Thermal measuring and testing – Differential thermal analysis
Reexamination Certificate
2000-08-23
2002-08-13
Gutierrez, Diego (Department: 2859)
Thermal measuring and testing
Differential thermal analysis
C374S001000, C374S032000, C374S033000
Reexamination Certificate
active
06431747
ABSTRACT:
BACKGROUND
1. Field of the Invention
The present invention relates to a thermal analysis instrument, and more particularly, to a differential scanning calorimeter.
2. Background of the Invention
Heat Flux Differential Scanning Calorimeters (DSCs) have a sensor which measures the temperature difference between a sample and a reference position. A sample to be analyzed is loaded into a pan and placed on the sample position of the sensor and an inert reference material is loaded into a pan and placed on the reference position of the sensor (an empty pan is often used as the reference). The sensor is installed in an oven whose temperature is varied dynamically according to a desired temperature program. The temperature program for conventional DSCs typically includes combinations of linear temperature ramps and constant temperature segments. Modulated DSC uses a temperature program in which periodic temperature modulations are superimposed on linear ramps. Modulated DSCs are described in U.S. Pat. No. 5,224,775, which is incorporated by reference herein. During the dynamic portion of the DSC experiment, a differential temperature is created between the sample and reference positions on the sensor. The temperature difference is the result of the difference between the heat flow to the sample and the heat flow to the reference. Because the temperature difference is proportional to the difference in heat flow to the sample as compared to the reference, that differential temperature may be used to measure the heat flow to the sample.
FIG. 1
shows a thermal network model that may be used to represent heat flux in certain DSC sensors. T
o
is the temperature at the base of the sensor near its connection to the oven, T
s
is the temperature of the sample position of the sensor and T
r
is the temperature of the reference position of the sensor. R
s
and R
r
represent the thermal resistance between the base of the sensor and the sample and reference positions, respectively. C
s
and C
r
represent the thermal capacitance of the sample and reference portions of the sensor. Thermal capacitance is the product of mass and specific heat and is a measure of the heat storage capacity of a body, i.e., it is the heat capacity of the body. The heat flow to the sample and the reference are q
s
and q
r
, respectively. It should be understood that q
s
and q
r
include heat flow to sample and reference pans. During the execution of a thermal program the base temperature of the sensor T
o
follows the thermal program. The temperatures at the sample and reference positions, T
s
and T
r
, lag the base temperature T
o
due to heat flowing to the sample and to the reference and heat which is stored within the sensor in sensor sample thermal capacitance C
s
and sensor reference thermal capacitance C
r
.
Performing a heat flow balance on the sample side of the sensor yields a heat flow
q
s
=
T
o
-
T
s
R
s
-
C
s
·
ⅆ
T
s
ⅆ
τ
trough the sensor sample thermal resistance R
s
minus the heat stored in C
s
. Similarly, a heat balance on the reference side of the sensor gives
q
r
=
T
o
-
T
r
R
r
-
C
r
·
ⅆ
T
r
ⅆ
τ
through sensor reference thermal resistance R
r
minus the heat stored in C
r
. In the equations herein, &tgr; represents time.
The desired quantity (the differential heat flow to the sample with respect to the reference) is the difference between the sample and reference heat flows:
q=q
s
−q
r
Substituting for q
s
and q
r
yields:
q
=
T
o
-
T
s
R
s
-
C
s
·
ⅆ
T
s
ⅆ
τ
-
T
o
-
T
r
R
r
+
C
r
·
ⅆ
T
r
ⅆ
τ
Substituting the following expressions for two temperature differences in a differential scanning calorimeter,
&Dgr;
T=T
s
−T
r
&Dgr;
T
o
=T
o
−T
s
where &Dgr;T is the temperature difference between the sample and the reference and &Dgr;T
o
is the temperature difference between the sample and a position at the base of the sensor, results in the DSC heat flow equation:
q
=
Δ
T
o
·
(
R
r
-
R
s
R
r
·
R
s
)
-
Δ
T
R
r
+
(
C
r
-
C
s
)
·
ⅆ
T
s
ⅆ
τ
-
Cr
·
ⅆ
Δ
T
ⅆ
τ
The DSC heat flow equation has 4 terms. The first term accounts for the effect of the difference between the sensor sample thermal resistance and the sensor reference thermal resistance. The second term is the conventional DSC heat flow. The third term accounts for the effect of the difference between the sensor sample thermal capacitance and the sensor reference thermal capacitance. The fourth term accounts for the effect of the difference between the heating rates of the sample and reference sides of the DSC. Conventionally, when this equation is applied to the DSC heat flow, the first and third terms are zero because R
s
and R
r
are assumed to be equal and C
s
and C
r
are also assumed to be equal.
In reality, because of imprecision in the manufacturing process, sensors are not perfectly balanced. This imbalance contributes to baseline heat flow deviations that may be significant. The first and third terms of the four-term heat flow equation account for the thermal resistance and thermal capacitance imbalances, respectively. The fourth term is generally very nearly equal to zero, except when a transition is occurring in the sample (for instance, during a melt), or during a Modulated DSC experiment. Usually, the heat flow signal is integrated over the area of the transition to obtain the total energy of the transition. Because the fourth term does not contribute to the area of the integration, it has been ignored in the prior art. However, it may contribute significantly to the shape of the heat flow curve during a transition. Therefore, including the fourth term improves the dynamic response of the heat flow curve. Also, as noted by Hohne, et. al. in “Differential Scanning Calorimetry: An Introduction for Practitioners,” (Springer-Verlag, 1996), the fourth term cannot be ignored and must be taken into account when partial integration of the transition peak is performed, e.g., in kinetic investigations for purity determinations. When the fourth term is included, the onset of a transition is sharper and the return to baseline heat flow when the transition is over is more rapid.
Because the resolution of a DSC is its ability to separate transitions that occur in a sample within a small temperature interval, and this is determined essentially by how quickly the heat flow signal returns to baseline after a transition is complete, including the fourth term of the DSC heat flow equation improves the resolution of the DSC sensor by increasing the return to baseline of the heat flow signal after a transition is complete.
The four-term heat flow equation has long been known in the art of differential scanning calorimetry. It can only be applied to heat flux DSC sensors that satisfy certain criteria. The structure of the sensor must be such that the thermal network model correctly represents the dynamic thermal behavior of sensor. Ideally, the sample and reference portions of the sensor should be absolutely independent, i.e., a transition that occurs on the sample side would not have any effect on the reference temperature. Typically, heat flux DSC sensors of the disk type as disclosed in U.S. Pat. No. 4,095,453 to Woo, U.S. Pat. No. 4,350,446 to Johnson, U.S. Pat. No. 5,033,866 to Kehl, et. al. and U.S. Pat. No. 5,288,147 to Schaefer, et. al. cannot use the four-term heat flow equation, because the sample and reference temperature are not independent, and because the four-term heat flow equation does not accurately represent the dynamic thermal behavior of those sensors.
A quantitative measure of the independence of prior art heat flux sensors can be obtained by a simple experiment: for example, if a sample of indium is placed on the reference position of a prior art sensor such as, for example, the type disclosed in U.S. Pat. No. 4,095,453 to Woo, and the sample is heated through the melt, in o
Gutierrez Diego
Shaw Pittman LLP
TA Instruments, Inc.
Verbitsky Gail
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