Differential Thermal Analysis Using High Frequency Electrical Fields Stephen A. Wald and Charles C. Winding, The Geer Laboratory for Rubber and Plastics, School of Chemical Engineering, Cornell University, Ithaca, N. Y.
thermal analysis (DTA) has been applied mainly to the study of physical transitions occurring in small (milligram) samples of materials into which heat is tranqmitted by conduction or radiation. X differential thermal analyzer employing heating by high frequency electrical fieldq (DTA/HF) has been developed which can be used to perform analyses of physical transitions and chemical reactions occurring in the solid state. Comparatively massive samples (up to 100 grams) of powdery, rubbery, or tacky materials are heated internally and quite uniformly by a high frequency electric field, and their temperature is monitored continuously. Deviations from the programmed rate of heating are caused by thermal effects accompanying transitions or reactions. This device is particularly well suited to studying curing reactions in rubbers and plastics where for several reasons large samples are preferable to small ones: large samples are easier to handle than small (milligram) ones, samples are normally compounded in large batches, micro nonuniformities arising both from imperfect filler and curative dispersion and irregularities in sample packing are less likely to bias the data, subsequent analysis for the state of cure must be performed on gram-sized samples, and thermocouples may be positioned much more accurately. The low thermal conductivity of rubbers and plastics leads to high thermal gradients when heat is supplied by transfer through the surface of large samples as with conventional DTA. However, this low conductivity is conducive t o temperature uniformity with high frequency heating. In DTA/HF the sample is isolated from the reference. Hence, DTA/HF acts to sustain the temperature difference between sample and reference, whereas in DTA, by design any diff erential temperature is quickly dissipated to the sample holder and thermocouple so as t o reestablish the base line. This characteristic of DTA/HF has the consequence of establishing temperature differences of as large as 50” C. as opposed to fractions of degrees encountered with DTA. The obvious procedural advantage is that sample and reference no longer need to be heated simultaneously but can be run sequentially; the time variation of their absoONVENTIONAL DIFFERENTIAL
1622
ANALYTICAL CHEMISTRY
lute temperatures may be superimposed and the (large) temperature differentials noted directly. Moreover, if the same type and amount of filler is used for all runs, a single reference run may suffice for an entire series of sample runs a t constant power level. Two operational advantages are that signal amplification and base line dril*t compensation are obviated.
temperature differencebetween the sample and reference caused by the transition of interest. Note that when the subject material does not entirely constitute the sample, Equation 4 must be multiplied by the ratio of the total mass t o the mass of the subject material. Non-Isothermal Enthalpy Changes. For the simple chemical reaction A 3 products:
THEORY
dH
Isothermal Enthalpy Changes. The energy balance for the inert material in the reference cell is:
where A H ,
Ai where W , = electronically generated heat, Cal/time
t
dAi
-dt=
-bHrz
=
molar heat of reaction
=
number of moles of 9 present at time i
Substituting Equation 5 into 3 :
= time
m, = mass of reference C, = heat capacity, cal./gm., O
Integrating Equation 6 from time 0 to gives :
c.
T, = uniform temperature of the reference L, = heat loss
Also, for this reaction the rate expression is:
For the sample :
dH/&
dL, + W , = maCadT, -+ dt dt
-
(2)
where z
=
order of reaction with respect to component A
k
=
specific rate constant
Vi
=
volume of reacting medium at time i (assumed to be constant)
where dH/dt = enthalpy change due to transition or reaction/unit time. Under the following conditions:
m, = m,
=
m
c, = c, = c
Equating 6 and 7 and rearranging:
dL,/dt = dL,/dt
W, =
w,
mC k = AH,A,ZVl-’
subtracting Equation 1 from 2 gives:
d ATi
(dt)
Substituting Equation 7 for Ai” in Equation 9 k =
Integrating Equation 3 gives: AH = CAT,,,
(4)
where AH, the heat of transition per gram of sample, is an intensive parameter; and ATmaxis the maximum
Referring to Equation 4 it is apparent that the term ( n ~ ~ A H , / misc just ) equal to the maximum value attained by AT, so Equation 10 simplifies to :
I II
I
/ ,, , ,
It.
IO
I
;
.
I
If I
I
I
! 8
o l
.
0
2
4
6
e
IO
I2
TIME, m i n u t e r
2
4
6
e
TIME, minuter
IO
I2
14
Figure 2. Thermogram of benzoic acid sample with polypropylene reference superimposed
Figure 1. Thermogram of diphenyl sample with polypropylene reference superimposed
---
Diphenyl/Millical ( 1 / 1 ) Polypropylene/Millicai ( 1 / 1 ) Type J, Fe-C thermocouple
=
VAH, (dATi/dt) (x) (AT,,, - AZ'i)'
(11)
The argument is easily extended to reactions having more complicated rate expressions. EXPERIMENTAL
Apparatus. -4 Radio Frequency Co. (Medfield, Mass.) Model 1500-F, 1.2KW, 86 megacycles - per - second generator, controlled by a motor driven autotransformer, and equipped with a parallel plate capacitor output, is used to provide the internal and uniform heating required. The temperature in the sample is sensed continuously with an iron-constantan thermocouple located a t the center of the sample, filtered through a Leeds & Northrup Type 9835-B stabilized microvolt amplifier, and displayed on a Sargent Model MR recorder. Sample Reparation. Samples of organics and certain powdered polymers are prepared by grinding in a mortar with an equal weight of calcium carbonate ("Millical," Diamond Alkali). This mixture is then packed into a 1-inch diameter by 1 inch high polycarbonate ring, cut from l/ls-inch wall tubing and is ready for heating. The Millical is electronically active and provides heat t o inactive ma-
terials such as diphenyl, polyethylene and polypropylene. Samples of rubbery materials are prepared by 2-roll mill mixing of the crude rubber with an equal weight of Millical and assorted curatives and plasticizers. The compounded stock is banded, 21/4-in~hdiameter by l/4inch thick disks are cut out, and these are stacked in a cylindrical compression mold where they are compressed a t room temperature to about 5000 p.s.i. and held until the pressure has decayed substantially. To prevent porositycaused swelling of the 21/4 X 1-inch rubber tablet as it is heated, the sample is encased in a sample holder of Teflon. Procedure. The sample is placed between the plates, the thermocouple inserted to the sample's center, Fiberglas insulating material placed around the sample to reduce convection heat losses, and the power manually adjusted t o a level predetermined to give the desired initial rate of heating. Following this run, operational variables are duplicated on a reference material thermally identical to the sample. For powdered organic materials undergoing transitions or reactions below 160' C., a one-to-one mixture of Millical and finely divided polypropylene is a satisfactory reference. For rubbery materials, the reference composition differs from that of the sample only by the omission of the curing
---
Benzoic acid/Millical ( 1 / 1 ) Polypropylene/Millical ( 1 / 1 ) Type J, Fe-C thermocouple
agent. -4hot compression molded Millical-polypropylene mixture has also been used successfully. The sample and reference may also be heated simultaneously. RESULTS AND DISCUSSION
I n Figure 1 are shown the heating and cooling thermograms for a one-to-one mixture of diphenyl and Millical. The extrapolated initial and end points of the arret in the heating curve, which differ by only about 1/2' C., correspond to the melting range observed independently. The cooling arret is broader than the heating arret because a zone freezing, non-isothermal process is occurring. The dotted line superimposed on Figure 1 is for a polypropylene-Millical reference mixture. The vertical distance between the end point of the heating arret and the reference curve, corresponding to AT,,, in Equation 4, is 42.0' C. Assuming that the average specific heat of the mixture is 0.3, Equation 4 predicts the heat of fusion to be 25.2 cal./gram. This agrees to within 4y0of the published value of 26.1 cal./ gram. Benzoic acid produces the thermogram of Figure 2 in which the melting range is identical to that measured by the capillary method. The heat of fusion agrees with the published value of 33.9 cal./gram only if the weight of the polycarbonate sample holder is inVOL. 37, NO. 12, NOVEMBER 1965
* 1623
4 Figure 3. Thermogram of linear polyethylene sample with polypropylene reference superimposed I'
.- .- -
Poiyethylene/Millicol ( 1 / I ) Polypropylene/Millical ( 1 / 1 ) .conventional DTA thermogrom of polyethylene Type J, Fe-C thermocouple
TIME, minutes
cluded in the total mass of the sample. From Figure 2 ATmsx= 38" C. Assuming that the average specific heat is 0.3 cal./gram, ' C., the calculated heat of fusion is 34 cal./gram in good agreement with the published figure.
High density polyethylene (Hi-Fax, Hercules Powder Co.) melts over the range 120' to 129' C based on the arret in Figure 3, and ATmax = 51' C. Assuming that the average specific heat is 0.4 cal./gram, " C., that the crystal-
linity is 90%, and including the mass of the polycarbonate sample holder, the calculated heat of fusion is 68 cal./gram. The accepted heat of fusion for crystalline polyethylene is 66.2 cal./gram. The dotted line on Figure 3 is a conventional DTA thermogram of this same material. Several quantitative advantages of DTA/HF over DTA are apparent. The enthalpy change accompanying a physical transition or a chemical reaction is proportional to the distance between two curves, rather than the area under a curve. There are no calibration coefficients in DTA/HF, whereas in DTA each individual apparatus must be calibrated. DTA/HF strictly defines a melting point or range by an arret, while in DTA the apex of the peak does not necessarily correspond to the melting temperature. Work is continuing on materials not easily handled in conventional DTA equipment.
Semiautomatic Precision Pipet Edgar L. Eckfeldt and E. W . Shaffer, Jr., Research and Development Center, Leeds and Northrup Co., North Wales, Pa. HE EXPERIMENTAL pipet described in Tthis paper was devised to meet a need in coulometric analysis. In the coulometric technique the sample aliquot should contain an amount of reactive material that is commensurate with the generating capacity of the coulometric equipment. If the sample is too large, the titration time will be undesirably long. Samples as small as 1 ml. may a t times be desired. Conventional methods for measuring samples of the order of 1 ml. in size are not entirely satisfactory. Ordinary pipets, while convenient, suffer from errors arising from variability of solution drainage. Transfer pipets that are calibrated to contain a specified volume require careful handling. Weight burets, though offering good precision, have the disadvantage of being tedious and time consuming to use. Seligson (3) has described a pipet for conveniently measuring small solution volumes with a maximum precision of about 0.370, but this precision is much below the capabilities of coulometry. Indeed, coulometric analysis is in-
1624
0
ANALYTICAL CHEMISTRY
herently suited for making highly precise measurements. Available coulometric techniques and apparatus can achieve a limit of error of 0.01 to 0.05% or better (1, 2 ) . It was therefore desirable to have a sampling device that was easy to operate and which measured with a precision corresponding to that of coulometry. Accordingly, the semiautomatic precision pipet illustrated in Figure 1 was devised. The measuring part of the equipment comprised a calibrated capillary tube or borosilicate glass (2.0- f 0.1-mm. bore and 31.8 cm. in length) sealed as shown between two three-way stopcocks (Corning 7400). The upper stopcock by one inlet tube made connection with the sample solution through a glass capillary tube of about 1-mm bore. By way of the other inlet the upper stopcock was connected to a reservoir bottle containing an auxiliary solution, the glass line between being provided with a stopcock and a chamber for roughly measuring out 10-ml. portions of solution. One outlet of the lower stopcock
led to the coulometric cell through a glass capillary tube of 2-mm. bore, provided with a discharge tip. The other outlet of the lower stopcock led through a capillary tip into a 10-ml. rough-measurement chamber. The chamber had a draw-off cock which discharged to drain. Solution connections were made by means of short sections of inert plastic tubing which closely butt-joined the glass lines. Some control over temperature was desirable, because the density of water and many aqueous solutions changes by 0.02 to 0.03% per degree in the range from 20" to 30' C. The water jacket surrounding the calibrated capillary served satisfactorily to stabilize against changes in room temperature and provided means for controlling, and in conjunction with the included thermometer, for measuring the temperature of the sample solution. Before constructing the calibrated capillary unit, the three-way stopcocks should be inspected to make sure that the holes through the plugs are of the same diameter as the bore of the measur-
