relating to the elements of the respective calorimeter 2, 3, 4, 5 from those described above with respect to the single calorimeter unit (i.e., calorimeter unit 5) in Figure 1 . Four temperature differences are measured; ΔTo is determined by measuring the voltage between the reference calorimeter area thermocouple and the base thermocouple, ΔT A is determined by measuring the voltage between the sample area thermocouple and the reference area thermocouple, ΔT B is determined by measuring the voltage between the sample area thermocouple and the reference area thermocouple, and ΔT C is determined by measuring the voltage between the sample area thermocouple and the reference area thermocouple. The temperature To is determined by measuring the voltage generated by the base thermocouple. The base 1 and tubes 11R, 11A, 11B, 11C, as well as platforms 12R, 12A, 12B, 12C are the negative elements of the thermocouples used to measure the temperature differences ΔTo, ΔT A , ΔT B , and ΔT C . The detectors 14R, 14A, 14B, 14C and leads 16R, 16A, 16B, 16C are the positive elements of the thermocouples used to measure the temperature differences ΔTo, ΔT A , ΔT B , and ΔT C . The positive thermocouple wire 9 and the negative thermocouple wire 10 form a base thermocouple attached to the base 1 measuring To. The temperature difference ΔTo is measured between the thermocouple wire 9 and the lead 16R, the temperature difference ΔT A is measured between the lead 16A and 16R, the temperature difference ΔT B is measured between the lead 16B and 16R, and the temperature difference ΔT C is measured between the lead 16C and 16R.

[0063] are measured to obtain ΔTo, ΔT A , ΔT B , and ΔTC and the value of the temperature T0 is used to calculate T R , T A , T B and T C according to the following formulae:

[0064] ( formula 9 ) ΔT0 = T0 - T R

[0065] ( formula 10 ) ΔT A = T A - T R

[0066] ( formula 11 ) ΔT B = T B - T R

[0067] ( formula 12 ) ΔT C = T C - T R

[0068] where T0 is the measured temperature of the base 1, T R is the measured temperature of the reference calorimeter unit 2, T A is the measured temperature of the sample calorimeter unit 3, T B is the measured temperature of the sample calorimeter unit 4 and T C is the measured temperature of the sample calorimeter unit 5. The signals T R , T A , T B and T C are considered to be combined signals because these values are not measured directly but are obtained by combining the measured signals.

[0069] Further temperatures and temperature differences are obtained by combining the measured electrical signals ΔT0, ΔT A , ΔT B and ΔT C according to the following formulae:

[0070] ( formula 13 )

[0071] ( formula 14 )

[0072] ( formula 15 )

[0073] ( formula 16 ) T R = T0 - ΔT0

[0074] ( formula 17 ) T A = T0 - ΔT 0A

[0075] ( Equation 18 ) T B = To - AT 0B

[0076] ( Equation 19 ) T C = To - AT 0C

[0077] where Ao is the temperature difference between base 1 and calorimeter unit 3, Ao is the temperature difference between base 1 and calorimeter unit 4, and Ao is the temperature difference between base 1 and calorimeter unit 5. The combination of a single temperature measurement and four temperature difference measurements can not be exclusive, and many other combinations of a single temperature measurement and four temperature difference measurements can be used to implement embodiments of the present invention, which can be similar to the nine combinations of a single temperature measurement and two temperature difference measurements according to conventional heat flow measurement methods.

[0078] Figure 3 is a thermal network model 200 of the DSC sensor 100. The thermal network model 200 shows how a heat flow rate measurement is made. The model elements include nodes that represent temperature, thermal resistance, and thermal capacitance. Thermal resistance represents a heat flow element, where heat flows through the thermal resistance according to the following equation:

[0079] ( Equation 20 )

[0080] where T x and T y are the temperatures at the terminals of the thermal resistance R (°C / W). Thermal capacitance represents a heat storage element, where the rate of heat storage is described by the following equation:

[0081] ( Equation 21 ) where C is the thermal capacitance (J / °C), and is the rate of change of temperature with respect to time for the thermal capacitance. The thermal capacitance is not explicitly shown in the thermal network model 200, but is connected to the calorimeter unit and sample container temperature nodes and the reference container temperature node. In the thermal model 200, To represents the temperature of the base 1 and is controlled by a temperature control module coupled to a computing system to follow a desired temperature trajectory for the experiment. To is measured between thermocouple wires 9 and 10 attached to the base 1 (see Figure 1 ). Thus, the temperature control module activates a heater to adjust the DSC enclosure temperature, which causes heat to flow through the thermal resistances depicted in the network model 200 to the sample inside the sample container and to be stored in the thermal capacitance. The temperature control module can also activate a cooling device attached to the DSC sensor 100, enabling operation below ambient temperature. The cooling device improves the cooling rate and temperature control when the desired temperature trajectory includes cooling the sample.

[0082] Ta, Tb, Tc, and Tr are the temperatures of the A, B, C, and R calorimeter units, measured by thermocouples formed by the junctions between detectors 14A, 14B, 14C, 14R and platforms 12A, 12B, 12C, and 12R. Temperatures T PA , T PB , T PC , and T PR are the temperatures of the A, B, C, and R sample containers and reference containers. Thermal resistances R A , R B , R C , and R R are the thermal resistances of the A, B, C, and R calorimeters, embodied primarily by tubes 11A, 11B, 11C, and 11R, respectively. C A , C B , C C , and C R (not shown) are the thermal capacitances of the A, B, C, and R calorimeters connected to the calorimeter temperature nodes. Since each component of DSC sensor 100 has the ability to store heat as it flows through DSC sensor 100, the thermal capacitances within thermal network model 200 are embodied by platforms 12A, 12B, 12C, 12R, detectors 14A, 14B, 14C, 14R, portions of tubes 11A, 11B, 11C, 11R, and portions of positive thermocouple leads 16A, 16B, 16C, 16R. R PA , R PB , R PC , and R PR represent the contact thermal resistances of calorimeter units A, B, C, and R to the respective sample containers and reference containers associated with calorimeter units A, B, C, and R. C PA , C PB , C PC , and C PR are the thermal capacitances of the sample containers and reference containers associated with calorimeter units A, B, C, and R. R AB , R AC , R AR , R BC , R BR , and R CR represent the thermal resistances between sample containers. The heat exchange between sample containers represented by these inter-pan thermal resistances R AB , R AC , R AR , R BC , R BR , and R CR is through a combination of thermal conduction of the gas in the calorimetric package and radiation between the sample container surface and the reference container surface. The inter-pan thermal resistances R AB , R AC , R AR , RBC , R BR , and R CR Convection of the gas is also included; however, based on the configuration of the DSC sensor 100, there is no contribution to the heat exchange by convection. The DSC sensor 100 determines the heat flowing into and out of the sample in the sample container associated with calorimeter cell 3, 4, 5, which is represented by the heat fluxes q sa , q sb , and q sc . The DSC sensor 100 is represented by the portion of the thermal network model 200 below the horizontal dashed line.

[0083] A heat balance is performed on each of the calorimeter temperature nodes to obtain the heat flow rate measurement equations for the four calorimeter cells A, B, C, and R. The equations are as follows:

[0084] (Equation 22)

[0085] (Equation 23)

[0086] (Equation 24)

[0087] (Equation 25)

[0088] The heat flow rates measured by the four calorimeter cells are equal to the heat flowing through the contact resistance R PA , R PB , R PC , and R PR between the calorimeter and the sample container:

[0089] (Equation 26)

[0090] (Equation 27)

[0091] (Equation 28)

[0092] (Equation 29) A further heat balance is performed on the sample container associated with calorimeter cell A, giving the following equation:

[0093] (Equation 30)

[0094] A heat balance is performed on the reference container associated with reference calorimeter cell B, and noting that q

[0095] (Equation 31)

[0096] The product of the container mass and the specific heat capacity of the container material is substituted into C PA and C PR The specific heat of the container material is eliminated from the sample container heat balance equation by solving for the container specific heat from the reference container heat balance equation and substituting it into the container specific heat in the sample container heat balance equation. The sum of the heat exchange between the sample container for sample container A and R are specified by the following equations, respectively:

[0097] (Equation 32)

[0098] (Equation 33) Thus, the equation for calculating the heat flow rate for the sample associated with calorimeter cell A becomes:

[0099] (Equation 34)

[0100] This equation is different from the one used in conventional heat flow measurements because it includes the heat exchanged between the sample container associated with calorimeter cell A and the other three sample containers, as well as the heat exchange between the sample container associated with reference calorimeter cell R and the other three sample containers. The new method and equations described herein impart the same performance advantages as the conventional heat flow measurement method, but also reduce cross-talk because the calorimeter cells are considered to be independent and the cross-talk caused by conduction through the DSC sensor 100, which includes the heat exchange between the sample and reference containers, is substantially eliminated, which is the main source of cross-talk.

[0101] Similar equations are written for the sample containers associated with calorimeter cells B and C, respectively, by replacing the A subscript with B and C, as shown in the following equations:

[0102] (Equation 35)

[0103] (Equation 36)

[0104] The equations for and have similar forms to those for and and are immediately written by inspection as follows:

[0105] (Equation 37)

[0106] (Equation 38)

[0107] The above equations are used to calculate the heat flow rate for the samples associated with the three sample calorimeter cells (i.e., A, B, C) and the reference calorimeter cell (i.e., R). The DSC sensor optionally includes more than three sample calorimeter cells. The interpan interpan heat flow rate between the sample containers of the “n” sample calorimeter cells and the reference container is represented as follows:

[0108] (Equation 39)

[0109] (Equation 40)

[0110] (Equation 41) and so on, up to calorimeter n:

[0111] (Equation 42)

[0112] where A is the temperature of the first sample container, B is the temperature of the second sample container, RAB is the thermal resistance between the first sample container and the second sample container, C is the temperature of the third sample container, RC is the thermal resistance between the first sample container and the third sample container, n is the temperature of the nth sample container, Rn is the thermal resistance between the first sample container and the nth sample container, T is the temperature of the reference container, and RA is the thermal resistance between the first sample container and the reference container. There can be any number of sample calorimeter units, including sample calorimeter units A, B, C, and a plurality of additional sample calorimeter units, up to n sample calorimeter units, where the variable“n” represents the last sample calorimeter unit in the sequence of sample calorimeter units. The ellipses represent a variable number of individual terms for calculating the heat flowing through the interpan thermal resistance of each sample container between sample calorimeter C and sample calorimeter n. For example, if the DSC sensor has five sample calorimeter units and a reference calorimeter unit, the interpan heat flow rate subscript E for the fifth sample container would be represented as follows:

[0113] (Equation 43)

[0114] where A is the temperature of the first sample container, E is the temperature of the fifth sample container, RE is the thermal resistance between the first sample container and the fifth sample container, T PB is the temperature of the second sample container, R BE is the thermal resistance between the second sample container and the fifth sample container, C is the temperature of the third sample container, RE is the thermal resistance between the third sample container and the fifth sample container, D is the temperature of the fourth sample container, DE is the thermal resistance between the fourth sample container and the fifth sample container, T is the temperature of the reference container, and RE is the thermal resistance between the fifth sample container and the reference container.

[0115] An alternative and more compact form of the equations for calculating the interpan heat flow rates of the sample containers associated with a plurality of sample calorimeter units and a reference calorimeter unit is An alternative formulation is for n sample containers on n sample calorimeter units and a reference container r on a reference calorimeter. The alternative formulation is expressed as follows:

[0116] (Formula 44) where i = 1, 2... n and j = 1, 2... n.

[0117] To employ the heat flow rate measurement formulation, the thermal resistance values between the sample containers and the reference container should be available for the heat flow rate calculation. The heat exchange between the sample containers and the reference container is by parallel heat conduction through the gas within the calorimeter enclosure and radiation between the containers. The heat exchange can also include gas convection; however, the configuration of the DSC sensor 100 substantially eliminates any contribution from convection. There are a total of six thermal resistances connecting four containers, with four having the same nominal value of four pairs of containers adjacent to each other, and the remaining two having the same nominal value of two pairs of containers opposite to each other at opposite corners of the square calorimeter array. The thermal resistances are temperature dependent and nonlinear because the thermal resistances depend on the thermal conductivity of the gas within the calorimeter enclosure, which varies nonlinearly with temperature. In addition, the thermal resistances are temperature dependent and nonlinear because radiation is included, and the radiation heat exchange is proportional to the difference between the fourth power of the absolute temperature of the sample containers, in addition to which the thermal emission rate of the container surfaces varies nonlinearly with temperature.

[0118] The thermal resistance values between the containers can be determined experimentally, where any suitable method including curve fitting, minimization or optimization methods, and trial and error are used to find the thermal resistance values that minimize the cross talk. Digital simulation methods can also be used to find the thermal resistance values. For example, finite element analysis can be used to calculate the thermal resistance values between the containers. In some embodiments, a combination of experiments and simulations can be used to determine the appropriate thermal resistances. The magnitude of the thermal resistances depends on the geometry, material properties of the heat transfer medium (i.e., the gas in the calorimeter enclosure), and the surface properties of the heat exchange surfaces. Therefore, different thermal resistances are needed when a different gas is used to purge the calorimeter enclosure, when sample containers with different geometries are used, and when containers constructed from different materials are used.

[0119] Figure 4is a schematic diagram of a DSC sensor in communication with a computing system 60. The computing system 60 has a processor for implementing a heat flow measurement method according to the embodiments described herein. The computing system 60 is a locally dedicated computer designed only to perform DSC experiments using a DSC sensor. Alternatively, the computing system 60 is a personal computer remotely coupled to a DSC sensor that runs various software applications specific to the DSC sensor. The computing system includes a temperature control module 61, a measurement module 62, and a heat flow measurement module 63. The modules 61, 62, 63 are a combination of one or more hardware-based modules and software-based modules. The hardware-based modules typically include independent components such as a chipset, a dedicated circuit, and one or more memory devices. The software-based modules typically include program code or are linked to program code containing specific programming instructions and are typically loaded into a memory device of a control unit or computing system. The temperature control module 61 is configured to vary and / or control the temperature of the susceptor 1 according to a predetermined temperature program over time according to the known heat flux DSC method. The temperature variation of the susceptor 1 causes a temperature variation of the sample in the sample container on top of the calorimeter unit, resulting in a heat flow to or from each sample. The measurement module 62 is configured to calculate the temperature and temperature differences from the voltage measured by the thermocouples of the DSC sensor. The thermocouples are in electrical communication with the computing system 60. The measurement module 62 communicates with an amplifier via an analog-to-digital conversion circuit for amplifying the voltage signal measured from the thermocouples. The heat flow measurement module 63 is configured to calculate the heat exchange between the sample container and the reference container respectively placed on the sample calorimeter unit and the reference calorimeter unit and determine the heat flow rate of the sample within the sample container. The computing system 60 outputs a DSC data file that can be analyzed using a data analysis program. Typically, the data analysis program creates a plot showing the heat flow rate versus temperature or time. The DSC curve output by the computing system determines the enthalpy of the sample, which additionally takes into account the heat exchanged between the containers.

[0120] Figure 5is a graphical illustration of heat flow rate versus temperature of the base 1. The graphical illustration shows the results for a 4.865 mg sample of indium in a 52.128 mg aluminum sample container on the sample calorimeter cell 3 of the DSC sensor 100. Empty sample containers with masses of 51.762 mg, 51.264 mg, and 51.731 mg were placed on the other calorimeter cells 2, 4, 5. The DSC including the calorimeter cells 2, 3, 4, and 5 was heated at 10 °C / min. The heat flow rates of the calorimeter cells 3, 4, 5 were measured with both the conventional heat flow rate measurement method and the new heat flow rate measurement method including the heat exchange between the sample container and the reference container. The heat flow rate was plotted versus T0, the temperature at the base 1. The heat flow rate curve 17 shows the heat flow rate of the calorimeter cell 3 measured using the conventional method. The heat flow rate curve 18 shows the heat flow rate of the calorimeter cell 3 measured using the new method including the heat exchange between the sample container and the reference container. The latent heat of fusion of the indium sample was found by determining the area enclosed by the heat flow rate curve and a straight baseline extending from a point on the heat flow rate curve before the onset of the peak to a point on the heat flow rate curve after the end of the peak. The area as a function of time determined by numerical integration equals the total energy absorbed by the sample during melting, which when divided by the sample mass gives the latent heat of fusion of the sample. The area between curve 18 and its baseline is larger than the area between curve 17 and its baseline. Using the method of the '747 patent the latent heat of fusion was found to be 27.13 J / g, and using the method including the heat exchange between the sample container and the reference container the latent heat of fusion was found to be 28.91 J / g. Compared to the known standard value of 28.71 J / g, i.e. the enthalpy of indium, the result using the new method is closer to the correct value than the result using the conventional method. This difference is the result of including the heat exchange between the sample container and the reference container which is not measured by the calorimeter cell 3. The heat flow rate curves 19 and 20 are the heat flow rates measured by the calorimeter cell 4 using the conventional method and the new method, respectively. The heat flow rate curves 21 and 22 are the heat flow rates measured by the calorimeter cell 5 using the conventional method and the new method, respectively. Because the sample containers on the calorimeters 4 and 5 are empty in this example, the heat flow rates measured by these two calorimeters should not be disturbed by the indium melt appearing in the sample on the calorimeter cell 3, i.e. there should be no cross-talk. The cross-talk is not obvious when plotted at full scale of the indium melt, but it is indeed present and can be seen by reducing the scale of the heat flow rate axis.

[0121] Figure 6 is a graphical illustration of heat flow rate measurements of the calorimeter cell 4 and the calorimeter cell 5 using the conventional method and the new method. The scale of the heat flow rate axis has been reduced to cover 400 μW, while Figure 5The full-scale indium melt plotted in the middle is 30 mW. Heat flow rate curve 19 represents the heat flow rate of calorimeter cell 4 measured using the conventional method, which shows a cross-talk peak of -0.1664 mW high, which is caused by the indium melt present on calorimeter cell 3. In contrast, Figure 4 The indium melt peak height for curve 17 in the middle is 19.255 mW, so the cross-talk is less than 1% of the calorimeter cell 3 measurement. Heat flow rate curve 20 represents the heat flow rate of calorimeter cell 4 measured using the new method, in which the heat exchange between the sample calorimeter vessel and the reference calorimeter vessel is included; there is no discernible cross-talk. Heat flow rate curve 21 represents the heat flow rate of calorimeter cell 5 measured using the conventional method; the cross-talk peak is -.0355 mW, which is 0.184% of the calorimeter cell 3 peak height. Heat flow rate curve 22 represents the heat flow rate of calorimeter cell 5 measured using the new method, and no discernible cross-talk reduction is shown. The reason why the new method does not reduce the cross-talk in this case is understood by considering the relative positions of the four calorimeter cells. Calorimeter cells 3 and 5 are adjacent to reference calorimeter cell 2, and calorimeter cell 4 is opposite reference calorimeter cell 2. Thus, the vessels of reference calorimeter cell 2 and calorimeter cell 4 are nearly identical in sum to the vessels of calorimeter cells 3 and 5, such that when the heat flow rate difference is calculated, the heat transfer between the sample vessel and the reference vessel of calorimeter cell 4 is almost completely cancelled out by the heat transfer between the sample vessel and the reference vessel of reference calorimeter cell 2, and no improvement is gained.

[0122] Figure 7 ​is a plot of heat flow rate versus temperature of the base 1. The plot shows the results for a 4.865 mg sample of indium in a 52.128 mg aluminum sample container on the DSC sensor 100 sample calorimeter cell 4. Empty sample containers with masses of 52.865 mg, 51.762 mg, and 51.731 mg were placed on calorimeter cells 3, 5, and 2, respectively. The DSC including calorimeter cells 2, 3, 4, and 5 was heated at 10 °C / min. The heat flow rate of calorimeter cells 3, 4, and 5 was measured using both the conventional heat flow measurement method and the new heat flow measurement method. The heat flow rate was plotted versus T0, the temperature at the base 1. Heat flow rate curve 23 shows the heat flow rate of calorimeter cell 4 measured using the conventional method. Heat flow rate curve 24 shows the heat flow rate of calorimeter cell 4 measured using the new method. The latent heat of fusion of the indium sample was found by determining the area enclosed by the heat flow rate curve and a straight baseline that extends from a point on the heat flow rate curve before the peak appears to a point on the heat flow rate after the peak ends. The area, which is determined by numerical integration over time, as the abscissa, equals the total energy absorbed by the sample during melting, which is divided by the sample mass to give the latent heat of fusion of the sample. The area between curve 24 and its baseline is greater than the area between curve 23 and its baseline. The latent heat of fusion was found to be 26.75 J / g using the conventional method and 28.27 J / g using the new method. The new method is closer to the correct value of 28.71 J / g, the known standard value for the enthalpy of indium, than the conventional method. This difference is a result of including the heat exchange between the sample container and the reference container that is not measured by calorimeter cell 4. Heat flow rate curves 25 and 26 are the heat flow rates measured by calorimeter cell 3 using the conventional method and the new method, respectively. Heat flow rate curves 27 and 28 are the heat flow rates measured by calorimeter cell 5 using the conventional method and the new method, respectively. Because the sample containers on calorimeter cells 3 and 5 are empty, the heat flow rates measured by these two calorimeters should not be disturbed by the indium melt appearing in the sample on calorimeter cell 4, i.e., there should be no cross-talk. The cross-talk is small but noticeable when plotted at full scale for the indium melt, and can be seen by reducing the scale of the heat flow rate axis.

[0123] Figure 8 is a plot of the heat flow rate measurements of calorimeter cells 3 and 5 using the conventional method and the new method. The scale of the heat flow rate axis has been reduced to cover 600 μW, while Figure 7 the full scale indium melt plotted in FIG. 5 is 30 mW. Heat flow rate curve 25 is the heat flow rate measured by calorimeter cell 3 using the conventional method, which shows a cross-talk peak of 0.0989 mW high, which is caused by the indium melt on the calorimeter cell. In contrast, Figure 7The indium melt peak height for the meso curve 23 was 18.192 mW, so the cross-talk was about 0.5% of the calorimeter cell 4 measurement. The heat flow rate curve 26 was the heat flow rate measured by the calorimeter cell 3 using the new method; there was no discernible cross-talk. The heat flow rate curve 27 was the heat flow rate for the calorimeter cell 5 measured using the conventional method, and the cross-talk peak was 0.148 mW. The cross-talk peak was 0.813% of the calorimeter cell 4 peak height. The heat flow rate curve 28 was the heat flow rate measured by the calorimeter cell 5 using the new method, and showed a cross-talk peak of 0.014 mW, a reduction of an order of magnitude. In this case, the size and shape of the cross-talk peak measured by the calorimeter cells 3 and 5 using the conventional method were similar. The calorimeter cell 4 with the indium sample was opposite the reference calorimeter cell 2 and adjacent to the calorimeter cells 3 and 5. Therefore, due to its mirrored position relative to the reference calorimeter cell 2 and the calorimeter cell 5, the cross-talk signal for the calorimeter cells 3 and 5 was nearly identical. In this case, when the heat exchange between the sample container and the reference container was included in the sum of the container heat flows and the sum was greater than the sum, the cross-talk peak was nearly eliminated.

[0124] Figure 9 is a graphical illustration of the results of a three sample DSC experiment performed using the four calorimeter DSC sensor 100. A 5.288 mg indium sample in a 51.576 mg aluminum sample container was mounted on the calorimeter cell 3, a 5.300 mg indium sample in a 51.608 mg aluminum sample container was mounted on the calorimeter cell 4, a 5.080 mg indium sample in a 52.258 mg aluminum sample container was mounted on the calorimeter cell 5, and an empty 51.731 mg aluminum sample container was mounted on the reference calorimeter cell 2. The DSC including the calorimeter cells 2, 3, 4, and 5 was heated at a rate of 10 °C / min, and the heat flow rate was measured according to the conventional method and the new method. The heat flow rate curves 29, 30, and 31 were the heat flow rates for sample A, sample B, and sample C measured using the method of the '747 patent. The heat flow rate curves 32, 33, and 34 were the heat flow rates measured by the calorimeter cells 3, 4, and 5 using the new method. The heat of fusion for the samples associated with the calorimeter cells 3, 4, and 5 measured using the conventional method was: 27.23 J / g, 27.17 J / g, and 26.94 J / g. The heat of fusion for the samples associated with the calorimeter cells 3, 4, and 5 measured using the new method was: 29.373 J / g, 29.29 J / g, and 28.05 J / g. All of the heat of fusion values measured using the new method were closer to the correct known standard value of 28.71 J / g than those measured using the conventional method. The improvement was obtained by including the heat exchange between the sample container and the reference container in the sum of the heat flow rate measurements.

[0125] Although the description provided above primarily relates to interpan thermal exchange as crosstalk for multiple sample DSCs, interpan thermal exchange also occurs in single sample DSCs. More specifically, such interpan thermal exchange occurs between the sample container and the reference container. Incorporating interpan thermal exchange as described below can be used to more accurately determine the heat flow rate in single sample DSCs.

[0126] Generally, in single sample DSCs, the uncalibrated enthalpy measurements for indium are a few percent lower than the true value. In some cases, the uncalibrated enthalpy measurements can be as low as 5%. The uncalibrated enthalpy measurements can be corrected by enthalpy calibration to produce an increased enthalpy value. Due to the low uncertainty of the enthalpy measurements, the accuracy of the correction value is generally within a few tenths of a percent. Furthermore, incorporating interpan thermal exchange in determining the heat flow rate of a single sample DSC can reduce the occurrence of baseline return overshoot.

[0127] Figure 10 is a diagram of an example of a single sample DSC sensor 200. The sensor 200 includes two calorimeter units 2 and 3 arranged on a base 1 and used to analyze a single sample relative to a reference. The calorimeter unit 2 is a reference calorimeter unit and receives a reference container, and the calorimeter unit 3 is a sample calorimeter unit and receives a sample container. Both the calorimeter unit 2 and the calorimeter unit 3 are present inside a common calorimeter housing. Figure 10 The structural components and features shown in Figure 1 the similar numbered components and features shown in

[0128] The single sample DSC sensor 200 can be part of a calorimeter system including a computing system such as Figure 4 shown. The computing system is in communication with the DSC sensor 200 and can be configured to calculate or otherwise determine parameters associated with various physical processes (e.g., temperature and heat transfer rates) associated with the operation of the DSC sensor 200. For example, the computing system can be configured to determine the interpan thermal exchange between the sample container and the reference container. The computing system can further be configured to determine a sample heat flow rate with reduced error based on the interpan thermal exchange.

[0129] With reference to equation 44, since there are only two pans in a single sample DSC, there is only one interpan thermal exchange term for determining the interpan heat flow rate:

[0130] (equation 45) Interpan Thermal Exchange is equal to the difference between the reference container temperature T pr and the sample container temperature T ps divided by the interpan thermal resistance R srIn some implementations, the container temperature is estimated in part based on the estimated disk contact resistance. To account for heat exchange between individual disks in a single-sample DSC, Add to the measured sample heat flow rate and subtract from the reference heat flow rate, and thus the sample heat flow rate If modifications are made to account for inter-disk heat exchange, the following shall apply:

[0131] (Formula 46)

[0132] Where m ps and m pr For the mass of the sample container and the mass of the reference container, and and These are the derivatives of the sample container temperature and the reference container temperature with respect to time, respectively.

[0133] If the distance between the disks is the same as the distance between adjacent disks in a multi-sample DSC, then the inter-disk thermal resistance of a single-sample DSC can be the same as the inter-disk thermal resistance of adjacent disks in a multi-sample DSC as described above. Alternatively, the inter-disk thermal resistance of a single-sample DSC can be calculated, for example, from a finite element model.

[0134] Figure 11 It uses TA purchased from Newcastle, Delaware. A graphical illustration of the heat flow rate of 4.861 mg indium melt measured by a Discovery 2500 DSC compared to the temperature of the calorimeter base. Figure 12 The same heat flow rate varies with the sample container temperature T. ps A diagram illustrating the changes. The diagram shows the symbols labeled... This set of measurement output data was determined according to the conventional heat flow measurement method disclosed in U.S. Patent No. 6,431,747. Another set of measurement output data shown in the figure is labeled as... It also indicates the heat flow rate considering inter-disk heat exchange between the sample disk and the reference disk, determined according to the method described in this paper.

[0135] Acquire multiple signals over time and use them to calculate, including inter-disk heat exchange. Heat flux rate. These signals include the sample heat flux rate q. s Reference heat flux rate q r Sample container temperature T ps and reference panel temperature T pr .

[0136] The results of the heat flux rate analysis include a peak height of 24.325 mW and an enthalpy of 27.91 Jg. and the heat flow rate analysis resulted in a peak height of 24.74 mW and an enthalpy of 28.79 Jg. As expected, when the inter-pan heat exchange was considered, a slight increase in the peak height and a significant improvement in the enthalpy were obtained. More specifically, the enthalpy derived from the measured output data was 0.28% higher than the correct value, while the enthalpy derived from the measured output data was 2.79% lower than the correct value. The increase in enthalpy present in the determination from the measured output data was similar to the increase observed in the determination using the multiple sample DSC with inter-pan heat exchange considered. Moreover, the inclusion of the inter-pan heat exchange effect in the calculation had no apparent effect on the baseline return overshoot.

[0137] While the disclosure has been described in connection with specific embodiments thereof, it will be readily appreciated by those skilled in the art that numerous alternatives, modifications and variations can be made thereto without departing from the scope of the application as set forth below. The preferred embodiments of the disclosure, as set forth hereinabove, are intended to be illustrative, not limiting. Various changes can be made without departing from the scope of the application as defined in the following claims. The claims are intended to cover all such changes and modifications as fall within the scope of the application.

Claims

1. A method for reducing errors in measured sample heat flow rates due to interpan flow, the method comprising: sensing, by a single sample differential scanning calorimeter sensor, a heat flow rate to or from a sample container placed on a sample calorimeter cell of the single sample differential scanning calorimeter sensor; sensing, by the single sample differential scanning calorimeter sensor, a reference heat flow rate to or from a reference container placed on a reference calorimeter cell of the single sample differential scanning calorimeter sensor; sensing, by a temperature detector, a temperature of the sample container; sensing, by the temperature detector, a temperature of the reference container; determining an interpan flow rate between the sample container and the reference container; and determining a sample heat flow rate with reduced error based on the sensed heat flow rate to or from the sample container and the determined interpan flow rate.

2. The method of claim 1, wherein determining an interpan flow rate is determined from: where T pr is the reference vessel temperature, T ps is the sample vessel temperature, R sr is the inter-pan thermal resistance defined between the reference vessel and the sample vessel, and is the inter-pan heat exchange flow rate.

3. The method of claim 2, wherein determining a sample heat flow rate with reduced error is determined from: wherein is a heat flow rate measured by the sample calorimeter unit, is a heat flow rate measured by the reference calorimeter unit, m ps is a mass of the sample container, m pr is a mass of the reference container, is a derivative of the temperature of the sample container with respect to time, is a derivative of the temperature of the reference container with respect to time, and is a determined sample heat flow rate.

4. The method of claim 1, wherein determining an inter-dish heat exchange flow rate between the sample container and the reference container comprises: calculating the interpan flow rate based on the sensed heat flow rates from the sample container and the reference container and the sensed temperatures of the sample container and the reference container.

5. The method of claim 1, further comprising: heating a base of the single sample differential scanning calorimeter sensor, wherein the sample calorimeter cell and the reference calorimeter cell are disposed on the base; sensing a temperature of the sample calorimeter cell using at least one thermocouple formed by an electrical junction between a platform and a detector of the sample calorimeter cell; and sensing a temperature of the reference calorimeter cell using at least one thermocouple formed by an electrical junction between a platform and a detector of the reference calorimeter cell.

6. The method of claim 1, wherein the interpan flow rate is achieved by at least one of conduction through a gas within a calorimeter housing of the single sample differential scanning calorimeter sensor, convection of the gas, and radiation between a surface of the sample container and a surface of the reference container.

7. A calorimeter system, the calorimeter system comprising: a differential scanning calorimeter sensor, the differential scanning calorimeter sensor comprising: a base; a single sample calorimeter cell attached to the base and configured to receive a sample container, and a reference calorimeter cell attached to the base and configured to receive a reference container; and a temperature detector. a computing system in communication with the differential scanning calorimeter sensor, wherein the computing system is configured to: determine an inter-pan heat exchange flow rate between the sample container and the reference container, and determine a sample heat flow rate with reduced error based on the sensed heat flow rate to or from the sample container and the inter-pan heat exchange flow rate.

8. The calorimeter system of claim 7, wherein the computing system is configured to determine the inter-pan heat exchange flow rate as a function of: where T pr is the reference vessel temperature, T ps is the sample vessel temperature, R sr is the inter-pan thermal resistance defined between the reference vessel and the sample vessel, and is the inter-pan heat exchange flow rate.

9. The calorimeter system of claim 8, wherein the computing system is configured to determine the sample heat flow rate with reduced error as a function of: wherein is a heat flow rate measured by the sample calorimeter unit, is a heat flow rate measured by the reference calorimeter unit, m ps is a mass of the sample container, m pr is a mass of the reference container, is a derivative of the temperature of the sample container with respect to time, is a derivative of the temperature of the reference container with respect to time, and is a measured sample heat flow rate.

10. The calorimeter system of claim 7, wherein the inter-pan heat exchange flow rate between the sample container and the reference container is determined as a function of the sensed heat flow rate to or from the sample container, the sensed heat flow rate to or from the reference container, the sensed temperature of the sample container, and the sensed temperature of the reference container.

11. The calorimeter system of claim 7, wherein the differential scanning calorimeter sensor further comprises a sample region thermocouple for measuring a temperature difference between the single sample calorimeter cell and the base, the sample region thermocouple formed by a detector connected to an underside of a platform of the single sample calorimeter cell.

12. The calorimeter system of claim 7, wherein the differential scanning calorimeter sensor further comprises a reference region thermocouple for measuring a temperature difference between the reference calorimeter cell and the base, the reference region thermocouple formed by a detector connected to an underside of a platform of the reference calorimeter cell.

Images