US 6,648,504 B2 · System and method for calibrating contact thermal resistances in differential scanning calorimeters

Abstract

A system and method for obtaining the contact thermal resistance for a sample and pan without a priori knowledge of the properties of either sample, by measuring the reversing heat capacity of a sample and its pan (or an empty pan on the reference side of the DSC) at a long period and a short period during a quasi-isothermal MDSC experiment and then finding the value of contact thermal resistance that makes the short and long period heat capacities match. Several different methods may be used to find the contact thermal resistance using quasi-isothermal MDSC with a long and a short period. Two methods are direct calculation methods that use the results from an MDSC experiment used with model equations to calculate the contact thermal resistance. A third method is another direct calculation method, based upon the phase angle between the heat flow and temperature signals. A fourth and fifth method use curve fitting of the apparent heat capacity for multiple values of pan contact thermal resistance.

Claims43

Dependent claims

A method for determining a contact thermal resistance in a differential scanning calorimeter comprising:

(a) measuring a first heat flow signal and a first temperature signal at a first period using a quasi-isothermal modulated differential scanning calorimeter technique;
(b) measuring a second heat flow signal and a second temperature signal at a second period using the quasi-isothermal modulated differential scanning calorimeter technique;
and
(c) applying two equations for heat capacity to calculate the contact thermal resistance, the first equation being based upon the first heat flow signal and the second being based upon the second heat flow signal.

1 more element

A method for determining a contact thermal resistance of a pan in a differential scanning calorimeter comprising:

(a) measuring a heat flow signal and a temperature signal at a long period using the quasi-isothermal modulated differential scanning calorimeter technique;
(b) measuring a heat flow signal and a temperature signal at a short period using the quasi-isothermal modulated differential scanning calorimeter technique;
(c) substituting components of the heat flow signal measured at the long period and the temperature signal measured at the long period into a first equation for pan temperature;
(d) substituting components of the heat flow signal measured at the short period and the temperature signal measured at the short period into a second equation for pan temperature;
(e) solving the first and second equations for pan temperature to obtain first and second expressions for heat capacity;
(f) eliminating heat capacity from the first and second expressions for heat capacity to obtain an equation for the contact thermal resistance of the pan;
and
(g) determining the contact thermal resistance of the pan from the equation for the contact thermal resistance of the pan.

5 more elements

A method for determining a contact thermal resistance Rp of a pan in a differential scanning calorimeter comprising:

(a) measuring a heat capacity Cp at a long period using a quasi-isothermal modulated differential scanning calorimeter technique, wherein the long period is selected from a range of periods in which the dependence of heat capacity on period essentially vanishes;
(b) measuring a heat flow signal and a temperature signal at a short period using the quasi-isothermal modulated differential scanning calorimeter technique,
(c) separating the heat flow signal and the temperature signal into their sine and cosine components;
(d) using at least four values of contact thermal resistance in an expression for apparent heat capacity C′p to calculate one value for the apparent heat capacity corresponding to each value of contact resistance, wherein said expression comprises the sine and cosine components of the heat flow signal and the temperature signal;
(e) fitting the values of the apparent heat capacity C′p and the contact thermal resistance Rp to an equation for the apparent heat capacity C′p as a function of the contact thermal resistance Rp;
and
(f) calculating the contact thermal resistance Rp.

4 more elements

A method for determining a contact thermal resistance Rp of a pan in a differential scanning calorimeter comprising:

(a) measuring a first heat flow signal and a first temperature signal at a long period using a quasi-isothermal modulated differential scanning calorimeter technique;
(b) measuring a second heat flow signal and a second temperature signal at a short period using the quasi-isothermal modulated differential scanning calorimeter technique;
(c) separating the first heat flow signals and the first temperature signals into first sine components and first cosine components;
(d) separating the second heat flow signals and the second temperature signals into second sine components and second cosine components;
(e) using at least four values of contact thermal resistance in a first expression for apparent heat capacity to calculate one value for the apparent heat capacity corresponding to each value of contact thermal resistance, wherein said first expression comprises the first sine components and the first cosine components of the first heat flow signal and the first temperature signal;
(f) using several values of contact thermal resistance in a second expression for apparent heat capacity to calculate one value for the apparent heat capacity corresponding to each value of contact thermal resistance, wherein said second expression comprises the second sine components and the second cosine components of the second heat flow signal and the second temperature signal;
(g) fitting the values of the apparent heat capacity C′p and the contact thermal resistance Rp obtained in step (e) to a first equation for the apparent heat capacity C′p as a function of the contact thermal resistance Rp;
(h) fitting the values of the apparent heat capacity C′p and the contact thermal resistance Rp obtained in step (f) to a second equation for the apparent heat capacity C′p as a function of the contact thermal resistance Rp;
(i) eliminating the apparent heat capacities from the first and second equations, yielding a quadratic equation;
and
(j) solving the quadratic equation to determine the contact thermal resistance Rp.

8 more elements

A method for determining a contact thermal resistance in a differential scanning calorimeter comprising:

(a) selecting a calibration temperature, a temperature amplitude, a first modulation period and a second modulation period;
(b) controlling the temperature of a cell in the differential scanning calorimeter at the selected calibration temperature;
(c) modulating the temperature of the cell at the first period, and measuring a first heat flow signal and a first period temperature signal;
(d) modulating the temperature of the cell at the second period, and measuring a second period heat flow signal and a second period temperature signal;
(e) separating the first period heat flow signal and the first period temperature signal into their sine and cosine components to calculate the sine and cosine amplitudes of the first period heat flow signal and the first period temperature signal;
(f) separating the second period heat flow signal and the second period temperature signal into their sine and cosine components to calculate the sine and cosine amplitudes of the second period heat flow signal and the second period temperature signal;
and
(g) calculating the pan contact thermal resistance from the sine and cosine amplitudes of the first period heat flow signal and the first period temperature signal and the sine and cosine amplitudes of the second period heat flow signal and the second period temperature signal.

5 more elements

A method for determining a pan contact thermal resistance in a differential scanning calorimeter comprising:

(a) selecting a calibration temperature, a temperature amplitude, a long modulation period and a short modulation period;
(b) allowing a cell in the differential scanning calorimeter to equilibrate at the calibration temperature;
(c) modulating the temperature of the cell at the long modulation period and measuring a long period heat flow signal and a long period temperature signal;
(d) modulating the temperature of the cell at the short modulation period and measuring a short period heat flow signal and a short period temperature signal;
(e) calculating a long period apparent heat capacity from the long period heat flow signal and the long period temperature signal;
(f) separating the short period heat flow signal and the short period temperature signal into their sine and cosine components to calculate the sine and cosine amplitudes of the short period heat flow signal and the short period temperature signal;
(g) calculating a range of heat capacity values as a function of a range of contact thermal resistances from the sine and cosine amplitudes of the short period heat flow signal and the short period temperature signal;
(h) fitting a quadratic polynomial to the range of heat capacity values as a function of the range of contact thermal resistances to obtain a quadratic equation;
and
(i) solving the quadratic equation to determine the pan contact thermal resistance.

7 more elements

A method for determining a pan contact thermal resistance in a differential scanning calorimeter comprising:

(a) selecting a calibration temperature, a temperature amplitude, a long modulation period and a short modulation period;
(b) allowing a cell in the differential scanning calorimeter to equilibrate at the calibration temperature;
(c) modulating the temperature of the cell at the long modulation period and measuring a long period heat flow signal and a long period temperature signal;
(d) modulating the temperature of the cell at the short modulation period and measuring a short period heat flow signal and a short period temperature signal;
(e) separating the long period heat flow signal and the long period temperature signal into their sine and cosine components to calculate the sine and cosine amplitudes of the long period heat flow signal and the long period temperature signal;
(f) separating the short period heat flow signal and the short period temperature signal into their sine and cosine components to calculate the sine and cosine amplitudes of the short period heat flow signal and the short period temperature signal;
(g) calculating a range of long period heat capacity values as a function of a range of contact thermal resistances from the sine and cosine amplitudes of the long period heat flow signal and the long period temperature signal;
(h) calculating a range of short period heat capacity values as a function of a range of contact thermal resistances from the sine and cosine amplitudes of the short period heat flow signal and the short period temperature signal;
(i) fitting a quadratic polynomial equation to the range of heat capacity values as a function of the range of contact thermal resistances to obtain a long period set of polynomial coefficients;
(j) fitting a short period quadratic polynomial equation to the range of short period heat capacity values as a function of the range of contact thermal resistances to obtain a short period set of polynomial coefficients;
(k) using the long period set of polynomial coefficients and the short period set of polynomial coefficients to obtain a quadratic equation in the pan contact resistance;
and
(l) solving the quadratic equation to determine the pan contact resistance.

10 more elements

Dependencies are inferred from the claim text.

System and method for calibrating contact thermal resistances in differential scanning calorimeters

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System and method for calibrating contact thermal resistances in differential scanning calorimeters

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Abstract

Claims43