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Determination of organic phase diagrams by the DSC method
Journal of Crystal Growth 65 (1983) 509-510 North-Holland, Amsterdam
509
D E T E R M I N A T I O N OF ORGANIC P H A S E DIAGRAMS BY T H E DSC M E T H O D R. RADOMSKI Institute of Organic and Physical Chemistry, Technical University of Wroctaw, Wabrze2e Wyspiatiskiego 27, 50-370 Wroctaw, Poland
A Differential Scanning Calorimeter (DSC) is basically an energy-measuring device in which the sample temperature is not being measured directly [1]. The search for a method of interpreting the readings of temperature from DSC curves is still an open problem. In this paper some methodical remarks about the determination of equilibrium phase diagrams are presented. The discussion has been limited to two problems: the temperature determination of isothermal transitions (Tt) , and the determination of the solidus and liquidus temperatures, Ts and T L, respectively, for solid solutions. The melting curve of the pure compound, as recorded by a DSC apparatus, does not satisfy the simple equation given by Gray [1]. A distinctive discrepancy is observed for the initial part of the melting peak: experimental curves depart from the base line at lower temperature than theoretically expected, and display considerable curvature (fig. 1). The curvature of the initial part of the DSC peak is due to both thermophysical properties of the material under study (presence of impurities and physi.cal defects, kinetics and mechanism of the transition in question) and instrumental factors (e.g. the working principle of the temperature
r,
r
Fig. 1. Schematic DSC curve for an isothermal transition. Experimental curve (solid lines), and theoretical curve (dashed lines).
regulator). The conclusions which can be drawn from analyzing theoretically the reasons for curvature are: the initial temperature, Ti, of any thermal transition should be determined by the point where the DSC curve departs from the base line for the first time (but not by the point of intersection of the extrapolated base line and the tangent drawn at the inflection point) if T~ does not depend upon the scanning rate. This initial temperature could be considered as a true, equilibrium temperature of a particular transition being studied ( T i = Ts for solid solutions, Ti = Tt for isothermal transitions). In fact, we did not observe a dependence of Ti on the scanning rate if the measurements were performed under the following conditions: (I) The sample temperature was raised just below the pre£ sumed melting point and maintained constant during several hours in order to "heal" the defects before the melting curve is recorded. (II) All measurements were carried out at the same R / S ratio (where R is the range and S the scanning rate), and the masses of the samples were similar. In ref. [2], a procedure for the determination of the solidus and liquidus temperatures from DSC data has been proposed. This procedure is easy to perform but the accuracy of the temperature determination is not greater than + 0.3 °. This accuracy may still be inadequate to solve the liquidus and solidus lines for phase diagrams of solid binary solutions with narrow mixed-phase regions (such as anthracene-Ha0/anthracene-D10 [3], to give an example). Here we wish to develop a new method which allows us to improve the relative accuracy up to _+0.03 ° . The method is based on the observation that better accuracy can be achieved if the initial and final melting temperatures of the solid solution (Ti M and TfM) are
0022-0248/83/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
510
R. Radomski / Determination of organic phase diagrams by DSC method
measured relative to those of the pure components A and B (TiA, TiB and TeA, Tea), and not on an absolute temperature scale.
where AT = TeM _ TiM. Assuming TiM = Ts ' eq. (3) becomes: TL = TeM _ A TisMo.
(4)
Analogous relations for the pure components may be written:
/ : . -- " : & rr': .... ,r,-;
r ~ - - r A + ~Tis~o,
(5)
TeB = T B + ATi~o.
(6)
The liquidus temperature of the solid solution m a y be calculated as an average value TL = (T~ 1) + T~2))/2, where
Fig. 2. Initial and final temperatures of melting peaks in DSC curves against square root of scanning rate (schematicrepresentation). See text for details. The melting peaks of the pure components should be recorded as a function of the scanning rate and the melting temperatures of pure components ( T A and T B) should be extrapolated by plotting the initial melting temperatures against the square root of the scanning rate (according to fig. 2). Subsequently, the melting curve of any solid solution under consideration can be recorded at a fixed scanning rate (chosen according to considerations to be given below). Then, the quantities A TiA and A TiB should be determined graphically by placing pairs of thermograms one above the other and reading the temperature differences:
A M T~1) = ATfA + T A + ATi~ o - ATiso,
--
+ r
+ ATi o -
Tis o,
(7)
(8)
and the quantities A TfA and ATeB are defined as follows: ATfA = TeM_ TeA,
ATeB= TeM _ TeB.
(9)
(10)
T A'
(1)
These quantities are estimated in a similar way as ATiA and ATi B. Eqs. (7) and (8) have been obtained from eq. (4) by substituting TfM using eqs. (9) and (10), respectively, and TA and TfB by using eqs. (5) and (6), respectively. According to ref. [2], the material-instrumental factor, ATiso, can be estimated by the relation:
ATi B = TiM _ TiB= T s _ T B,
(2)
A Tiso = k S ' / 2 A H ' / 2 ,
ATi A = Ti M _ TiA = T s _
where TiM is the initial melting temperature of the solid solution. The solidus temperature of the solid solution m a y be estimated as an average value Ts = (Ts~1)+ Ts~2))/2 using the equations: T (1) = A T i A + T A,
Ts(2) = ATiB -F Z B.
The Ts values so obtained are independent of the scanning rate within experimental error. For solid solutions with small value of T L - Ts the material-instrumental factor, A TisMoo[2] becomes nearly equal to the melting interval, AT, and eq. (11) in ref. [2] may be rewritten as follows: TL - r s = a T -
A Ti~,
(3)
(11)
where A H is the heat of fusion of the sample and k is a calibration factor. By using this procedure the phase diagrams of the binary systems naphthalene-H8/-D 8 and anthracene-Hlo/-D10 have been determined [3]. These results will be published in a separate paper.
References [1] A.P. Gray, in: Analytical Calorimetry, Vol. 1, Eds. R.S. Porter and J.F. Johnson (Plenum, New York, 1968) p. 209. [2] R. Radomski and M. Radomska, J. Thermal Anal. 24 (1982) 101. [3] N. Karl and R. Radomski, unpublished results.
509
D E T E R M I N A T I O N OF ORGANIC P H A S E DIAGRAMS BY T H E DSC M E T H O D R. RADOMSKI Institute of Organic and Physical Chemistry, Technical University of Wroctaw, Wabrze2e Wyspiatiskiego 27, 50-370 Wroctaw, Poland
A Differential Scanning Calorimeter (DSC) is basically an energy-measuring device in which the sample temperature is not being measured directly [1]. The search for a method of interpreting the readings of temperature from DSC curves is still an open problem. In this paper some methodical remarks about the determination of equilibrium phase diagrams are presented. The discussion has been limited to two problems: the temperature determination of isothermal transitions (Tt) , and the determination of the solidus and liquidus temperatures, Ts and T L, respectively, for solid solutions. The melting curve of the pure compound, as recorded by a DSC apparatus, does not satisfy the simple equation given by Gray [1]. A distinctive discrepancy is observed for the initial part of the melting peak: experimental curves depart from the base line at lower temperature than theoretically expected, and display considerable curvature (fig. 1). The curvature of the initial part of the DSC peak is due to both thermophysical properties of the material under study (presence of impurities and physi.cal defects, kinetics and mechanism of the transition in question) and instrumental factors (e.g. the working principle of the temperature
r,
r
Fig. 1. Schematic DSC curve for an isothermal transition. Experimental curve (solid lines), and theoretical curve (dashed lines).
regulator). The conclusions which can be drawn from analyzing theoretically the reasons for curvature are: the initial temperature, Ti, of any thermal transition should be determined by the point where the DSC curve departs from the base line for the first time (but not by the point of intersection of the extrapolated base line and the tangent drawn at the inflection point) if T~ does not depend upon the scanning rate. This initial temperature could be considered as a true, equilibrium temperature of a particular transition being studied ( T i = Ts for solid solutions, Ti = Tt for isothermal transitions). In fact, we did not observe a dependence of Ti on the scanning rate if the measurements were performed under the following conditions: (I) The sample temperature was raised just below the pre£ sumed melting point and maintained constant during several hours in order to "heal" the defects before the melting curve is recorded. (II) All measurements were carried out at the same R / S ratio (where R is the range and S the scanning rate), and the masses of the samples were similar. In ref. [2], a procedure for the determination of the solidus and liquidus temperatures from DSC data has been proposed. This procedure is easy to perform but the accuracy of the temperature determination is not greater than + 0.3 °. This accuracy may still be inadequate to solve the liquidus and solidus lines for phase diagrams of solid binary solutions with narrow mixed-phase regions (such as anthracene-Ha0/anthracene-D10 [3], to give an example). Here we wish to develop a new method which allows us to improve the relative accuracy up to _+0.03 ° . The method is based on the observation that better accuracy can be achieved if the initial and final melting temperatures of the solid solution (Ti M and TfM) are
0022-0248/83/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
510
R. Radomski / Determination of organic phase diagrams by DSC method
measured relative to those of the pure components A and B (TiA, TiB and TeA, Tea), and not on an absolute temperature scale.
where AT = TeM _ TiM. Assuming TiM = Ts ' eq. (3) becomes: TL = TeM _ A TisMo.
(4)
Analogous relations for the pure components may be written:
/ : . -- " : & rr': .... ,r,-;
r ~ - - r A + ~Tis~o,
(5)
TeB = T B + ATi~o.
(6)
The liquidus temperature of the solid solution m a y be calculated as an average value TL = (T~ 1) + T~2))/2, where
Fig. 2. Initial and final temperatures of melting peaks in DSC curves against square root of scanning rate (schematicrepresentation). See text for details. The melting peaks of the pure components should be recorded as a function of the scanning rate and the melting temperatures of pure components ( T A and T B) should be extrapolated by plotting the initial melting temperatures against the square root of the scanning rate (according to fig. 2). Subsequently, the melting curve of any solid solution under consideration can be recorded at a fixed scanning rate (chosen according to considerations to be given below). Then, the quantities A TiA and A TiB should be determined graphically by placing pairs of thermograms one above the other and reading the temperature differences:
A M T~1) = ATfA + T A + ATi~ o - ATiso,
--
+ r
+ ATi o -
Tis o,
(7)
(8)
and the quantities A TfA and ATeB are defined as follows: ATfA = TeM_ TeA,
ATeB= TeM _ TeB.
(9)
(10)
T A'
(1)
These quantities are estimated in a similar way as ATiA and ATi B. Eqs. (7) and (8) have been obtained from eq. (4) by substituting TfM using eqs. (9) and (10), respectively, and TA and TfB by using eqs. (5) and (6), respectively. According to ref. [2], the material-instrumental factor, ATiso, can be estimated by the relation:
ATi B = TiM _ TiB= T s _ T B,
(2)
A Tiso = k S ' / 2 A H ' / 2 ,
ATi A = Ti M _ TiA = T s _
where TiM is the initial melting temperature of the solid solution. The solidus temperature of the solid solution m a y be estimated as an average value Ts = (Ts~1)+ Ts~2))/2 using the equations: T (1) = A T i A + T A,
Ts(2) = ATiB -F Z B.
The Ts values so obtained are independent of the scanning rate within experimental error. For solid solutions with small value of T L - Ts the material-instrumental factor, A TisMoo[2] becomes nearly equal to the melting interval, AT, and eq. (11) in ref. [2] may be rewritten as follows: TL - r s = a T -
A Ti~,
(3)
(11)
where A H is the heat of fusion of the sample and k is a calibration factor. By using this procedure the phase diagrams of the binary systems naphthalene-H8/-D 8 and anthracene-Hlo/-D10 have been determined [3]. These results will be published in a separate paper.
References [1] A.P. Gray, in: Analytical Calorimetry, Vol. 1, Eds. R.S. Porter and J.F. Johnson (Plenum, New York, 1968) p. 209. [2] R. Radomski and M. Radomska, J. Thermal Anal. 24 (1982) 101. [3] N. Karl and R. Radomski, unpublished results.