Differential scanning calorimetry and calibration methods for use therewith
View Patent ↗Certain embodiments herein are directed to a differential scanning calorimeter comprising a sample holder thermally coupled to a first furnace, a reference holder thermally coupled to a second furnace, and a processor electrically coupled to the first furnace and the second furnace, the processor configured to receive data during a scan of a sample to provide a heat flow trace and further configured to subtract a calculated baseline from the heat flow trace, the calculated baseline comprising the sum of an isothermal baseline function, a scanning baseline function and a transient baseline function. Calibration methods are also described.
1. A differential scanning calorimeter comprising:
a sample holder thermally coupled to a first furnace;
a reference holder thermally coupled to a second furnace;
a processor electrically coupled to the first furnace and the second furnace, the processor configured to receive data during a scan of a sample to provide a heat flow trace and further configured to subtract a calculated baseline from the heat flow trace, the calculated baseline comprising the sum of an isothermal baseline function, a scanning baseline function, and a transient baseline function to represent a plurality of instances of transients produced in a scan of a sample, wherein the processor determines the transient baseline function using principle components analysis, and wherein the processor calculates at least two principle component factors for the transient baseline function, which are expressed as functions of temperature.
2. The differential scanning calorimeter of claim 1 , in which the processor is further configured to receive data during a scan in the absence of a sample to provide a background heat flow trace, to express as mathematical functions at least the isothermal and scanned components of the background heat flow trace, and to store the mathematical functions of the isothermal baseline function and the scanning baseline function.
3. The differential scanning calorimeter of claim 2 , in which the processor is further configured to calculate a baseline using the stored mathematical functions.
4. The differential scanning calorimeter of claim 2 , in which the stored mathematical functions for each of the isothermal and scanned components are fifth order polynomials.
5. The differential scanning calorimeter of claim 1 , further comprising a first temperature sensor in the first furnace and a second temperature sensor in the second furnace, each of the first and second temperature sensors electrically coupled to the processor.
6. A differential scanning calorimeter comprising:
a furnace comprising a sample space, a reference space, a first heating element in thermal communication with the sample space and a second heating element in thermal communication with the reference space; and
a processor electrically coupled to the first and second heating elements and configured to detect a difference in power provided to the first and second heating elements at each of a plurality of different temperatures within a temperature range to provide a heat flow trace in the absence of a sample and within the temperature range, the processor further configured to provide a mathematical fit for isothermal, scanned, and transient components of the heat flow trace in which the transient mathematical fit is representative of a plurality of instances of transients produced in a scan of a sample, wherein the transient mathematical fit is determined using principal components analysis, and wherein the transient mathematical fit includes at least two principal component factors expressed as functions of temperature.
7. The differential scanning calorimeter of claim 6 , further comprising a computer readable medium electrically coupled to the processor and configured to store the provided mathematical fit for each of an isothermal, a scanned and a transition portion of the heat flow trace.
8. The differential scanning calorimeter of claim 6 , in which the processor is further configured to generate a baseline using the mathematical fit for each of the isothermal, the scanned and the transition components of the heat flow trace and to subtract the generated baseline from a sample heat flow trace obtained in the presence of a sample.
9. The differential scanning calorimeter of claim 6 , in which the mathematical fit for each of the isothermal and scanned components is a fifth order polynomial.
10. A method of characterizing the baseline of a differential scanning calorimeter comprising:
using a differential scanning calorimeter to enerate measurements the differential scanning calorimeter comprising a sample holder thermally coupled to a first furnace, a reference holder thermally coupled to a second furnace, and a processor electrically coupled to the first furnace and the second furnace;
using the processor, generating data from measurements made with the calorimeter and generating a heat flow trace therefrom over each of a number of different temperature intervals with no sample present, the temperature being held constant a number of different temperatures for a time sufficient for thermal equilibrium to be achieved, and
using the processor, expressing as mathematical functions isothermal, scanned and transient components of the heat flow trace, wherein the transient function is expressed by subtracting from the heat flow trace the calculated isothermal and scanned functions, and analyzing the remainder using principal components analysis, wherein the transient function is calculated via the processor so that it includes at least two principal component factors expressed as functions of temperature, and wherein the transient function is representative of a plurality of instances of transients produced in a scan of a sample.
11. The method of claim 10 , further comprising storing the mathematical functions on a computer readable medium.
12. The method of claim 10 , wherein each of the isothermal and scanned components is expressed as a fifth order polynomial in temperature.
13. A method of determining a baseline in a differential scanning calorimeter, the method comprising:
using a differential scanning calorimeter to generate measurements, the differential scanning calorimeter comprising a sample holder thermally coupled to a first furnace, a reference holder thermally coupled to a second furnace, and a processor electrically coupled to the first furnace and the second furnace;
using the processor, generating data from measurements made with the calorimeter and generating a heat flow trace therefrom, and independently fitting a mathematical function to isothermal components and scanned components of the heat flow trace comprising a plurality of heat flow values obtained using no sample and holding the temperature constant at a number of different temperatures for a time sufficient for thermal equilibrium to be achieved for each of the heat flow values; and
using the processor, independently fitting a mathematical function to transient components of the heat flow trace, and generating a baseline using the fitted mathematical functions, in which the transient function is expressed by subtracting from the heat flow trace the calculated isothermal and scanned functions, and analyzing the reminder using principal components analysis, wherein the transient function is calculated via the processor so that it includes at least two principal component factors expressed as functions of temperature, and wherein the transient function is representative of a plurality of instances of transients produced in a scan of a sample.
14. The method of claim 13 , in which the mathematical function fitted to each of the isothermal and scanned components is a fifth order polynomial.
15. The method of claim 13 , in which the generated baseline is subtracted from a heat flow trace obtained in the presence of a sample.
16. The method of claim 13 , in which the generated baseline is stored on a computer readable medium.
17. A method of performing calorimetric measurements in a differential scanning calorimeter, the method comprising:
using a differential scanning calorimeter to generate measurements, the differential scanning calorimeter comprising a sample holder thermally coupled to a first furnace, a reference holder thermally coupled to a second furnace, and a processor electrically coupled to the first furnace and the second furnace;
using the processor, generating data from measurements made with the calorimeter by scanning over a temperature range in the absence of a sample to generate a heat flow trace comprising a plurality of heat flow values obtained by holding the temperature constant at a number of different temperatures for a time sufficient for thermal equilibrium to be achieved for each of the heat flow values;
using the processor, fitting an isothermal and a scanned portion of the heat flow trace to a mathematical function;
using the processor, fitting a transient portion of the heat flow trace to a mathematical function;
using the processor, storing the fitted mathematical functions; and
using the stored fitted mathematical functions to generate a baseline signal for use in the calorimetric measurements, wherein the mathematical function for the transient portion is calculated using principal components analysis, and the mathematical function for the transient portion is calculated via the processor so that it includes at least two principal component factors expressed as functions of temperature, and wherein the mathematical function for the transient portion is representative of a plurality of instances of transients produced in a scan of a sample.
18. A differential scanning calorimeter comprising furnace means for heating a sample and a reference, and processing means coupled to the furnace means, the processing means having been calibrated by a method according to claim 10 .