CALIBRATION METHOD FOR A DIFFERENTIAL SCANNING CALORIMETER

Abstract

A differential scanning calorimeter includes a temperature-controlled heat source and a sensor arrangement with sample- and reference-side pan support regions and measurement regions. Measurement region sensor(s) output a differential heat flow signal representative of a difference between heat flowing across the sample- and reference-side measurement regions and a sample- and reference-side local heater arrangement. A sample and reference pan are arranged on the sample and reference-side pan support region, respectively. A volume surrounding the pans is filled with a measuring gas. A steady state situation of a desired temperature is created, and once reached, heating power is applied to one of the pan support regions using the respective local heater arrangement. A second calibration factor is determined based on a ratio of a differential heat flow signal (U) and a differential heating power.

Claims

1. A method for determining a second calibration factor C.sub.E of a differential scanning calorimeter, wherein the differential scanning calorimeter comprises: a. a temperature-controlled heat source; b. a sensor arrangement, whereby the sensor arrangement comprises: i. sample-side and reference-side pan support regions adapted to receive thereon, in heat conductive contact therewith, a bottom region of a sample pan and a reference pan, respectively; ii. sample-side and reference-side measurement regions, surrounding the sample-side and the reference-side pan support regions, respectively, and 1. a sample-side and reference-side measurement region sensor operative to output a differential heat flow signal (U) representative of a difference between heat flowing across the sample-side and reference-side measurement regions; and/or 2. a sample-side measurement region sensor operative to output a sample-side heat flow signal (U.sub.S) representative of the heat flowing across the sample-side measurement region and a reference-side measurement region sensor operative to output a reference-side heat flow signal (U.sub.R) representative of the heat flowing across the reference-side measurement region; iii. a sample-side and reference-side local heater arrangement adapted to apply heating power to the sample-side and the reference-side pan support regions, respectively; and c. whereby a sample pan of a desired pan type is arranged on the sample-side pan support region and a reference pan of the same desired pan type is arranged on the reference-side pan support region, whereby a volume surrounding the sample and the reference pan is filled with a desired measuring gas; and wherein said the method comprises the steps of: a. creating a first steady state situation of a desired temperature by use of the heat source; b. once the first steady state is reached, applying heating power to either the sample-side pan support regions or to the reference-side pan support region by the use of the respective local heater arrangement such that a second steady state is reached; and c. determining the second calibration factor based on the ratio of: i. the differential heat flow signal U, either measured directly or determined to be the difference between the sample-side and the reference-side heat flow signal U=U.sub.S?U.sub.R; and ii. the differential heating power, which is the difference between the heating power applied to the sample-side and the heating power applied to the reference-side, during the second steady state.

2. The method of claim 1, wherein: a. the sample-side and the reference-side local heater arrangement are electrical heater arrangements; and b. the heating power applied to the sample-side and the reference-side, respectively, is determined by a measurement of the electrical voltage and the electrical current between two terminals of the respective electrical heater arrangement.

3. A self-calibrating differential scanning calorimeter suitable to determine a second calibration factor C.sub.E using the method of claim 1, said differential scanning calorimeter comprising: a. a temperature-controlled heat source; b. a sensor arrangement, whereby the sensor arrangement comprises: i. sample-side and reference-side pan support regions adapted to receive thereon, in heat conductive contact therewith, a bottom region of a sample pan and a reference pan, respectively; ii. sample-side and reference-side measurement regions, surrounding the sample-side respectively the reference-side pan support regions, and 1. a sample-side and reference-side measurement region sensor operative to output a differential heat flow signal (U) representative of a difference between heat flowing across a sample-side and reference-side measurement region; and/or 2. a sample-side measurement region sensor operative to output a sample-side heat flow signal representative of the heat flowing across the sample-side measurement region and a reference-side measurement region sensor operative to output a reference-side heat flow signal representative of the heat flowing across the reference-side measurement region; iii. a sample-side and a reference-side local heater arrangement adapted to apply heating power to the sample-side respectively the reference-side pan support region; and c. a data evaluation unit configured to receive the differential heat flow signal U and/or the sample-side and the reference-side heat flow signals and signals indicating the differential heating power and/or the heating power applied to the sample-side respectively the reference-side; and d. wherein the data evaluation unit comprises a memory with a set of instructions, which when executed, configure the self-calibrating differential scanning calorimeter to execute the method of claim 1 to determine the second calibration factor C.sub.E.

4. The self-calibrating differential scanning calorimeter of claim 3, wherein: the data evaluation unit is configured to access a first default calibration factor C.sub.Hd, which depends on the pan type, the measurement gas and the temperature.

5. The self-calibrating differential scanning calorimeter of claim 3, wherein: the sensor arrangement is arranged in a volume which is surrounded by the same temperature-controlled heat source.

6. A method for determining a conversion factor (F) with a differential scanning calorimeter which is a self-calibrating differential scanning calorimeter according to claim 3, said method comprising the steps of: a. executing the method of claim 1 to determine the second calibration factor C.sub.E at the first desired temperature whereby the pan comprises a calibration sample which is known to undergo an exothermic or endothermic transition at a transition temperature which is different from the first desired temperature; b. controlling the heat source such that the transition temperature is achieved and the transition of the sample takes place while no heat is applied by the sample-side or the reference-side local heater arrangement; c. integrating the differential heat flow signal U, during the transition of the calibration sample and comparing this result with the theoretical enthalpy of the transition of the calibration sample; and d. storing the ratio of the first and the second calibration factor (C.sub.H/C.sub.E) as the conversion factor F.

7. A method for determining the conversion factor (F) with a differential scanning calorimeter which is a self-calibrating differential scanning calorimeter according to claim 3, said method comprising the steps of: a. executing the method of claim 1 to determine a second calibration factor C.sub.E at a third temperature; b. accessing the first default calibration factor C.sub.Hd for the pan type, and the measuring gas; and c. storing the ratio of the first default and the second calibration factor (C.sub.Hd/C.sub.E) as the conversion factor F.

8. A method for determining a conversion factor (F) for a given pan type to be arranged in a given furnace at a sample-side pan support region, to be used by a differential scanning calorimeter, which uses the pan type, the furnace as temperature-controlled heat source, and the sample-side pan support region, said method comprising the steps of: a. estimating a geometric factor (g.sub.L) which is the thermal resistance between a pan of the given pan type arranged on the sample-side pan support region and the furnace, assuming the thermal conductivity of the gas equals 1; and b. estimating a value of the conversion factor F based on a geometric factor (g) and a radius (r) of a bottom of the pan type.

9. A method for evaluating a heat flow to or from a sample in a sample pan using a differential scanning calorimeter, said method comprising the steps of: a. placing the sample in the sample pan of a pan type, placing the sample pan on a sample-side pan support region, placing an empty reference pan of the same pan type on a reference-side pan support region; b. controlling a temperature-controlled heat source such that it follows a desired temperature program; c. measuring or determining a differential heat flow signal (U) while no heat is applied by a sample-side or the reference-side local heater arrangement; and d. estimating the heat flow to or from the sample using a differential heart flow signal (U), a conversion factor (F) and a second calibration factor C.sub.E, whereby the conversion factor F is chosen depending on the pan type, while the second calibration factor C.sub.E is chosen depending on the pan type, the measurement gas and the temperature of the measurement.

10. The method of claim 9, wherein: the second calibration factor C.sub.E is determined using the method of claim 1 without removing the sample pan or the reference pan between the determination of C.sub.E and the evaluation of the heat flow.

11. The method of claim 9, wherein: a. the conversion factor F is chosen depending on the pan type and the temperature of the temperature-controlled heat source; and b. the measurement gas is selected by choosing a second calibration factor C.sub.E which is determined with a pan of the pan type, the measurement gas and the temperature of the temperature-controlled heat source.

12. A method for evaluating a heat flow to or from a sample in a sample pan using a differential scanning calorimeter, said method comprising: an evaluation step; and at least one calibration step and a measurement step which are both conducted using a same pan type and a same measurement gas; wherein the calibration step comprises: i. placing the sample pan which comprises a calibration sample which is known to undergo an exothermic or endothermic transition at a transition temperature on a sample-side pan support region and an empty reference pan of the same pan type on a reference-side pan support region; ii. controlling a temperature-controlled heat source such that a transition temperature is achieved and that a transition of the sample takes place while no heat is applied by a sample-side or a reference-side local heater arrangement; and iii. integrating a differential heat flow signal (U) during the transition of the calibration sample and comparing this result with a theoretical enthalpy of the transition of the calibration sample; wherein the measurement step comprises: i. placing the sample pan which comprises a sample of a material of interest on the sample-side pan support region and an empty reference pan of the same pan type on the reference-side pan support region; ii. controlling the temperature-controlled heat source such that it follows a desired temperature program while no heat is applied by the sample-side or the reference-side local heater arrangement; and iii. observing the differential heat flow signal U; wherein the evaluation step comprises estimating the heat flow to or from the sample of the material of interest from the differential heat flow signal U and the result of the comparison of the calibration step.

13. A method for evaluating a heat flow to or from a sample in a sample pan using a differential scanning calorimeter which is a self-calibrating differential scanning calorimeter according to claim 3, said method comprising the steps of: a. placing the sample in the sample pan of a pan type, placing the sample pan on a sample-side pan support region, placing an empty reference pan of the same pan type on a reference-side pan support region; b. controlling a temperature-controlled heat source such that it follows a desired temperature program; c. controlling a sample-side and reference-side local heater arrangements such that an absolute value of a differential heat flow signal (U) is minimized; d. measuring or determining a differential heating power P.sub.el as well as the differential heat flow signal U; and e. estimating the heat flow to or from the sample using the differential heat flow signal U and the differential heating power P.sub.el, a conversion factor F and a second calibration factor C.sub.E, whereby the conversion factor F is chosen depending on the pan type, while the second calibration factor C.sub.E is chosen depending on the pan type, the measurement gas, and the temperature of the measurement.

14. The method of claim 13 wherein: the differential heating power P.sub.el is controlled by a proportional controller with a gain k.sub.p to minimize the absolute value of the differential heat flow signal U.

15. The method of claim 13, wherein: the second calibration factor C.sub.E is determined using the method of claim 1 without removing the sample pan or the reference pan between the determination of C.sub.E and the evaluation of the heat flow.

16. A method of evaluating a heat flow to or from a sample in a sample pan using a differential scanning calorimeter, said method comprising: at least one calibration step and a measurement step, which are both conducted using a same pan type and a same measurement gas; and an evaluation step which is conducted after the calibration and the measurement step; wherein the calibration step comprises: i. placing the sample pan which comprises a calibration sample which is known to undergo an exothermic or endothermic transition at a transition temperature on a sample-side pan support region and an empty reference pan of the same pan type on a reference-side pan support region; ii. determining a second default calibration factor C.sub.Ed; iii. controlling a heat source such that a transition temperature is achieved and a transition of the sample takes place while local heaters are controlled to minimize a differential heat flow signal (U); iv. measuring or determining a differential heating power P.sub.el as well as the differential heat flow signal U during the transition of the sample; v. integrating, over a time of the transition of the sample, a difference (U?P.sub.elC.sub.Ed) between: 1. the differential heat flow signal U; and 2. a product of the second default calibration factor C.sub.Ed with the differential heating power P.sub.el (P.sub.elC.sub.Ed); and vi. comparing the integral with a theoretical enthalpy of the transition of the calibration sample; wherein the measurement step comprises: i. placing the sample pan which comprises a sample of a material of interest on the sample-side pan support region and an empty reference pan of the same pan type on the reference-side pan support region; ii. controlling the temperature-controlled heat source such that it follows a desired temperature program; iii. controlling the sample-side and the reference-side local heater arrangements such that the absolute value of the differential heat flow signal U is minimized; and iv. measuring or determining the differential heating power P.sub.el as well as the differential heat flow signal U; wherein the evaluation step comprises estimating the heat flow to or from the sample P.sub.s using the differential heating power P.sub.el, the differential heat flow signal U, the default second calibration factor C.sub.Ed and the result of the comparison of the calibration step.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0141] FIG. 1 is a highly schematic illustration of a self-calibrating differential scanning calorimeter; and

[0142] FIG. 2 is a corresponding thermal circuit model.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

[0143] The illustration of FIG. 1 is a highly schematical partial cross-section of a self-calibrating differential scanning calorimeter in a plane that extends normal to the horizontally extending pan support regions 4r. As an example of a temperature-controlled heat source, a furnace 1 forming a heat source whose temperature T.sub.F is controlled in accordance with a predetermined temperature program is shown and appears as a rectangle surrounding a volume enclosing the sensor arrangement. The sensor arrangement comprises a sample side S and a reference side R which differ only by the presence of a sample 7 inside the pan 2s of the sample side S. The self-calibrating differential scanning calorimeter comprises further a data evaluation unit 10.

[0144] To avoid crowded figures, most of the reference signs are only shown at the reference side of the sensor arrangement, but the respective structure is present at the sample side too. Similarly, the heat flows are illustrated at the sample side but apply the same way to the reference side.

[0145] The sensor arrangement 9 comprises the sample-side and reference-side pan support regions 4r, the sample-side and a reference-side measurement regions comprising thermoelectric arrangements operative to output at least one thermoelectric voltage signal representative of a heat flow 6m across a measurement region 5r surrounding the respective pan support region 4r. The sensor arrangement 9 comprises further the sample-side and a reference-side local heater arrangements in the form of electrical heater arrangements 3r.

[0146] A pan 2s, 2r adapted to receive therein a sample 7, which is the substance to be analysed, is supported by the thermally conductive pan support region 4r which is part of the sensor arrangement 9. The sensor arrangement 9 is in thermal contact with the furnace 1. The measurement regions 5r are arranged in such a way that the mechanical contact between the furnace 1 and the sensor arrangement 9 is only established by one end of the measurement regions 5r while the other end of the measurement regions 5r is a region in thermal contact with the electrical heater arrangement 3r and the pan support regions 4r.

[0147] A thermally conductive member, formed by the measurement regions 5r, thereby establishes a heat flow path 6m between the furnace 1 and the pan support region 4r. This heat flow path 6m will be called measurement heat flow path 6m in the following and its properties are denoted with a subscript m.

[0148] Circles drawn in the measurement region 5 symbolize thermoelectric junctions located at turning regions of a thermoelectric arrangement meandering around the pan position. Due to this configuration, the thermoelectric arrangement generates a thermoelectric voltage signal representative of the measurement heat flow 6m flowing thereacross. This thermoelectric voltage signal is an embodiment of a heat flow signal. The thermoelectric arrangement is an embodiment of a measurement region sensor.

[0149] The electrical heater arrangements 3r are located beneath the respective pan support region 4r. A straight arrow symbolizes heat flow from the region of the electrical heater arrangement 3r towards the respective pan 2r, 2s. This heat flow path 6k will be called contact heat flow path 6k in the following and its properties are denoted with a subscript k.

[0150] Besides the measurement heat flow 6m and the contact heat flow 6k, the respective pan 2s, 2r is in thermal contact with the furnace 1 via the measurement gas 8 which fills the volume between the sensor arrangement 9 and the pans 2 and the furnace 1. This heat flow path 6l is also indicated by a straight arrow. It will be called gas heat flow path 6l in the following and its properties are denoted with a subscript l.

[0151] In a typical differential scanning calorimeter, the overall arrangement is on both, the sample and the reference side, axially symmetric with respect to a central axis normal to the respective pan support region 4r so that both, the sample side and the reference side pan support regions 4r have a circular outer circumference and the respective thermoelectric arrangement meanders between an inner concentric circle of thermoelectric junctions and an outer concentric circle of thermoelectric junctions forming thereby sample-side and reference side measurement regions 5r which appear in the projection ring-shaped and surrounding the respective pan support region.

[0152] Each of the sample-side and reference-side portions of the calorimeter may be modelled as the circuit diagram illustrated in FIG. 2. The model uses the analogy between electrical and thermal systems: Temperature differences are modelled as voltages; heat flows are modelled as currents. Thermal resistances are modelled as electrical resistances while heat capacities are modelled as electrical capacitors. A heater producing heating power is modelled as a current source. A temperature-controlled heat source has a similar function as a ground in an electric circuit.

[0153] The representations of the different parts of the self-calibrating differential scanning calorimeter are denoted with dashed reference numbers of the respective parts.

[0154] In this circuit diagram T.sub.F indicates the temperature of the furnace 1 and T.sub.T the temperature of the sample/reference pan 2. T.sub.m indicates the temperature of the pan support region 4. The measurement heat flow 6m between the furnace 1 and the pan support region 4 experiences a measuring resistance R.sub.m and is driven by the temperature difference between the furnace temperature level T.sub.f and pan support region temperature level T.sub.m. Parallelly connected thereto is the heat capacity C.sub.m of the measurement region 5r.

[0155] Thermal contact resistance R.sub.k characterizes the contact heat flow between the pan support region with the temperature T.sub.m and the pan with the pan temperature T.sub.T. This thermal contact resistance R.sub.k is dominated by an unavoidable gap between the pan support region and the pan deposited thereon. It is the contact heat flow path 6k which experiences the contact resistance R.sub.k.

[0156] Gas resistance R.sub.L characterizes the gas heat flow path 6l between furnace 1 with the furnace temperature T.sub.f and the pan with the pan temperature T.sub.T. The gas resistance R.sub.L depends on the geometry of the calorimeter and the measurement gas 8. Connected in parallel to the gas resistance R.sub.L is the heat capacitance C.sub.T of sample/reference pan 2.

[0157] P*.sub.el represents the flow of heat supplied to the sample/reference position or the heating power created by energizing the electrical heater arrangement 3. P.sub.s symbolizes heat flow caused by a sample 7 received within the sample pan 2s. P*.sub.DSC measures the measuring heat flow 6m through the measuring resistance R.sub.m.

[0158] The heat flow signal U.sub.s respectively U.sub.r or a differential heat flow signal U=U.sub.s?U.sub.r generated by the respective or both measurement regions, preferably by thermoelectric arrangements, is one of the raw measurement results and the basis to determine the desired properties of the sample 7. Another raw measurement result can be the heat flow P*.sub.el produced by energizing the electrical heater arrangement 3.

[0159] The model shown in FIG. 2 can be used for both, the sample and the reference side. The two sides differ only by the fact that there is no sample of the reference side and that therefor P*.sub.S=0 on the reference side while P*.sub.S=P.sub.S on the sample side.

[0160] In the following, P.sub.el,s and P.sub.el,r refer to the heating power produced by energizing the electrical heater arrangement 3 at the sample respectively at the reference side, i.e., P*.sub.el=P.sub.el,r on the reference side and P*.sub.el=P.sub.el,s on the sample side. In the following P.sub.el should denote the differential heating power produced by energizing the electrical heater arrangements, i.e., P.sub.el=P.sub.el,s?P.sub.el,r.

[0161] In the following, P.sub.DSCs and P.sub.DSCr refer to heat flow at the sample respectively at the reference side, i.e., P*.sub.DSC=PDSCr on the reference side and P*.sub.DSC=P.sub.DSCs on the sample side. In the following P.sub.DSC should denote the differential heat flow, i.e., P.sub.DSC=P.sub.DSCs?P.sub.DSCr.

[0162] The following equations

[00011]$\begin{array}{cc}{C}_T{\stackrel{?}{T}}_T=-\frac{T_T-T_m}{R_k}-\frac{T_T-T_F}{R_L}+P_S^{*}& \mathrm{Equation}1\end{array}$$\begin{array}{cc}{C}_m{\stackrel{?}{T}}_m=\frac{T_T-T_m}{R_k}-\frac{T_m-T_F}{R_m}+P_{el}^{*}& \mathrm{Equation}2\end{array}$ [0163] describe the heat balance in this thermal circuit model. In the steady state the time derivatives of the furnace and sample-side pan support region temperatures T.sub.T and T.sub.m, respectively, are zero. Further considering that according to Ohm's Law

T.sub.m?T.sub.F=P.sub.DSC.sup.*R.sub.m Equation 3 [0164] the above equations (1) -(3) may be combined to yield

[00012]$\begin{array}{cc}{P}_S^{*}=P_{DSC}^{*}\left(1+\frac{R_m+R_k}{R_L}\right)-P_{el}^{*}\left(1+\frac{R_k}{R_L}\right)& \mathrm{Equation}4\end{array}$

[0165] In one embodiment of the invention, the sample-side and the reference-side electrical heater arrangement are controlled to minimize the differential measurement heat flow. If this control is perfect, P.sub.DSC=P.sub.DSC,s?P.sub.DSC,r=0. As there is no sample on the reference side, it cannot produce any heat and therefore, P.sub.S.sup.*=0 on the reference side. These relationships allow equation (4) to be expressed using the differential heating power P.sub.el of the electrical heater arrangements (P.sub.el=P.sub.el,s?P.sub.el,r):

[00013]$\begin{array}{cc}{P}_s=-P_{el}\left(1+\frac{R_k}{R_L}\right)& \mathrm{Equation}5\end{array}$

[0166] In another embodiment of the invention, neither the sample-side nor the reference-side electrical heater arrangements are energized. In this case P.sub.el.sup.*=P.sub.el,s=P.sub.el,r=0. As there is no sample on the reference side, it cannot produce any heat and therefore, P.sub.S.sup.*=0 on the reference side. These relationships allow equation (4) to be expressed using the differential heat flow (P.sub.DSC=P.sub.DSC,s?P.sub.DSC,r):

[00014]$\begin{array}{cc}{P}_S=P_{DSC}\left(1+\frac{R_m+R_k}{R_L}\right)& \mathrm{Equation}6\end{array}$

[0167] In a further embodiment of the invention, the sample-side and the reference-side electrical heater arrangements are energized, but not sufficient to reduce the differential heat flow through the measurement regions to be negligibly small. In these cases, equation (4) yields:

[00015]$\begin{array}{cc}{P}_S=P_{DSC}\left(1+\frac{R_m+R_k}{R_L}\right)-P_{el}\left(1+\frac{R_k}{R_L}\right)& \mathrm{Equation}7\end{array}$

[0168] Finally, in the absence of heat produced by a sample (P.sub.S.sup.*=0 on both, sample and reference side) but in the presence of heating power produced by the local heating arrangement only, on either the reference or the sample side, the following relationship result from equation (7):

[00016]$\begin{array}{cc}{P}_{DSC}\left(1+\frac{R_m+R_k}{R_L}\right)=P_{el}\left(1+\frac{R_k}{R_L}\right)& \mathrm{Equation}8\end{array}$$\mathrm{or}{P}_{el}=P_{DSC}\left(\frac{R_l+R_m+R_k}{R_L+R_k}\right)$

[0169] In order to evaluate the expression (5) to (7) however, calibration factors are needed to describe on the one hand the different thermal resistances terms and on the other hand, link the measured or determined differential heat flow signal U to the differential heat flow P.sub.DSC.

[0170] The first calibration factor may be written as the ratio of the differential heat flow signal U detected while measuring a transition of an established reference substance as a sample and the know heat flow value P.sub.s of this established reference substance at the given measurement conditions. The electrical heater arrangements are not used during this measurement. This first calibration factor is defined to be

[00017]$\begin{array}{cc}{C}_H=\frac{U}{P_S}& \mathrm{Equation}9\end{array}$

[0171] Similarly, the second calibration factor may be written as the ratio of the differential heat flow signal U measured while producing a known differential heat flow P.sub.el with the electrical heater arrangements and this known differential heat flow P.sub.el. There is no heat produced by a sample during this measurement. This second calibration factor is defined to be:

[00018]$\begin{array}{cc}{C}_E=\frac{U}{P_{el}}& \mathrm{Equation}10\end{array}$

[0172] By applying the mathematical relation of equation (6), which describes a situation in the absence of heating power by the local heaters, the first calibration factor C.sub.H may therefore be expressed as follows:

[00019]$\begin{array}{cc}{C}_H=\frac{U}{P_{DSC}}{\left(1+\frac{R_m+R_k}{R_L}\right)}^{-1}={?\left(1+\frac{R_m+R_k}{R_L}\right)}^{-1}& \mathrm{Equation}11\end{array}$

[0173] Whereby the conversion factor between the measured differential heat flow signal, for example a thermoelectric voltage signal, and the heat flow is

[00020]$\frac{U}{P_{DSC}}=?.$

[0174] By applying the mathematical relation of equation (8), which describes a situation in the absence of heating power by a sample, the second calibration factor C.sub.E may therefore be expressed as follows:

[00021]$\begin{array}{cc}{C}_E=\frac{U}{P_{DSC}}{\left(\frac{R_l+R_m+R_k}{R_L+R_k}\right)}^{-1}={?\left(\frac{R_l+R_m+R_k}{R_L+R_k}\right)}^{-1}& \mathrm{Equation}12\end{array}$

[0175] Expressions (11) and (12) show that the first and the second calibration factor depend on the details of the measurement region and the sensor arrangement which are characterized by the thermal resistance of the measurement region R.sub.m and by the conversion factor ?.

[0176] The ratio F of the two calibration factors however, is independent of the measurement region and the sensor arrangement with which it was determined and depends only on the ratio of the contact resistance R.sub.k and the gas resistance R.sub.L:

[00022]$\begin{array}{cc}F=\frac{C_H}{C_E}={\left[1+\frac{R_k}{R_L}\right]}^{-1}& \mathrm{Equation}13\end{array}$

[0177] This independence from the sensor arrangement allows the factor F to be determined for a set of likely measurement conditions with one differential scanning calorimeter of a given type and to reuse the data for other instruments of the same type or for the same instrument but after an exchange of the sensor arrangement.

[0178] As the contact resistance is dominated by the resistance of a thin gas layer between the pan and the pan support region and as this gas it the measurement gas which is responsible for the gas resistance, the specific heat conductivity of the measurement gas cancels out of the fraction

[00023]$\frac{R_k}{R_L}$

and F can be approximately be regarded as a number describing the geometry of the pans inside the furnace. This allows F to be calculated theoretically, for example with a computer simulation.

[0179] Further, this observed independence from the sensor arrangement allows to use the same value of F for different measurements conducted with the same type of pan. To adapt the calibration to different temperatures and different measurement gases, the second calibration factor C.sub.E can be determined by the use of the electrical heater arrangement on one side of the sensor arrangement.

[0180] In contrast to C.sub.H, determining C.sub.E does not require a reference substance. C.sub.E can therefore be determined for essentially every desired temperature while the temperatures at which C.sub.H can be determined are limited to the transition temperatures of the known reference substances. As F is approximately independent of the temperature, the use of C.sub.E and F allows to interpolate C.sub.H values for temperatures at which C.sub.H cannot be measured directly.

[0181] To evaluate the heat flow to or from a sample, using the first and the second conversion factor and the adjustment factor F, the combination of equations (7), (11) and (13) results in:

[00024]$P_S=\frac{U}{C_H}-\frac{P_{el}}{F}$

[0182] This can be rewritten to require only the knowledge of C.sub.E and F:

[00025]$P_S=\frac{U}{F{C}_E}-\frac{P_{el}}{F}$

[0183] The user may choose if the uses the electrical heater arrangement during the measurement, if he uses the electrical heater arrangement controlled to minimize the absolute value of the differential heat flow signal U or if he uses the electrical heater arrangement not at all. Depending on this choice, U or P.sub.el may be set to 0 or they may need to be measured and considered. In a preferred embodiment F is chosen based on the pan type and C.sub.E is determined before or after the measurement of the sample, thereby allowing a precise adaption to the temperature at which the measurement will take place or should take place and at the measurement gas and its conditions during the measurement.

[0184] The example illustrates the calculations and the definitions of the calibration factors with formulas in a readable format. In the implementation of the use of F and the determination of C.sub.E in a self-calibrating differential scanning calorimeter, the calculations may vary for example by providing intermediate results such as calculating the measurement heat flow P.sub.DSC from the measured heat flow signal U and using these P.sub.DSC values instead of U to determine the heat flow to or from the sample. Further, the reciprocals of the first and the second calibration factor and/or of F can be used to realize the invention. Further variations are possible in the choice of the signs for the differential quantities. Therefore, the second calibration factor is preferably any calibration factor which is determined by applying differential heating power to the pan support regions by the use of local heater arrangements and comparing this value to the measured differential heat flow signal U. Further, the conversion factor F is preferably any factor which characterizes the ratio of the thermal contact resistance and the thermal gas resistance.

List of Reference Signs

[0185] 1 furnace [0186] 2 pan (s: sample, r:reference) [0187] 3 electrical heater arrangement (s: sample, r:reference) [0188] 4 pan support region (s: sample, r:reference) [0189] 5 measurement region with thermoelectric junctions [0190] 6 heat flow path [0191] 6m measurement heat flow path, [0192] 6k contact heat flow path [0193] 6l gas heat flow path [0194] 7 sample [0195] 8 measurement gas [0196] 9 sensor arrangement [0197] 10 data evaluation unit