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Automatic microcalorimetric apparatus for the study of thermal processes resulting from mechanical deformation of polymers
METHODS OF INVESTIGATION AUTOMATIC MICROCALORIMETRIC A P P A R A T U S FOR THE STUDY OF T H E R M A L PROCESSES RESULTING FROM MECHANICAL DEFORMATION OF POLYMERS * Yu. K. GODOVSKII,G. L. SLONINISKIIand V. F. ALEKSEYEV Institute of Hetero-organic Compounds, U.S.S.R. Academy of Sciences
(Received 21 June 1968) i ~ E C ~ I C A L deformation of solids is accompanied by thermal effects. I t was Joule who established that, in drawing, rubber strips became hot and are cooled when returned to the initial state [I]. I t was later found that steel wire when loaded absorbs heat from the surrounding atmosphere and when relieved liberates heat. These effects are ignored in practice and material deformation is considered solely as a mechanical problem. At the same time quantitative information on thermal effects accompanying material deformation enables us to understand more fully the molecular nature of deformation. An example of this approach is given b y a series of studies b y Miiller et at. dealing with thermal effects accompanying the deformation of various materials, including polymers [2-4]. Thermodynamic examination of the simplest type of deformation - - elongation, gives a ratio which relates the heat of elastic deformation Q to the deforming force Z and the linear coefficient of thermal expansion
[1]: dQ= flTldZ
(la)
Z
AQ = f flTldZ = flTlZ
(lb)
0
where T is the absolute temperature; I is specimen length; fl is the linear coefficient of thermal expansion. Equation (Ib) is only correct to a first approximation since fl and 1 are functions of Z. However, with small deformations these values can be regarded as constant. A simple conversion of equation (lb) gives a ratio between heat and relative elongation:
AQ m
riTE - -pc
(2)
whore m is the specimen weight; p is the density; E is Young's moduls; 8 is the relative elongation. The coefficient of thermal expansion determines the sign of the thermal effect produced in deformation. Elongation of materials with a positive coefficient of thermal expansion (metals, glass) is accompanied b y an endothermal effect and the deformation of rubber (for these fl is negative when e ~ 8-10°/o) by on exothermal effect. I t can be seen from equation (2) that the proportion of specific thermal effect to relative elongation incorporates structurally sensitive parameters (fl, p, E). This suggests that deformation of specimens of differing structures will be accompanied b y various thermal effects. This paper describes an automatic micro-calorimetric apparatus used for recording thermal effects resulting from mechanical deformation of elastic bodies (mainly polymers) and gives examples of the thermal behaviour of polymers in elastic and plastic deformation. * Vysokomol. soyed. A l l : No. 5, 1181-1188, 1969. 1345
1346
Yu. K. GODOVSKII et al.
Layout of the microcalorimetric apparatus. The construction of the microcalorimetrio apparatus takes into account the following main practical requirements: 1) type of deformation--elongation; 2) the samples used for the investigation should be fairly small (not exceeding 100 rag) in the form "of film or fibre; 3) the construction of the apparatus should facilitate 800-900~o deformation of specimens (with an initial length of 10 ram) over a fairly wide temperature range and a wide range of deformation rates. An analysis of the experimental data available indicates that thermal effects accompanying the deformation of samples of the above dimensions do not exceed 0.1-0"2 calorie. This necessitates a highly sensitive calorimeter. The microcalorimetric apparatus is based on measurement of heat flow, developed
I FIG. 1. F u n d a m e n t a l layout of a microcalorimetric apparatus: 1,2--electronic potentiometer, 3--stressing device; 4--dynamometric unit; 5--thermostatic device; 6--thermostat; 7-microcalorimeter; 8--sample. by Tian and Kal've [5] a n d the principle of tensometric determination of stress in deformation [6]. A layout of the apparatus is shown in Fig. 1. The sample fixed in clamps inside the measuring cell of the calorimetric is stretched b y a loading device incorporating a dyna* mometric unit. The heat flow produced during deformation of the specimen produces a temperature difference between the microcalorimetric cells, which is automatically recorded for a given time by an electronic potentiometer. At the same time the force of deformation is recorded in the other electronic potentiometer as a function of time. Layout of the microcalorimeter. The microcalorimeter is a cylindrical copper u n i t of 80 m m diameter a n d 140 m m height with two symmetrical cylindrically arranged holes 15 m m in diameter. The unit consists of two semi-cylinders and the line of cross section goes through the diameter of the openings. I n each of the holes a microcalorimetrie cell of the following construction is set up. On a brass sleeve 11.2 m m in outer diameter a thermocouple is assembled consisting of 810 differential copper-eonstantan thermal junctions (R----126 ohm) prepared eleetrolytically [7]. The thermocouple is assembled on 18 thin ceramic rings (I m m thick), on each of which there are 45 differential thermal junctions. The thermoCouple is fixed on a brass sleeve by a thin adhesive layer, which at the same time insulates it from the sleeve. The micreealorimetric cells thus assembled are situated in the opening of
Study of thermal processes resulting from mechanical deformation of polymers 1347 one of the semi-cylinders and are covered by the other semi-cylinder. The outer junctions are also insulated from the copper unit with a thin adhesive layer. The semi-cylinders are tightly drawn by special bolts to ensure good thermal contact between the thermal b a t t e r y and the ~mit. The thermocouples of both ceils are connected externally through the base of the unit and with each other.
z x z x r:
.--
_//
"-
~4X
-
x x
_
Y
Y
-
~^^ \
FIG. 2. Microcalorimeter and thermostatic device: / - - t e f l o n ring; 2 - - a l u m i n i u m cylinder; 3--polyurethane foam insulation; 4 - - t h e r m o s t a t i c water jacket; 5 - - e x p a n d e d plastic compartment; 6--teflon ring; 7 - - e x p a n d e d plastic top; 8 - - I n v a r rods; 9--teflon tops; 10--top; / / - - e a s i n g on which the thermal battery is assembled; 12--upper clamps; 13--sample; 14--lower clamps; 15--insulating plate; 16--microcalorimeter. Ground calorimetric I n v a r sockets with an inner diameter of 10 m m are inserted in the brass sleeves of the microcalorimetric cells. At the base of the calorimeetric socket, which is 125 m m in height, a device is arranged to strengthen lower clamp with the specimen studied. The sockets are closed with teflon stoppers which have openings for the passage of current. The specimen is deformed in one of the microcalorimetric cells and the corresponding specimen in the unstressed state is placed in the other to ensure equal inertia properties of the cells. After charging the cells are closed with a teflon lid with recesses for the stoppers and the lid is fastened by screws to the unit. When small heat flows are recorded the thermostatic control of the calorimeter is extremely important. To maintain constant temperature, a special device was developed (Fig. 2). The calorimeter is placed in an aluminium socket with a wall thickness of 15 mm, and is separated from the socket walls by an air gap of 10 m m thickness and centered in the socket by two teflon rings. The ainminium socket equalizes the external thermal variations en route to the microcalorimeter. On the outside an insulating polyurethane foam jacket is fixed on the socket. This system is placed in the metal thermostat, which is provided with a cavity for the circulation of the heat-transfer medium supplied from a ttoppler
1348
Yu. K. GODOVSKII c t a / .
thermostat. The metal thermostat is placed in the expanded plastic compartment. The whole system is rigidly fastened on a plate, which can be m o v ed vertically by a screw mechanism. The materials used in the microcalorimeter enable work to be carried out up to 85-90 °. F o r operation at temperatures sonsiderably different from room temperature a device is provided for simultaneous thermostatic control of the current with an upper clamp protrudlng from the microcalorlmetric cell. The loading system and dynamometric unit. The loading system of the specimen incorporates a reversible electric motor, V-belt transmission, eight-phase worm reducer and a dynamometric unit. The eight-phase reduction enables the rate of loading to be varied from 112 to 0"875 ram/rain with a reduction coefficient of 2. A system for reading deformation is also arranged on the worm reducer. The whole apparatus is assembled on a pedestal table. At the top of the table the drive and loading system is arranged and the thermostat with the calorimeter is in the pedestal. Deformation forces are measured by a spring dynamometer, on which tensometric data units are fixed at the points of m a x i m u m camber. We used a system of 8 wire tensom e t r i c ' d a t a units (140 ohm resistance each)' four of which were situated on the operating d y n am o m et er and the other four on the compensating dynamometer. The data units on each dynamometer were connected sequentially and these systems were joined by a bridge. The data units are supplied with direct curernt from a b at t er y of standard cells. According to the purpose of investigation and the materials studied a set of dynamometers of different rigidity is provided. The operating dynamometer is arranged on two prims with a variable distance between them, which are rigidly fixed on a cross piece actuated by the screw of the worm reductor. The upper clamp is suspended by a rod system on the dynamometer. Temperature measurements and stress are recorded on two EZ-2 (Czechoslovakia) recording electronic potentiometers with sensitivities of 5; 2; 1; 0.5; 0.2 and 0.1 mV full scale deflection. Calibration of the device. The operating dynamometer is calibrated using small weights. U p to m a x i m u m loads (5 kg) linearity is observed between the recording on the potentiometer and the load. The calorimeter was calibrated by means of the Joule effect. D.c. power supplied t o the calorimetric cell was measured potentiometrically. The heater h a s placed on polymerspecimens in the form of films of varying lenghts and thicknesses, which were arranged in. clamps. The current supplied to the heater was measured by a multiscale M-82 galvanometer. milliampermeter. W i t h prolonged current through the heater the steady deviation from the~ zero line was recorded in the potentiometer, which with this current was practically independent of the size and shape of the specimen with the heater (heaters placed on films 10, 40,. 60 and 80 m m long were investigated). Power W (t) in relation to aslow thermal process can be calculated from the equatiorL
W(t)=k[~T(t)+~d~d---~]
(3)
where k is the constant of calibration according to deviation; ~ is a time constant; AT (t) are the readings of the recording device. The total heat effect is calculated by integration of the thermal power
Q : f W (t)dt.
(4)
I t was established b y calibration according to deviation t h a t at 20±0.1 ° an d w i t h a potentiometer sensitivity of 0-1 m V a deviation of 1 m m from the zero line is caused b y
Study of thermal processes resulting from mechanical deformation of polymers 1349 heat liberation of 5 × 10 -~ cal/sec.mm. Hence it follows t h a t the value of K at given potentiometer sensitivity is 5 × 10 -6 cal/sec.mm.* The time constant v of the microcalorimeter depends on the contents of the calorimetric vessel. I t was determined from the time of half-deviation t0.s, the constant thermal power being disconnected. v=t0.Jln 2 (5) I t appeared during calibration t h a t with the specimen dimensions to be investigated values of ~ vary from 30 to 70 sec (zE3 sec), according to the weight and thermo-physical properties of the polymer samples. Therefore, the dependence of T on the dimensions and thermo-physical properties of the polymers examined was determined. I t could be anticipated t h a t a large number of measurements will be conducted by the so-called ballistic method, i.e. when heat liberation takes place during a short period of
AT~Tma× 10 -
~.+~._.-----'~ "~'°'-+'°'-~
0.5- z~3 ,~./ /
/~
I !
I 2
I 3
t/'~
F i e . 3. Dependence of r a t i o of peak m a x i m u m ztT' to m a x i m u m deviation zITma= on relative heating t i m e (time constant v was used as t i m e unit); v is: 1--30; 2--50; 3 - - 7 0 see.
time (e.g. loading the elastic material to a considerable extent is achieved in a second; times of heat absorption accompanying these processes are, of course, of the same order). The ballistic properties of the microcalorimeter were therefore studied in detail. I t is known t h a t when the duration of heat liberation is less than the time constant of the device, the diagram of the process shows an acute peak and its m a x i m u m under certain conditions is proportional to the ~hermal effect [5]. Two series of measurements were made: the first was with constant duration of heat liberation and varying amounts of heat; the second with constant heat liberation but varying duration of heating. The tabulated results bring us to the conclusion t h a t with a heating time less than 3/4 the ratio of m a x i m u m temperature difference (peak maximum) to the amount of heat liberated is a constant value with an accuracy of not less than ± 2 ~o- This ratio subsequently begins to decrease. Figure 3 illustrates the dependence on heating time of the ratio of peak m a x i m u m AT' to the m a x i m u m deviation zlTma~ for a given thermal power. Figure 3 illustrates t h a t AT" reaches ATmax in practice when t = 3 v . * I t should be noted t h a t the sensitivity of the microcalorimeter can be easily increased by one order of magnitude at least by using a photocompensating amplifier. However, we refrained from using this owing to its considerable sensitivity to even the slightest mechanical vibration.
Yu. K. GODOVSKII et al.
1350
W i t h this duration of action of the heat source (10-15 sec), when a strict proportionality is observed between the peak m a x i m u m and the thrmal effect which causes this peak, numerous experiments can be conducted to determine the thermal effect of elastic deformation. RESULTS OF BALLISTIC CALIBRATIONS Experiment No.
Resistance of the heater, ohm
I,mA
16"28 16.28 16.28 16.28 16.28 16.28 24.55 24.55 24.55 24.55
16"8 16"8 16'8 16"8 16'8 16'8 6"17 10"48 15"70 23"55
H e a t in g time, sec
.3 5 6 10 15 50 10 10 10 10
Q × 10-L cal
3.295 5.491 6.589 10.982 16-473 54.910 2.235 6.141 13.200 32.415
AT,
AT'IQ,
inIn
mm/cal
8.0 13.4 16.3 26.8 37.6 91.8 5.4 15.0 32.3 79.2
2428 2440 2473 2441 2283 1670 2438 2453 2451 2447
In those cases when this duration appears inadequate, the AT'/ATmax ratio can be easily determined from Fig. 3 for any duration. I n addition, the time constant v can be artificially increased by increasing the thermal value of the cell (i.e. also v) by placing in it a suitable insulator.
lfm]~
I
M
tl/¢
k
k
t~
!
tY' 7/r~ FIG. 4. Thermograms of heat effects during stressing and releasing of a polystyrene film: 1,2,3,4--loading; 1", 2", 3", d'--releasing. The use of the ballistic method facilitates the study of two simultaneous processes, one of which is ballistic and the other slow. Rapid loading and subsequent relaxation can, for example, be regarded as such effects. The m e t h o d of analysing the curves recorded in these cases has been previously described in detail [5].
Study of thermal processes resulting from mechanical deformation of polymers 1351 An analysis of possible errors in determining thermal power and integral thermal effects shows t h a t errors of measurement are chiefly determined b y the inaccuracy in the graphical differentiation of the curve plotted and in planimetric measurements of areas. I t was found t h a t the accuracy of determining W (t) and Q is within -4-2~o. The accuracy of determining stress in deformation is also 4-2%. Analysis indicates that deformation is the most difficult to determine, the accuracy of determination being not more t h a n 4-10~o for average elastic deformations (a=5-10~o) and moderate rates of loading.
Q~rncal
mcal/g a I/
5
200 _
]9
o
._p.+o,"2 ~ I00
I
!
!
2
Z,~
2
3 C,%
FIG. 5. Dependence of the thermal effect on loading for a polystyrene film (a) and of the ratio on relative deformation 8 (b): / - - l o a d i n g ; 2--releasing.
Q/m
As examples of the thermal behaviour of polymers during deformation let us examine the nature and magnitude of thermal effects accompanying elastic elongation of polystyrene films and elastic and plastic deformation of polyethylene films. Figure 4 reproduces curves of heat liberation and heat absorption and even stress-time
O/A
5
FIG. 6. Dependence of the
Q/A ratio
i
i
1
2
¢,%
on relative deformation e of a polystyrene film.
curves for a polystyrene film 3 m m in width, 70 m m in length a n d 0.12 m m in thickness. The specimen was subjected to i n t e r m i t t e n t stres (and then released) using a force which gradually increased.
Y r . K. GODOVSKZZet al.
1352
With small forces of deformation thermal effects in stress and release agreed and practically no stress relaxation was observed. Under considerable load, stress relaxation was observed and thermal effects during release were somewhat smaller t h a n on loading. This proves that stress relaxation in a polystyrene film is accompanied by an exothormal effect. Figure 5a illustrates the dependence of heat on deforming force. The data are very well expressed b y a linear relation, from the slope of which the linear coefficient of thermal expansion was calculated according to equation (1). I t appeared to be 6.77 × 10 -5 degree -1. This value shows satisfactory agreement with data obtained previously b y the same method [2] and with other literature data [8]. Figure 5b shows the dependence of specific heat on relative deformation. Hero a somewhat larger variation of experimental data is observed duo to the low accuracy of measuring deformation. F r o m the gradient of the straight line obtained, the elasticity modulus Eq was c~lculated according to equation (2) using values p = 1.05 g/cm 8 and fl,= 6.77 × I0 -~ degree -1. The modulus thus calculated was E q = 199 kg/mm 2. This value was compared with modulus E, determined from mechanical characteristics. This modulus was E , = 1 7 0 kg/mm. The deviation was about 15%. This example indicates that an investigation of thermal effects accompanying elastic deformation of polymers opens up the possibility of determining mechanical and other characteristics (e.g. fl) from purely thermal data.
2"
z,~ t
0
I
g
g
#
Time,min
4
FIG. 7. Thermal effects during elongation of a polyethylene film: a--dependence of the force of elongation Z and b--dependence of the thermal power W on time. I n this example it is also of interest to compare the macharfical work A with the heat Q. Figure 6 indicates the dependence of the Q/A ratio on relative elongation. (Work was calculated from the ratio A = 0.5 Z Al). Theoretically this ratio is Q/A = 2fiT~8. This is the equation of an equilateral hyperbola, from which it follows that at very low relative elongations the thermal effect m a y m a n y times exceed the value of mechanical work (e.g. for 6=0.005, T = 3 0 0 ° K and fl=6.77 × 10 -5 degree-i; the ratio of Q/A=8.1). Figure 6 shows that a variation in the Q/A ratio for a polystyrene film is, in fact, expressed by a hyperbolic relation, the experimental values of this ratio showing satisfactory agreement with theoretical values. Figure 7 shows data concerning the deformation of an isotropic polyethylene film 0.2 m m in thickness and 2.5 m m in width at a rate of 0"233 mm/sec. During the initial stage of stress an endothermal effect is observed which corresponds to elastic deformation, then as "neck" formation goes on in the specimen the endothermal effect becomes exothermal, and reaches
Study of thermal processes resulting from mechanical deformation of polymers 1353 a practically stationary state corresponding to a constant rate of neck formation in th(, sample. The thermal power Wit) produced at constant rate of neck formation is 3.08 .< l0 nmal/sec and the mechanical power is 4 . 1 5 × 10 -~ mcM/sec (the force of' deformation Z in neck formation is 0.76 kg). The ratio of these powers is close to unity (0.75). I f stress is stopped during neck formation stress in the specimen is relaxed (see Fig. 7) and the thermal power ceases. When the sCress is subscctuently fully released an endothermal effect is observed. An inverse pattern is observed when the isotropic polyettwleue fihn undergoes elastic deformation in the range in which no neck formation has occurred ( ~ 12 150o). In this case the endothermal effect corresponds to stress of the specimen and the (~xothermal effect to release. A change in sign of the thermal effect when the polye,thylen(~ fihn changes from the isotropic to tile oriented state I)oints to the fact theft the m~ture e l deformation of oriented polyethylene is different in principle from the nature of (h~f~)rnmtion of an isotropic sample. A similar effec~ is also observed for many other crystalline polym(,rs [2, 9]. CONCLUSIONS A description is given el" an automatic low-inerbia microcalorilnetrie apparatus used for the study of thermal processes resulting from mechanical deformation of I)olymer fihns and fibres and examples are given of the thermal behaviom' of polymers during elastic and plastic deformation. Tra~slctted by 1£. SEMFRE REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
O. D. KttVOL'SON, Kurs fiziki (Course on Physics), voI. 3. Izd. I / SFSR, 19(~2 A. EN(IELTER and F. II. MtILLER, Kolloid-Z. und Z. flit Polymere 157: 89, 195s W. DICK and F. It. Mt~LLER, Kolloid-Z. und Z. fiir Polymere 172: 1, 1962 B. KI, Noveishie metody issledovaniya polimerov (I,%test Methods for the Investigati,)n of Polymers). Izd. "Mir", 1966 E. KAL'VE and A. PRAT, Mikrokatorimdriya (Microcalorimetry). Izd. inostr, lit., 1963 Izmerenie napryazhenii i usilii v detalyakh mashin (Measurement of Stresses and Forces in Machine Components). Edited by N. I. PRIGOROVSKII, Mashgiz, 1955 Yu. K. GODOVSKII and Yu. P. BARSKII, Plast. massy, No. 7, 57, 1965; Vysok~nnel. soyed. 8: 395, 1966 Physik der Kunstoffe, Pub. W. Holzmiiller und K. Altenburg, Berlin, 1961 (I. L. SLONIMSKII, Yu. K. (IODOVSKII, V. S. PAPKOV and T. A. DIKAREVA, \:ysokomol, soyed. B10: 798, 1968
(Received 21 June 1968) i ~ E C ~ I C A L deformation of solids is accompanied by thermal effects. I t was Joule who established that, in drawing, rubber strips became hot and are cooled when returned to the initial state [I]. I t was later found that steel wire when loaded absorbs heat from the surrounding atmosphere and when relieved liberates heat. These effects are ignored in practice and material deformation is considered solely as a mechanical problem. At the same time quantitative information on thermal effects accompanying material deformation enables us to understand more fully the molecular nature of deformation. An example of this approach is given b y a series of studies b y Miiller et at. dealing with thermal effects accompanying the deformation of various materials, including polymers [2-4]. Thermodynamic examination of the simplest type of deformation - - elongation, gives a ratio which relates the heat of elastic deformation Q to the deforming force Z and the linear coefficient of thermal expansion
[1]: dQ= flTldZ
(la)
Z
AQ = f flTldZ = flTlZ
(lb)
0
where T is the absolute temperature; I is specimen length; fl is the linear coefficient of thermal expansion. Equation (Ib) is only correct to a first approximation since fl and 1 are functions of Z. However, with small deformations these values can be regarded as constant. A simple conversion of equation (lb) gives a ratio between heat and relative elongation:
AQ m
riTE - -pc
(2)
whore m is the specimen weight; p is the density; E is Young's moduls; 8 is the relative elongation. The coefficient of thermal expansion determines the sign of the thermal effect produced in deformation. Elongation of materials with a positive coefficient of thermal expansion (metals, glass) is accompanied b y an endothermal effect and the deformation of rubber (for these fl is negative when e ~ 8-10°/o) by on exothermal effect. I t can be seen from equation (2) that the proportion of specific thermal effect to relative elongation incorporates structurally sensitive parameters (fl, p, E). This suggests that deformation of specimens of differing structures will be accompanied b y various thermal effects. This paper describes an automatic micro-calorimetric apparatus used for recording thermal effects resulting from mechanical deformation of elastic bodies (mainly polymers) and gives examples of the thermal behaviour of polymers in elastic and plastic deformation. * Vysokomol. soyed. A l l : No. 5, 1181-1188, 1969. 1345
1346
Yu. K. GODOVSKII et al.
Layout of the microcalorimetric apparatus. The construction of the microcalorimetrio apparatus takes into account the following main practical requirements: 1) type of deformation--elongation; 2) the samples used for the investigation should be fairly small (not exceeding 100 rag) in the form "of film or fibre; 3) the construction of the apparatus should facilitate 800-900~o deformation of specimens (with an initial length of 10 ram) over a fairly wide temperature range and a wide range of deformation rates. An analysis of the experimental data available indicates that thermal effects accompanying the deformation of samples of the above dimensions do not exceed 0.1-0"2 calorie. This necessitates a highly sensitive calorimeter. The microcalorimetric apparatus is based on measurement of heat flow, developed
I FIG. 1. F u n d a m e n t a l layout of a microcalorimetric apparatus: 1,2--electronic potentiometer, 3--stressing device; 4--dynamometric unit; 5--thermostatic device; 6--thermostat; 7-microcalorimeter; 8--sample. by Tian and Kal've [5] a n d the principle of tensometric determination of stress in deformation [6]. A layout of the apparatus is shown in Fig. 1. The sample fixed in clamps inside the measuring cell of the calorimetric is stretched b y a loading device incorporating a dyna* mometric unit. The heat flow produced during deformation of the specimen produces a temperature difference between the microcalorimetric cells, which is automatically recorded for a given time by an electronic potentiometer. At the same time the force of deformation is recorded in the other electronic potentiometer as a function of time. Layout of the microcalorimeter. The microcalorimeter is a cylindrical copper u n i t of 80 m m diameter a n d 140 m m height with two symmetrical cylindrically arranged holes 15 m m in diameter. The unit consists of two semi-cylinders and the line of cross section goes through the diameter of the openings. I n each of the holes a microcalorimetrie cell of the following construction is set up. On a brass sleeve 11.2 m m in outer diameter a thermocouple is assembled consisting of 810 differential copper-eonstantan thermal junctions (R----126 ohm) prepared eleetrolytically [7]. The thermocouple is assembled on 18 thin ceramic rings (I m m thick), on each of which there are 45 differential thermal junctions. The thermoCouple is fixed on a brass sleeve by a thin adhesive layer, which at the same time insulates it from the sleeve. The micreealorimetric cells thus assembled are situated in the opening of
Study of thermal processes resulting from mechanical deformation of polymers 1347 one of the semi-cylinders and are covered by the other semi-cylinder. The outer junctions are also insulated from the copper unit with a thin adhesive layer. The semi-cylinders are tightly drawn by special bolts to ensure good thermal contact between the thermal b a t t e r y and the ~mit. The thermocouples of both ceils are connected externally through the base of the unit and with each other.
z x z x r:
.--
_//
"-
~4X
-
x x
_
Y
Y
-
~^^ \
FIG. 2. Microcalorimeter and thermostatic device: / - - t e f l o n ring; 2 - - a l u m i n i u m cylinder; 3--polyurethane foam insulation; 4 - - t h e r m o s t a t i c water jacket; 5 - - e x p a n d e d plastic compartment; 6--teflon ring; 7 - - e x p a n d e d plastic top; 8 - - I n v a r rods; 9--teflon tops; 10--top; / / - - e a s i n g on which the thermal battery is assembled; 12--upper clamps; 13--sample; 14--lower clamps; 15--insulating plate; 16--microcalorimeter. Ground calorimetric I n v a r sockets with an inner diameter of 10 m m are inserted in the brass sleeves of the microcalorimetric cells. At the base of the calorimeetric socket, which is 125 m m in height, a device is arranged to strengthen lower clamp with the specimen studied. The sockets are closed with teflon stoppers which have openings for the passage of current. The specimen is deformed in one of the microcalorimetric cells and the corresponding specimen in the unstressed state is placed in the other to ensure equal inertia properties of the cells. After charging the cells are closed with a teflon lid with recesses for the stoppers and the lid is fastened by screws to the unit. When small heat flows are recorded the thermostatic control of the calorimeter is extremely important. To maintain constant temperature, a special device was developed (Fig. 2). The calorimeter is placed in an aluminium socket with a wall thickness of 15 mm, and is separated from the socket walls by an air gap of 10 m m thickness and centered in the socket by two teflon rings. The ainminium socket equalizes the external thermal variations en route to the microcalorimeter. On the outside an insulating polyurethane foam jacket is fixed on the socket. This system is placed in the metal thermostat, which is provided with a cavity for the circulation of the heat-transfer medium supplied from a ttoppler
1348
Yu. K. GODOVSKII c t a / .
thermostat. The metal thermostat is placed in the expanded plastic compartment. The whole system is rigidly fastened on a plate, which can be m o v ed vertically by a screw mechanism. The materials used in the microcalorimeter enable work to be carried out up to 85-90 °. F o r operation at temperatures sonsiderably different from room temperature a device is provided for simultaneous thermostatic control of the current with an upper clamp protrudlng from the microcalorlmetric cell. The loading system and dynamometric unit. The loading system of the specimen incorporates a reversible electric motor, V-belt transmission, eight-phase worm reducer and a dynamometric unit. The eight-phase reduction enables the rate of loading to be varied from 112 to 0"875 ram/rain with a reduction coefficient of 2. A system for reading deformation is also arranged on the worm reducer. The whole apparatus is assembled on a pedestal table. At the top of the table the drive and loading system is arranged and the thermostat with the calorimeter is in the pedestal. Deformation forces are measured by a spring dynamometer, on which tensometric data units are fixed at the points of m a x i m u m camber. We used a system of 8 wire tensom e t r i c ' d a t a units (140 ohm resistance each)' four of which were situated on the operating d y n am o m et er and the other four on the compensating dynamometer. The data units on each dynamometer were connected sequentially and these systems were joined by a bridge. The data units are supplied with direct curernt from a b at t er y of standard cells. According to the purpose of investigation and the materials studied a set of dynamometers of different rigidity is provided. The operating dynamometer is arranged on two prims with a variable distance between them, which are rigidly fixed on a cross piece actuated by the screw of the worm reductor. The upper clamp is suspended by a rod system on the dynamometer. Temperature measurements and stress are recorded on two EZ-2 (Czechoslovakia) recording electronic potentiometers with sensitivities of 5; 2; 1; 0.5; 0.2 and 0.1 mV full scale deflection. Calibration of the device. The operating dynamometer is calibrated using small weights. U p to m a x i m u m loads (5 kg) linearity is observed between the recording on the potentiometer and the load. The calorimeter was calibrated by means of the Joule effect. D.c. power supplied t o the calorimetric cell was measured potentiometrically. The heater h a s placed on polymerspecimens in the form of films of varying lenghts and thicknesses, which were arranged in. clamps. The current supplied to the heater was measured by a multiscale M-82 galvanometer. milliampermeter. W i t h prolonged current through the heater the steady deviation from the~ zero line was recorded in the potentiometer, which with this current was practically independent of the size and shape of the specimen with the heater (heaters placed on films 10, 40,. 60 and 80 m m long were investigated). Power W (t) in relation to aslow thermal process can be calculated from the equatiorL
W(t)=k[~T(t)+~d~d---~]
(3)
where k is the constant of calibration according to deviation; ~ is a time constant; AT (t) are the readings of the recording device. The total heat effect is calculated by integration of the thermal power
Q : f W (t)dt.
(4)
I t was established b y calibration according to deviation t h a t at 20±0.1 ° an d w i t h a potentiometer sensitivity of 0-1 m V a deviation of 1 m m from the zero line is caused b y
Study of thermal processes resulting from mechanical deformation of polymers 1349 heat liberation of 5 × 10 -~ cal/sec.mm. Hence it follows t h a t the value of K at given potentiometer sensitivity is 5 × 10 -6 cal/sec.mm.* The time constant v of the microcalorimeter depends on the contents of the calorimetric vessel. I t was determined from the time of half-deviation t0.s, the constant thermal power being disconnected. v=t0.Jln 2 (5) I t appeared during calibration t h a t with the specimen dimensions to be investigated values of ~ vary from 30 to 70 sec (zE3 sec), according to the weight and thermo-physical properties of the polymer samples. Therefore, the dependence of T on the dimensions and thermo-physical properties of the polymers examined was determined. I t could be anticipated t h a t a large number of measurements will be conducted by the so-called ballistic method, i.e. when heat liberation takes place during a short period of
AT~Tma× 10 -
~.+~._.-----'~ "~'°'-+'°'-~
0.5- z~3 ,~./ /
/~
I !
I 2
I 3
t/'~
F i e . 3. Dependence of r a t i o of peak m a x i m u m ztT' to m a x i m u m deviation zITma= on relative heating t i m e (time constant v was used as t i m e unit); v is: 1--30; 2--50; 3 - - 7 0 see.
time (e.g. loading the elastic material to a considerable extent is achieved in a second; times of heat absorption accompanying these processes are, of course, of the same order). The ballistic properties of the microcalorimeter were therefore studied in detail. I t is known t h a t when the duration of heat liberation is less than the time constant of the device, the diagram of the process shows an acute peak and its m a x i m u m under certain conditions is proportional to the ~hermal effect [5]. Two series of measurements were made: the first was with constant duration of heat liberation and varying amounts of heat; the second with constant heat liberation but varying duration of heating. The tabulated results bring us to the conclusion t h a t with a heating time less than 3/4 the ratio of m a x i m u m temperature difference (peak maximum) to the amount of heat liberated is a constant value with an accuracy of not less than ± 2 ~o- This ratio subsequently begins to decrease. Figure 3 illustrates the dependence on heating time of the ratio of peak m a x i m u m AT' to the m a x i m u m deviation zlTma~ for a given thermal power. Figure 3 illustrates t h a t AT" reaches ATmax in practice when t = 3 v . * I t should be noted t h a t the sensitivity of the microcalorimeter can be easily increased by one order of magnitude at least by using a photocompensating amplifier. However, we refrained from using this owing to its considerable sensitivity to even the slightest mechanical vibration.
Yu. K. GODOVSKII et al.
1350
W i t h this duration of action of the heat source (10-15 sec), when a strict proportionality is observed between the peak m a x i m u m and the thrmal effect which causes this peak, numerous experiments can be conducted to determine the thermal effect of elastic deformation. RESULTS OF BALLISTIC CALIBRATIONS Experiment No.
Resistance of the heater, ohm
I,mA
16"28 16.28 16.28 16.28 16.28 16.28 24.55 24.55 24.55 24.55
16"8 16"8 16'8 16"8 16'8 16'8 6"17 10"48 15"70 23"55
H e a t in g time, sec
.3 5 6 10 15 50 10 10 10 10
Q × 10-L cal
3.295 5.491 6.589 10.982 16-473 54.910 2.235 6.141 13.200 32.415
AT,
AT'IQ,
inIn
mm/cal
8.0 13.4 16.3 26.8 37.6 91.8 5.4 15.0 32.3 79.2
2428 2440 2473 2441 2283 1670 2438 2453 2451 2447
In those cases when this duration appears inadequate, the AT'/ATmax ratio can be easily determined from Fig. 3 for any duration. I n addition, the time constant v can be artificially increased by increasing the thermal value of the cell (i.e. also v) by placing in it a suitable insulator.
lfm]~
I
M
tl/¢
k
k
t~
!
tY' 7/r~ FIG. 4. Thermograms of heat effects during stressing and releasing of a polystyrene film: 1,2,3,4--loading; 1", 2", 3", d'--releasing. The use of the ballistic method facilitates the study of two simultaneous processes, one of which is ballistic and the other slow. Rapid loading and subsequent relaxation can, for example, be regarded as such effects. The m e t h o d of analysing the curves recorded in these cases has been previously described in detail [5].
Study of thermal processes resulting from mechanical deformation of polymers 1351 An analysis of possible errors in determining thermal power and integral thermal effects shows t h a t errors of measurement are chiefly determined b y the inaccuracy in the graphical differentiation of the curve plotted and in planimetric measurements of areas. I t was found t h a t the accuracy of determining W (t) and Q is within -4-2~o. The accuracy of determining stress in deformation is also 4-2%. Analysis indicates that deformation is the most difficult to determine, the accuracy of determination being not more t h a n 4-10~o for average elastic deformations (a=5-10~o) and moderate rates of loading.
Q~rncal
mcal/g a I/
5
200 _
]9
o
._p.+o,"2 ~ I00
I
!
!
2
Z,~
2
3 C,%
FIG. 5. Dependence of the thermal effect on loading for a polystyrene film (a) and of the ratio on relative deformation 8 (b): / - - l o a d i n g ; 2--releasing.
Q/m
As examples of the thermal behaviour of polymers during deformation let us examine the nature and magnitude of thermal effects accompanying elastic elongation of polystyrene films and elastic and plastic deformation of polyethylene films. Figure 4 reproduces curves of heat liberation and heat absorption and even stress-time
O/A
5
FIG. 6. Dependence of the
Q/A ratio
i
i
1
2
¢,%
on relative deformation e of a polystyrene film.
curves for a polystyrene film 3 m m in width, 70 m m in length a n d 0.12 m m in thickness. The specimen was subjected to i n t e r m i t t e n t stres (and then released) using a force which gradually increased.
Y r . K. GODOVSKZZet al.
1352
With small forces of deformation thermal effects in stress and release agreed and practically no stress relaxation was observed. Under considerable load, stress relaxation was observed and thermal effects during release were somewhat smaller t h a n on loading. This proves that stress relaxation in a polystyrene film is accompanied by an exothormal effect. Figure 5a illustrates the dependence of heat on deforming force. The data are very well expressed b y a linear relation, from the slope of which the linear coefficient of thermal expansion was calculated according to equation (1). I t appeared to be 6.77 × 10 -5 degree -1. This value shows satisfactory agreement with data obtained previously b y the same method [2] and with other literature data [8]. Figure 5b shows the dependence of specific heat on relative deformation. Hero a somewhat larger variation of experimental data is observed duo to the low accuracy of measuring deformation. F r o m the gradient of the straight line obtained, the elasticity modulus Eq was c~lculated according to equation (2) using values p = 1.05 g/cm 8 and fl,= 6.77 × I0 -~ degree -1. The modulus thus calculated was E q = 199 kg/mm 2. This value was compared with modulus E, determined from mechanical characteristics. This modulus was E , = 1 7 0 kg/mm. The deviation was about 15%. This example indicates that an investigation of thermal effects accompanying elastic deformation of polymers opens up the possibility of determining mechanical and other characteristics (e.g. fl) from purely thermal data.
2"
z,~ t
0
I
g
g
#
Time,min
4
FIG. 7. Thermal effects during elongation of a polyethylene film: a--dependence of the force of elongation Z and b--dependence of the thermal power W on time. I n this example it is also of interest to compare the macharfical work A with the heat Q. Figure 6 indicates the dependence of the Q/A ratio on relative elongation. (Work was calculated from the ratio A = 0.5 Z Al). Theoretically this ratio is Q/A = 2fiT~8. This is the equation of an equilateral hyperbola, from which it follows that at very low relative elongations the thermal effect m a y m a n y times exceed the value of mechanical work (e.g. for 6=0.005, T = 3 0 0 ° K and fl=6.77 × 10 -5 degree-i; the ratio of Q/A=8.1). Figure 6 shows that a variation in the Q/A ratio for a polystyrene film is, in fact, expressed by a hyperbolic relation, the experimental values of this ratio showing satisfactory agreement with theoretical values. Figure 7 shows data concerning the deformation of an isotropic polyethylene film 0.2 m m in thickness and 2.5 m m in width at a rate of 0"233 mm/sec. During the initial stage of stress an endothermal effect is observed which corresponds to elastic deformation, then as "neck" formation goes on in the specimen the endothermal effect becomes exothermal, and reaches
Study of thermal processes resulting from mechanical deformation of polymers 1353 a practically stationary state corresponding to a constant rate of neck formation in th(, sample. The thermal power Wit) produced at constant rate of neck formation is 3.08 .< l0 nmal/sec and the mechanical power is 4 . 1 5 × 10 -~ mcM/sec (the force of' deformation Z in neck formation is 0.76 kg). The ratio of these powers is close to unity (0.75). I f stress is stopped during neck formation stress in the specimen is relaxed (see Fig. 7) and the thermal power ceases. When the sCress is subscctuently fully released an endothermal effect is observed. An inverse pattern is observed when the isotropic polyettwleue fihn undergoes elastic deformation in the range in which no neck formation has occurred ( ~ 12 150o). In this case the endothermal effect corresponds to stress of the specimen and the (~xothermal effect to release. A change in sign of the thermal effect when the polye,thylen(~ fihn changes from the isotropic to tile oriented state I)oints to the fact theft the m~ture e l deformation of oriented polyethylene is different in principle from the nature of (h~f~)rnmtion of an isotropic sample. A similar effec~ is also observed for many other crystalline polym(,rs [2, 9]. CONCLUSIONS A description is given el" an automatic low-inerbia microcalorilnetrie apparatus used for the study of thermal processes resulting from mechanical deformation of I)olymer fihns and fibres and examples are given of the thermal behaviom' of polymers during elastic and plastic deformation. Tra~slctted by 1£. SEMFRE REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.
O. D. KttVOL'SON, Kurs fiziki (Course on Physics), voI. 3. Izd. I / SFSR, 19(~2 A. EN(IELTER and F. II. MtILLER, Kolloid-Z. und Z. flit Polymere 157: 89, 195s W. DICK and F. It. Mt~LLER, Kolloid-Z. und Z. fiir Polymere 172: 1, 1962 B. KI, Noveishie metody issledovaniya polimerov (I,%test Methods for the Investigati,)n of Polymers). Izd. "Mir", 1966 E. KAL'VE and A. PRAT, Mikrokatorimdriya (Microcalorimetry). Izd. inostr, lit., 1963 Izmerenie napryazhenii i usilii v detalyakh mashin (Measurement of Stresses and Forces in Machine Components). Edited by N. I. PRIGOROVSKII, Mashgiz, 1955 Yu. K. GODOVSKII and Yu. P. BARSKII, Plast. massy, No. 7, 57, 1965; Vysok~nnel. soyed. 8: 395, 1966 Physik der Kunstoffe, Pub. W. Holzmiiller und K. Altenburg, Berlin, 1961 (I. L. SLONIMSKII, Yu. K. (IODOVSKII, V. S. PAPKOV and T. A. DIKAREVA, \:ysokomol, soyed. B10: 798, 1968