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Dielectric secondary relaxation effects in polyvinyl p-methoxybenzoate and poly-p-methoxystyrene in the microwave region
Short Communications
Dielectric secondary relaxation effects in polyvinyl p-methoxybenzoate and poly-p-methoxystyrene in the microwave region* In spite of the recent increased interest in organic high polymers for applications as dielectrics at ultra-high frequencies, there is little information in the scientific literature regarding the dielectric behaviour of these materials in the microwave region. With the object of furnishing additional experimental data and of continuing the systematic work on this subject initiated a few years ago, we are in this paper reporting some results regarding the dielectric behaviour, in the centimetre wavelength range, of two polymers: polyvinyl-p-methoxybenzoate (I) and poly-p-methoxystyrene (II):
above the relevant softening points in an inert atmosphere (dry nitrogen devoid of oxygen) and then ground on a lathe. Finally, to eliminate residual stresses set up during the thermal and mechanical treatment, the samples were annealed for 48 hours at 60°C, under vacuum. In Fig. 1 are reported curves which describe the variations of the microwave dielectric constant, e', and of the loss tangent, tan &,as functions of temperature for polyvinyl-p-methoxybenzoate. 2.70
30
2.5(3
.= 6'
_- =-"
20
2.50
i
1l°
~---Tg
C=O
o-c% (I)
o-CH 3
(rr)
These polymers were prepared by bulk polymerization, starting from the corresponding monomers, at 65°C in the presence of benzoyl peroxide as initiator, in closed phials under high vacuum. Both polymers are linear, completely amorphous, with a glass transition temperature of about 85°C for (I) and 80°C for (II). The transition point from the glassy to the elastoplastic state, Tg, was determined by means of dynamic Young's modulus measurements. For the determination of the dielectric properties at microwavelengths, a dielectrometer of the Central Research Laboratories Inc. (Minnesota) (model 3, series No. 37) (suitably modified for making measurements at different temperatures 1) was employed. Measurements were carried out at frequencies of the order of 101° c.p.s, and in the temperature range of 150-420°K. Specimens were prepared in the form of small cylinders (24.45 mm diameter by 17.5 mrn thick) by moulding at temperatures * Work carried out with the support of the Consiglio Nazionale delle Richerche.
I
l
t
I
150
200
250
300
11
350
/ I
|
400T°K
Fig. 1. Dielectric constant, ~', and loss tangent, tan f, for polyvinyl p-methoxybenzoate as functions of temperature ( f = 8.6 x 109 c.p.s.).
At the lowest temperature reached in the measurements, E is equal to 2.60; with increasing temperature it first remains constant until about 270°K, then increases, reaching a maximum value at about 300°K, it then decreases. At temperatures above the glass transition point it begins to rise again, indefinitely. The loss tangent at the lowest temperature is of the order of 10 x 10- 3. With increasing T it remains almost constant up to about 225°K, then starts to rise gradually and passes through a maximum at about 350°K, it then decreases, reaching a minimum, and finally begins once more to increase, as soon as the glass transition point has been passed. The E-T and tan f - T plots of poly-p-methoxystyrene at microwavelengths are set out in Fig. 2. For this polymer, e', in the temperature interval between 150 ° and 260°K, remains almost constant (about 2.70); above this temperature it increases gradually with increasing T up to about 330°K, when a bend appears in the E-T curve. At still higher temperatures, the dielectric constant increases continuously as the temperature rises.
Materials Science and Engineering American Society for Metals, Metals Park, Ohio, and Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
275
SHORT COMMUNICATIONS
e
lower temperatures, well below the glass transition points (Fig. 3). Similar behaviour is shown by polyvinyl p-methoxybenzoate.
i~-T0
3.2
~
1
50
',
% '~0~
3.0
'<
2.e
20
6 5o
i
i
200
3so
o
4 OTOK
Fig.?.. Dielectric constant, E, and loss tangent, tan ~, for poly-
p-methoxystyrene as functions of temperature (f=g.6x 109 c.p.s.).
The loss tangent, at the lowest temperature, is of the order of 20 × 10- 3. With rising T it increases, goes through a flattened maximum at about 350°K, then decreases and finally begins again to increase when the glass transition point is exceeded. Repeating for poly-p-methoxystyrene measurements at lower frequencies (in a coaxial cable) it can be noted that the loss maximum is shifted towards 3.5 3.3
3.1 2.9 2.7
10C
%C
%
6C
4o! I
2OI
1
I
I
2~ 30O 3~ 4.OO T°K Fig. 3, Dielectric constant, e', and loss tangent, tan &,for polyp-methoxystyreneas functions of temperature at two different frequencies: (O) f = 3 x 109 c.p.s.; (C))f = 8.6 x 109 c.p.s, 2OO
Discussion
The microwave dielectric behaviour of the two polymers examined, namely polyvinyl-p-methoxybenzoate and poly-p-methoxystyrene, indicates the presence of a loss maximum at temperatures below the glass transition point. The experimental results strongly suggest that such a phenomenon is due to a "secondary" relaxation effect, probably associated with the orientational polarization of small polar groups, whose motions are thermally excited well below the glass transition point, when motions of the skeleton of the macromolecule are still frozen in. In fact, in the glassy state, e' in general assumes values higher than the "optical dielectric constant", n 2 (n = refractive index) z, and tends to increase with increasing temperature, indicating the existence of a certain contribution, due to orientational polarization, to the permittivity of the material, which increases with temperature, largely overcoming the opposite effect due to thermal expansion. On the other hand, the dielectric loss, in the glassy state, is also rather high; it increases with rising temperature and passes through a maximum before the transition point is reached. Moreover, the position of the maximum, on the temperature scale, changes with frequency. With reference to the nature of the mechanism responsible for the secondary relaxation effect found in polyvinyl-p-methoxybenzoate and poly-p-methoxystyrene, in the microwave region, and the characterization of the kinetic units participating in the process, no conclusions can be drawn without additional information being obtained from other sources. Nevertheless, on the basis of the fact that in polar polymers there is often a good correspondence between mechanical and dielectric relaxations, specially with regard to secondary processes, it seems useful to compare the present results with those previously obtained by us from dynamic mechanical measurements, at acoustic frequencies, on the polymers under discussion. From the latter measurements it has been ascertained that polyvinyl, p-methoxybenzoate and polyp-methoxystyrene exhibit a secondary relaxation effect (designated "delta-process") thermally excitable from the lowest temperatures, which has Mater. Sci. Eng., 6
(1970) 274-277
276
SHORT COMMUNICATIONS
been tentatively attributed to oscillations or "wagging" of the pendant aromatic groups 3- 5 (Fig. 4). For these processes the relaxation time, 'c, has been found to vary with temperature following an Arrhenius type equation: "C ~ "CO c A E / R T
with an average limiting relaxation time, 'co,equal to 4 × 10-14 sec and an apparent activation energy AE of the order of 5 kcal/mole.
relaxation times which characterizes it, extends itself over a very wide temperature range. Finally, we wish to point out that p-methoxyring-substituted polystyrenes and polyvinyl benzoates appear to be, as far as we know, the only examples of amorphous linear polymers which display thermal activated molecular motions, dielectrically active, able to cause the appearance of a loss peak in the microwave region of the electromagnetic spectrum, at relatively low temperatures ( T < Tg)•
30 1C
8
20
% U
!
O
10 .....
Q dietettr. [ O diel.et~r. I
2 NpMe0Bz A mecc.
0
60
•
|
100
•
i
1/,0
•
/
180
•
1
220
,
i
260
i
I
I
300T°K
Fig. 4. Mechanical damping factor, Q-I, as function of temperature for polyvinyl p-methoxybenzoate (O) and poly-pmethoxystyrene (Q) ( f = 7 x 104 c.p.s.).
Reporting on a log f - 1 / T plot, the absolute temperatures of the mechanical delta-peaks and those of the dielectric loss maxima at microwavelengths for the polymers considered as functions of the frequency (Fig. 5), it can be observed that the various experimental points fall, with a good approximation, on a straight line. From these considerations, the hypothesis can be advanced that the dielectric secondary relaxation phenomenon found in the microwave region in polyvinyl-p-methoxybenzoate and in poly-pmethoxystyrene corresponds to the "6-process" found from mechanical measurements and, analogously to this, may be assigned to motions of the pendant aromatic groups• It is to be noted that the movement in question seems to be rather complex, inasmuch as both the benzene ring ( - ( ~ ) - ) and the methoxy group (-OCH3) participate. The coupling of such motions leads, however, to a unique macroscopic relaxation effect which, owing to the wide distribution of the
T "1 °K-1 x 103
Fig. 5. Frequency dependence of the mechanical and dielectric loss peak temperature for the secondary relaxation process in polyvinyl p-methoxybenzoate and poly-p-methoxystyrene.
In fact, in all the other amorphous linear polymers investigated, where secondary relaxation effects are known to occur in the glassy state, at lower frequencies, no dielectric loss peaks are detectable at the microwavelengths 6-1 o The peculiar behaviour of the two polymers here considered has to be viewed in relation to the particular values of the activation parameters of the 6-process which allow the relevant mean relaxation time, 'c, to reach values of the order of 10- xo sec at temperatures below the glass transition point. V. Frosini and E. Butta
Istituto di Chimica Industriale ed Applicata, Facoltd di Ingegneria dell' Universita di Pisa, Pisa (Italia)
Mater. Sei. Eng., 6 (1970) 274-277
277
SHORT COMMUNICATIONS REFERENCES 1 M. CALAM1A,E. BUTTAAND V. FROSINI, J. Appl. Polymer Sci., 10 (1966) 1067. 2 P. L. MAGAGNINI, Chim. Ind. (Milan) 49, (1967) 1041. 3 V. FROSINI AND P. L. MAGAGNINI, European Polymer J., 2 (1966) 129. 4 P. L. MAGAGNINI AND V. FROSINI, European Polymer J., 2 (1966) 139.
6 A. M. LOBANOV,Fiz. Dielektrokov Sb., 10 (1968) 146. 7 G. P. MIKHA1LOVAND A. M. LOBANOV, Zh. Tekhn. Fiz., 28 (1958) 273. 8 E. AMRHEtN, in J. A. PRINS, Proc. Intern. Conf. on Physics of Non Crystalline Solids, Delft, 1964, North-Holland Publ. Co., Amsterdam, p. 283. 9 E. AMRHEIN, KolloMZ., 216 (1967) 38. 10 V. FROSINI, E. BUTTA AND M. CALAMIA,J. Appl. Polymer Sci.,
11 (1967)527.
5 M. BACCAREDDA, E. BUTTA, V. FROSINI AND S. DE PETRIS,
Mater. Sci. Eng., 3 (1968/69) 157.
Received March 30, 1970 Mater. Sci. Eno., 6 (1970) 274-277
Heat capacity above 320°K and heat of fusion of hexagonal selenium In the course of a systematic investigation of physical properties of chalcogenide glasses we have recently had occasion to determine the heat capacity above room temperature and the heat of fusion of hexagonal selenium. While our results are not of the precision that is being reached today with more sophisticated apparatus, they are of sufficient accuracy to prompt us to report them here. Selenium powder, "Certified Reagent" grade, obtained from Fisher Scientific Company, was purified by vacuum distillation in Pyrex glass. Hexagonal selenium was prepared from the distillate by sealing a small sample into an evacuated Pyrex tube and holding it for three days at a constant temperature of 195°C. The heat capacity and the heat of fusion of the hexagonal selenium were measured with a Perkin-Elmer DSC-1B Differential Scanning Calorimeter. The procedure described by O'Neill 1 was used in the heat capacity determinations; a sample of single crystal alumina served as the heat capacity comparison standard. The heat of fusion was determined by comparing the area traced out on the recorder chart during a scan through the melting of a known mass of hexagonal selenium (melting point 494°K) with similar areas traced out for the melting of two standard metals, tin (AHf = 1720 cal/g-at.) and indium (AHf=780 cal/g-at.) 2. In Fig. 1 the results of our measurements for the heat capacity in the temperature interval 320 ~480°K are shown, along with the adiabatic calorimetry results ofAnderson 3, Desorbo 4, and Borelius and Paulson 5. Earlier results reported by Monval 6, obtained by drop calorimetry, are also shown on the same Figure, but more recent results reported by Gattow and Heinrich 7, which exhibit rather irregular behavior at higher temperatures, are not included. Each of the 17 points obtained from our
measurements is the average of from five to twelve results for that temperature, with the error bars indicating the average deviation of those results from their mean. On the basis of reproducibility, our results are considered to be accurate to _+0.2-0.3 cal/g-at, deg, since there are no known systematic errors in our method. A least-squares fit of our data to an equation linear in temperature yields, for the interval 320~-480°K, Cp (cal/g-at. deg) = 4.96+0.00253 T (°K),
(I)
a plot of which is shown in Fig. 1.
x×X x
++ ++ ++ + + + + + ++++++++++++
E o
~ &
6
~
5
4 200
I
I 300
L
[ 400
L~ 500
(°~) Fig. 1. Heat capacities for hexagonal selenium. • present results, Ref. 3, O Ref. 4, x Ref. 5, + Ref. 6, - eqn. (1), - - - eqn. (2). T
We have also joined our data with that of Anderson 3 and that of Desorbo 4 in a linear leastsquares fit over the temperature interval 200 °480°K. The resulting equation is Cp (cal/g-at. deg) = 5.40+0.00154 T (°K).
(2)
A plot of eqn. (2) is also shown in Fig. 1 and is seen to connect the two sets of data reasonably well, except for Desorbo's last five data points, between 275 ° and 300°K. These data points depart rather sharply from the results of Anderson, and from those of DeSorbo himself, when extrapolated from below Mater. Sei. Eng., 6 (1970) 277-278
Dielectric secondary relaxation effects in polyvinyl p-methoxybenzoate and poly-p-methoxystyrene in the microwave region* In spite of the recent increased interest in organic high polymers for applications as dielectrics at ultra-high frequencies, there is little information in the scientific literature regarding the dielectric behaviour of these materials in the microwave region. With the object of furnishing additional experimental data and of continuing the systematic work on this subject initiated a few years ago, we are in this paper reporting some results regarding the dielectric behaviour, in the centimetre wavelength range, of two polymers: polyvinyl-p-methoxybenzoate (I) and poly-p-methoxystyrene (II):
above the relevant softening points in an inert atmosphere (dry nitrogen devoid of oxygen) and then ground on a lathe. Finally, to eliminate residual stresses set up during the thermal and mechanical treatment, the samples were annealed for 48 hours at 60°C, under vacuum. In Fig. 1 are reported curves which describe the variations of the microwave dielectric constant, e', and of the loss tangent, tan &,as functions of temperature for polyvinyl-p-methoxybenzoate. 2.70
30
2.5(3
.= 6'
_- =-"
20
2.50
i
1l°
~---Tg
C=O
o-c% (I)
o-CH 3
(rr)
These polymers were prepared by bulk polymerization, starting from the corresponding monomers, at 65°C in the presence of benzoyl peroxide as initiator, in closed phials under high vacuum. Both polymers are linear, completely amorphous, with a glass transition temperature of about 85°C for (I) and 80°C for (II). The transition point from the glassy to the elastoplastic state, Tg, was determined by means of dynamic Young's modulus measurements. For the determination of the dielectric properties at microwavelengths, a dielectrometer of the Central Research Laboratories Inc. (Minnesota) (model 3, series No. 37) (suitably modified for making measurements at different temperatures 1) was employed. Measurements were carried out at frequencies of the order of 101° c.p.s, and in the temperature range of 150-420°K. Specimens were prepared in the form of small cylinders (24.45 mm diameter by 17.5 mrn thick) by moulding at temperatures * Work carried out with the support of the Consiglio Nazionale delle Richerche.
I
l
t
I
150
200
250
300
11
350
/ I
|
400T°K
Fig. 1. Dielectric constant, ~', and loss tangent, tan f, for polyvinyl p-methoxybenzoate as functions of temperature ( f = 8.6 x 109 c.p.s.).
At the lowest temperature reached in the measurements, E is equal to 2.60; with increasing temperature it first remains constant until about 270°K, then increases, reaching a maximum value at about 300°K, it then decreases. At temperatures above the glass transition point it begins to rise again, indefinitely. The loss tangent at the lowest temperature is of the order of 10 x 10- 3. With increasing T it remains almost constant up to about 225°K, then starts to rise gradually and passes through a maximum at about 350°K, it then decreases, reaching a minimum, and finally begins once more to increase, as soon as the glass transition point has been passed. The E-T and tan f - T plots of poly-p-methoxystyrene at microwavelengths are set out in Fig. 2. For this polymer, e', in the temperature interval between 150 ° and 260°K, remains almost constant (about 2.70); above this temperature it increases gradually with increasing T up to about 330°K, when a bend appears in the E-T curve. At still higher temperatures, the dielectric constant increases continuously as the temperature rises.
Materials Science and Engineering American Society for Metals, Metals Park, Ohio, and Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
275
SHORT COMMUNICATIONS
e
lower temperatures, well below the glass transition points (Fig. 3). Similar behaviour is shown by polyvinyl p-methoxybenzoate.
i~-T0
3.2
~
1
50
',
% '~0~
3.0
'<
2.e
20
6 5o
i
i
200
3so
o
4 OTOK
Fig.?.. Dielectric constant, E, and loss tangent, tan ~, for poly-
p-methoxystyrene as functions of temperature (f=g.6x 109 c.p.s.).
The loss tangent, at the lowest temperature, is of the order of 20 × 10- 3. With rising T it increases, goes through a flattened maximum at about 350°K, then decreases and finally begins again to increase when the glass transition point is exceeded. Repeating for poly-p-methoxystyrene measurements at lower frequencies (in a coaxial cable) it can be noted that the loss maximum is shifted towards 3.5 3.3
3.1 2.9 2.7
10C
%C
%
6C
4o! I
2OI
1
I
I
2~ 30O 3~ 4.OO T°K Fig. 3, Dielectric constant, e', and loss tangent, tan &,for polyp-methoxystyreneas functions of temperature at two different frequencies: (O) f = 3 x 109 c.p.s.; (C))f = 8.6 x 109 c.p.s, 2OO
Discussion
The microwave dielectric behaviour of the two polymers examined, namely polyvinyl-p-methoxybenzoate and poly-p-methoxystyrene, indicates the presence of a loss maximum at temperatures below the glass transition point. The experimental results strongly suggest that such a phenomenon is due to a "secondary" relaxation effect, probably associated with the orientational polarization of small polar groups, whose motions are thermally excited well below the glass transition point, when motions of the skeleton of the macromolecule are still frozen in. In fact, in the glassy state, e' in general assumes values higher than the "optical dielectric constant", n 2 (n = refractive index) z, and tends to increase with increasing temperature, indicating the existence of a certain contribution, due to orientational polarization, to the permittivity of the material, which increases with temperature, largely overcoming the opposite effect due to thermal expansion. On the other hand, the dielectric loss, in the glassy state, is also rather high; it increases with rising temperature and passes through a maximum before the transition point is reached. Moreover, the position of the maximum, on the temperature scale, changes with frequency. With reference to the nature of the mechanism responsible for the secondary relaxation effect found in polyvinyl-p-methoxybenzoate and poly-p-methoxystyrene, in the microwave region, and the characterization of the kinetic units participating in the process, no conclusions can be drawn without additional information being obtained from other sources. Nevertheless, on the basis of the fact that in polar polymers there is often a good correspondence between mechanical and dielectric relaxations, specially with regard to secondary processes, it seems useful to compare the present results with those previously obtained by us from dynamic mechanical measurements, at acoustic frequencies, on the polymers under discussion. From the latter measurements it has been ascertained that polyvinyl, p-methoxybenzoate and polyp-methoxystyrene exhibit a secondary relaxation effect (designated "delta-process") thermally excitable from the lowest temperatures, which has Mater. Sci. Eng., 6
(1970) 274-277
276
SHORT COMMUNICATIONS
been tentatively attributed to oscillations or "wagging" of the pendant aromatic groups 3- 5 (Fig. 4). For these processes the relaxation time, 'c, has been found to vary with temperature following an Arrhenius type equation: "C ~ "CO c A E / R T
with an average limiting relaxation time, 'co,equal to 4 × 10-14 sec and an apparent activation energy AE of the order of 5 kcal/mole.
relaxation times which characterizes it, extends itself over a very wide temperature range. Finally, we wish to point out that p-methoxyring-substituted polystyrenes and polyvinyl benzoates appear to be, as far as we know, the only examples of amorphous linear polymers which display thermal activated molecular motions, dielectrically active, able to cause the appearance of a loss peak in the microwave region of the electromagnetic spectrum, at relatively low temperatures ( T < Tg)•
30 1C
8
20
% U
!
O
10 .....
Q dietettr. [ O diel.et~r. I
2 NpMe0Bz A mecc.
0
60
•
|
100
•
i
1/,0
•
/
180
•
1
220
,
i
260
i
I
I
300T°K
Fig. 4. Mechanical damping factor, Q-I, as function of temperature for polyvinyl p-methoxybenzoate (O) and poly-pmethoxystyrene (Q) ( f = 7 x 104 c.p.s.).
Reporting on a log f - 1 / T plot, the absolute temperatures of the mechanical delta-peaks and those of the dielectric loss maxima at microwavelengths for the polymers considered as functions of the frequency (Fig. 5), it can be observed that the various experimental points fall, with a good approximation, on a straight line. From these considerations, the hypothesis can be advanced that the dielectric secondary relaxation phenomenon found in the microwave region in polyvinyl-p-methoxybenzoate and in poly-pmethoxystyrene corresponds to the "6-process" found from mechanical measurements and, analogously to this, may be assigned to motions of the pendant aromatic groups• It is to be noted that the movement in question seems to be rather complex, inasmuch as both the benzene ring ( - ( ~ ) - ) and the methoxy group (-OCH3) participate. The coupling of such motions leads, however, to a unique macroscopic relaxation effect which, owing to the wide distribution of the
T "1 °K-1 x 103
Fig. 5. Frequency dependence of the mechanical and dielectric loss peak temperature for the secondary relaxation process in polyvinyl p-methoxybenzoate and poly-p-methoxystyrene.
In fact, in all the other amorphous linear polymers investigated, where secondary relaxation effects are known to occur in the glassy state, at lower frequencies, no dielectric loss peaks are detectable at the microwavelengths 6-1 o The peculiar behaviour of the two polymers here considered has to be viewed in relation to the particular values of the activation parameters of the 6-process which allow the relevant mean relaxation time, 'c, to reach values of the order of 10- xo sec at temperatures below the glass transition point. V. Frosini and E. Butta
Istituto di Chimica Industriale ed Applicata, Facoltd di Ingegneria dell' Universita di Pisa, Pisa (Italia)
Mater. Sei. Eng., 6 (1970) 274-277
277
SHORT COMMUNICATIONS REFERENCES 1 M. CALAM1A,E. BUTTAAND V. FROSINI, J. Appl. Polymer Sci., 10 (1966) 1067. 2 P. L. MAGAGNINI, Chim. Ind. (Milan) 49, (1967) 1041. 3 V. FROSINI AND P. L. MAGAGNINI, European Polymer J., 2 (1966) 129. 4 P. L. MAGAGNINI AND V. FROSINI, European Polymer J., 2 (1966) 139.
6 A. M. LOBANOV,Fiz. Dielektrokov Sb., 10 (1968) 146. 7 G. P. MIKHA1LOVAND A. M. LOBANOV, Zh. Tekhn. Fiz., 28 (1958) 273. 8 E. AMRHEtN, in J. A. PRINS, Proc. Intern. Conf. on Physics of Non Crystalline Solids, Delft, 1964, North-Holland Publ. Co., Amsterdam, p. 283. 9 E. AMRHEIN, KolloMZ., 216 (1967) 38. 10 V. FROSINI, E. BUTTA AND M. CALAMIA,J. Appl. Polymer Sci.,
11 (1967)527.
5 M. BACCAREDDA, E. BUTTA, V. FROSINI AND S. DE PETRIS,
Mater. Sci. Eng., 3 (1968/69) 157.
Received March 30, 1970 Mater. Sci. Eno., 6 (1970) 274-277
Heat capacity above 320°K and heat of fusion of hexagonal selenium In the course of a systematic investigation of physical properties of chalcogenide glasses we have recently had occasion to determine the heat capacity above room temperature and the heat of fusion of hexagonal selenium. While our results are not of the precision that is being reached today with more sophisticated apparatus, they are of sufficient accuracy to prompt us to report them here. Selenium powder, "Certified Reagent" grade, obtained from Fisher Scientific Company, was purified by vacuum distillation in Pyrex glass. Hexagonal selenium was prepared from the distillate by sealing a small sample into an evacuated Pyrex tube and holding it for three days at a constant temperature of 195°C. The heat capacity and the heat of fusion of the hexagonal selenium were measured with a Perkin-Elmer DSC-1B Differential Scanning Calorimeter. The procedure described by O'Neill 1 was used in the heat capacity determinations; a sample of single crystal alumina served as the heat capacity comparison standard. The heat of fusion was determined by comparing the area traced out on the recorder chart during a scan through the melting of a known mass of hexagonal selenium (melting point 494°K) with similar areas traced out for the melting of two standard metals, tin (AHf = 1720 cal/g-at.) and indium (AHf=780 cal/g-at.) 2. In Fig. 1 the results of our measurements for the heat capacity in the temperature interval 320 ~480°K are shown, along with the adiabatic calorimetry results ofAnderson 3, Desorbo 4, and Borelius and Paulson 5. Earlier results reported by Monval 6, obtained by drop calorimetry, are also shown on the same Figure, but more recent results reported by Gattow and Heinrich 7, which exhibit rather irregular behavior at higher temperatures, are not included. Each of the 17 points obtained from our
measurements is the average of from five to twelve results for that temperature, with the error bars indicating the average deviation of those results from their mean. On the basis of reproducibility, our results are considered to be accurate to _+0.2-0.3 cal/g-at, deg, since there are no known systematic errors in our method. A least-squares fit of our data to an equation linear in temperature yields, for the interval 320~-480°K, Cp (cal/g-at. deg) = 4.96+0.00253 T (°K),
(I)
a plot of which is shown in Fig. 1.
x×X x
++ ++ ++ + + + + + ++++++++++++
E o
~ &
6
~
5
4 200
I
I 300
L
[ 400
L~ 500
(°~) Fig. 1. Heat capacities for hexagonal selenium. • present results, Ref. 3, O Ref. 4, x Ref. 5, + Ref. 6, - eqn. (1), - - - eqn. (2). T
We have also joined our data with that of Anderson 3 and that of Desorbo 4 in a linear leastsquares fit over the temperature interval 200 °480°K. The resulting equation is Cp (cal/g-at. deg) = 5.40+0.00154 T (°K).
(2)
A plot of eqn. (2) is also shown in Fig. 1 and is seen to connect the two sets of data reasonably well, except for Desorbo's last five data points, between 275 ° and 300°K. These data points depart rather sharply from the results of Anderson, and from those of DeSorbo himself, when extrapolated from below Mater. Sei. Eng., 6 (1970) 277-278