TGA Maximum Heat Release Rate and Mass Loss Rate and Comparison with the Cone Calorimeter

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1 TGA Maximum Heat Release Rate and Mass Loss Rate and Comparison with the Cone Calorimeter JIANPING ZHANG, and MICHAL DLICHATSIOS FireS School of Built nvironment & Research Institute of Built nvironment University of Ulster Newtownabbey, BT37 0QB, Northern Ireland ABSTRACT Thermoravimetric analysis (TGA) is a fundamental tool to study the deradation and pyrolysis behaviours of milliram-sized samples in inert or oxidisin atmospheres. One of the most important outputs of TGA measurements is the imum heat release rate (MHRR) or the imum mass loss rate (MMLR). Analytical solutions of the MHHR/MMLR have been developed for infinitely fast heat transfer between the as and solid. It has also been proposed that the MHRR in a TGA apparatus is proportional to the heat of combustion divided by the heat of asification of the material. This conclusion was reached by the observed nearly linear relation of the MHRR in the TGA with the heat release rate per unit area in the cone calorimeter for thermally thick samples. In this work, we investiate the MMLR in the TGA for both finite and infinite rates heat transfer by analytical solutions and numerical calculations. A universal expression between the MMLR and equipment and material parameters is deduced. The derived expression is subsequently validated aainst experimental data of two polymers (PA6 and PBT). Finally, we discuss how the pyrolysis rate or heat release rate for a thermally thick solid, as measured for example in a cone calorimeter, is related with the MMLR in the TGA apparatus. KYWORDS: TGA, heat release rate, mass loss rate, cone calorimeter. NOMNCLATUR A pre-exponential factor (/s) x dimension into solid (m) C characteristic parameter, = h c /(ρδl) X fractional mass loss c p specific heat (J/k-K) Greek activation enery (J/mol) β heatin rate (K/min) h c heat transfer coefficient (W/m K) δ characteristic size of the sample (m) ΔH total heat of pyrolysis (kj/k) γ exponent in the MMLR in q. ΔH c heat of combustion (kj/k) Θ dimensionless MLR in q. 8b k thermal conductivity (W/m K) λ reaction order L latent heat of pyrolysis (kj/k) Π dimensionless variable in q. 8b M mass () ρ density (k/m 3 ) q net net heat flux (kw/m ) subscripts S surface area (m ) as t time (s) temperature at which MHHR occurs in TGA T temperature (K) o Initial condition V volume (m 3 ) s surface INTRODUCTION Thermoravimetric analysis (TGA) involves heatin a milliram-sized sample in inert or oxidisin atmospheres and measurin the weiht and also, the temperature of the sample if the experiment is combined with differential scannin calorimetry (DSC). The weiht and temperature chanes over specific temperature ranes provide indications of the chemical deradation of the sample and thermal stability of the material. One of the most important outputs of TGA measurements is the imum heat release rate (MHRR). The MHRR in a TGA apparatus can be found in three ways: a) indirectly, by multiplyin the imum mass loss rate (MMLR) in the TGA experiments in nitroen by the heat of combustion of evolved ases obtained by simultaneous mass spectroscopy analysis [], b) directly, by oxyen depletion FIR SAFTY SCINC-PROCDINGS OF TH TNTH INTRNATIONAL SYMPOSIUM, pp COPYRIGHT 0 INTRNATIONAL ASSOCIATION FOR FIR SAFTY SCINC / DOI: 0.380/IAFSS.FSS

2 after the evolved ases from TGA are completely burned online in a micro furnace [] and c) by bomb calorimetry. In Refs. [3,4], an analytical solution of the MHRR was proposed, which was then used to correlate with the steady HRR of a thick sample in the cone colorimeter. The analytical solution of the MHRR for non-charrin materials takes the followin form (for hih heat transfer rates and hih activation enery); H q c, (a) e c or in terms of the MMLR: dx (b) e where T is the temperature at which the MHRR occurs, R the universal constant, and γ, the exponent of the natural number e in the denominator, havin the followin form [3]: (c) For lare values of activation enery, i.e. /( ), γ is approximately one. It has been shown in Ref. [3] that qs. a c correlate well with TGA measurements of PMMA, polyethylene (P) and phenolic triazine (PT) at heatin rates from to 00 K/min. However, an important assumption in derivin qs. a c is that the temperature of the solid sample is the same as the as temperature in the TGA, which would only be the case for infinitely fast heat transfer. This assumption renders that q. is invalid for the cases with finite rates heat transfer, which sometimes have to be applied in order to produce a measurable difference between the as and material temperatures. For example, in a DSC apparatus this temperature difference is used to calculate the heat of meltin or the heat of pyrolysis. The first objective of this study is thus to extend the MMLR in TGA for finite rates heat transfer by takin into account the effects of the equipment and material characteristics (i.e., the heat transfer coefficient and density, thickness and heat of pyrolysis of the material). Analytical and numerical results show that the relation in q. b is valid only when a characteristic parameter, C = h c /(ρδl) (where h c is the effective total heat transfer coefficient, ρ sample density, L latent heat of pyrolysis, and δ the characteristic size of the sample) is sufficiently lare. For smaller values of C, i.e., the cases of finite rates heat transfer, the MMLR is found to be a function of C. A universal expression of the MMLR is deduced numerically. Finally, the derived expression is validated aainst TGA measurements of PA6 and PBT at different heatin rates. The last section before the conclusions addresses how the pyrolysis rate or heat release rate for a thermally thick solid, as measured for example in a cone calorimeter, is related with the MMLR in the TGA apparatus. MTHODOLOGY Mass and nery Balance in the TGA Apparatus in an Inert Atmosphere The heatin of the solid in an inert atmosphere occurs in three reimes as sketched in Fi. plottin the fractional mass loss or the conversion fraction (X) versus the solid temperature. In the first reime I, only heatin occurs, followed by pyrolysis in reime II at a nearly constant temperature and by further heatin in reime III if there is char remainin. This behaviour is specifically applicable when the activation enery is hih (/ >> ). 334

3 Fraction of mass loss, X III II I Temperaure Fi.. Three reimes for the heatin of the solid in an inert atmosphere, showin the fractional mass loss or the conversion factor (X) as a function of the solid temperature. As usual in TGA experiments, we consider samples small enouh that they behave as thermally thin. In addition, we consider experiments in an inert atmosphere where the as temperature increases at a steady rate with time. This condition is satisfied if the diffusion time into the solid ( /, where δ is a characteristic size and α the thermal diffusivity) is both less than a time characteristic of the as temperature rise in the TGA (e.. of the solid. [ / / T ] and a characteristic reaction time for the decomposition The enery balance and mass balance equations includin pyrolysis of the material from solid to as are: c p M dm hc ( T T) S L () where the solid mass M decays followin a first order lobal Arrhenius deradation reaction: dm MAe (3) In qs. and 3, h c is the total effective heat transfer coefficient includin both convection and radiation, and S the surface area of the solid. For simplicity but without loss of enerality, we assume that the volume of the solid remains constant so the density decreases as M / V and the followin transformations are possible: M X, M o o X (4) Substitutin q. 4 in qs. and 3, we obtain: c o X hc T T S / V o X Ae L (5) dx X Ae (6) Note that the ratio of surface to volume is the inverse of the characteristic size of the material, namely: 335

4 S V (7) The as temperature in q. 5 increases at a steady rate with time: (8) Determination of the Temperature at which the MMLR Occurs By takin the time derivative of the RHS of q. 6 and notin that the MMLR occurs when the time derivative of the LHS of q. 6 is zero, we obtain: Ae (9) where T denotes the solid temperature at which the MMLR occurs. We also note that in the second reime in Fi. where decomposition occurs the temperature is nearly constant so that the term on the LHS of q. 5, can be inored, one obtains h ( T T) / ( X ) A e L 0 (0) c o r 3.0e+6 Three terms in q. 5 (W/m 3 ).0e+6.0e+6 st term on the RHS nd term on the RHS LHS term Temperaure (K) Fi.. Three terms in q. 5 calculated by the numerical model, verifyin that the term on the LHS in q. 5 is less than the two terms on the RHS by more than an order of manitude. To support this proposition, we plot in Fi. the three terms in q. 5 as a function of temperature obtained by numerically interatin qs. 5 and 6 for PMMA. Numerical interations were performed usin the subroutine HPCG, where evaluation was done by Hammins modified predictor-corrector method [5], and a fourth order Rune-Kutta method [6] was used for adjustment of the initial increment and for computation of startin values. Fiure clearly shows that at the main deradation temperature rane the transient term on the LHS of q. 5 is less than the two terms on the RHS by more than an order of manitude. The model parameters used are: β = 0 K/min, c p = 500 J/k K, L = J/k [7], ρ o = 90 k/m 3, δ = 0. mm, h c = 5000 W/m K, A = s -, = J/mol [8]. Rearranin q. 0, we obtain 336

5 hc ( T T) dx C( T T) L o (a) where hc C (b) L o Takin the time derivative of q. a and notin that the MMLR occurs when the time derivative of the RHS is zero, so C d( T T) 0 or () quation indicates that at the MMLR the derivative of the solid temperature, /, is equal to the heatin rate, β. This relation is verified by the numerical result in Fi. 3 showin the derivate of the solid temperature (/) for different heat transfer coefficients. For a very hih heat transfer coefficient h c = 5000 W/m K, the history of / is almost the same as β since heat transfer is very fast. For lower heat transfer coefficients, / is initially less than β but becomes equal to β at around K reardless of the heat transfer coefficient W /m -K / (K/s) W /m -K W/m -K Temperature (K) 50 W /m -K 636.3K Fi. 3. Predicted derivative of the solid temperature (/) as a function of the solid temperature for different heat transfer coefficients. This temperature, correspondin to the temperature at which the MMLR (T ) occurs, can also be derived analytically by substitutin q. into q. 9:, m Ae m, (3) quation 3 indicates that T is independent of equipment and material parameters, such as h c, L, δ, ρ, but only depends on the heatin rate and the kinetic parameters (activation enery and pre-exponential factor). This result is further supported by the numerical results in Fis. 4a and 4b, where the MLR is plotted aainst time and the solid temperature respectively for different heat transfer coefficients. Althouh the times to reach the MMLR are different for different heat transfer coefficients as shown in Fi. 4a, the temperatures at which the MMLR occurs are the same as noted in Fi. 4b. The value of the MMLR with a heat transfer coefficient of 5000 W/m K is s -, which is close to the one iven by q. b, i.e., 337

6 s -. However, at lower heat transfer coefficients, the MMLR is sinificantly lower. The fact that the MMLR decreases as the heat transfer coefficient decreases can be explained by examinin q. 6. Because T is the same for different values of h c, the MMLR is proportional to (-X ), where X is the fractional mass loss at the MMLR, which would be hiher for lower heat transfer coefficients as shown in Fi. 5. dx/ dx/ (s - (s ) - ) W /m -K 5000 W /m -K 500 W /m -K 500 W /m -K (a) (a) 50 W /m -K 50 W /m -K 5 W /m -K 5 W /m -K dx/ dx/ (s - (s ) - ) Time (s) Time (a) (s) W /m -K (b) 5000 W /m -K 500 W /m -K (b) W /m -K W /m -K 50 W /m -K W /m -K W /m -K 636.3K K Temperature (K) Temperature (K) (b) Fi. 4. Predicted MLR as a function of: (a) time; (b) the solid temperature for different heat transfer coefficients. Determination of the MMLR as a Function of C h L quation a shows that the MMLR is a function of C. In order to determine the dependence of the MMLR on C, we randomly enerated one hundreds sets of values for ρ o, h c, and L, and δ usin q. 4. L L c min h h r r L h L min c, min c, c, min h o r o, min 3 o, o, min min 4 min r (4) c o 338

7 W /m -K X W /m -K 636.3K Temperature (K) Fi. 5. Predicted fractional mass loss as a function of the solid temperature for different heat transfer coefficients. where r, r, r 3 and r 4 are random numbers uniformly distributed in the rane of [0,], and the minimum and imum values of each individual parameter are iven in Table. The other parameters remain the same as those used to enerate the results of PMMA in Fis. 5, i.e. β = 0 K/min, c p = 500 J/k-K, A = s -, = J/mol. Table. Minimum and imum values of ρ o, h c, and L, and δ. L min L h c,min h c, ρ o,min ρ o, δ min δ (J/k) (J/k) (W/m K) (W/m K) (k/m 3 ) k/m 3 ) (mm) (mm) Fiure 6 shows the calculated MMLR aainst C, as well as the analytical solution calculated usin q. b. Clearly, q. b is only valid when C is sufficiently lare (above 0.0 K - s - for the present parameters). As expected, this threshold value would vary with the equipment and material parameters. The next objective is thus to derive a universal expression of the MMLR DX/Dt (s - ) s - by q. b from [] C (K - s - ) Fi. 6. Predicted MMLR versus C ; the constant value for s - is calculated by q. b. In total, 00 sets of data of ρ o, h c, and L, and δ were randomly enerated usin q

8 Analytical asymptotic solutions for the MMLR have been derived by takin the time derivative of the terms in the enery balance q. 0 and usin q. 6. Namely, the time derivative of the sample temperature usin q. 6 is: C ( X )( Ae C A( X ) e / / ) ( / ) (5) From q. 6 and usin q. 5 we can find the variation of the conversion factor with the sample temperature: dx dx / / C A( X ) e ( / A( X ) e / / C ( X )( Ae ) ) (6) Next, we can interate q. 6 from the initial sample temperature to the imum sample temperature, which is iven by q. 3. Some consistent asymptotic analysis shows that at the MMLR conditions the followin functional relation is valid: / Ae X fcn( ) (7) C The temperature at the MMLR is iven by q. 3. We can not obtain analytically the functional relation in / C q. 7. However, for small values of and lare values of activation enery (i.e. / ), we obtain : Ae (e.. lare values of the heat transfer coefficient) / X /e when Ae C (8a) Note that this result arees with the previous solutions [3,4] as shown in qs. a c. This result is also supported by the numerical results in Fi. 7, where we plot a modified MMLR ( dx ) C ( X Ae ) / C ( X ) as a function of (8b) / C where Ae 340

9 y=x/e (K - s - ) (K - s - ) / Fi. 7. Dimensionless imum mass loss rate, ( X ) Ae C / Ae C, as a function of for a heatin rate of 0 K/min. In total, 00 sets of data of ρ o, h c, and L, and δ were randomly enerated usin q. 4. As mentioned earlier, we could not obtain analytically the functional relation in q. 7 for larer values of Π. However; this can be achieved by bestin fittin the numerical results. In order to enerate all possible values of Π, we performed calculations with a wider rane of heatin rates (from to 500 K/min), for each of which 0 sets of data were enerated for ρ o, h c, and L, and δ usin q. 4. The numerical results are shown in Fi. 8, where all data collapse into one sinle curve, indicatin the validity of q. 7 for all heatin rates. (K - s - ) 0. K/min K/min 5 K/min 0 K/min 0 K/min 50 K/min 00 K/min 00 K/min 500 K/min q (K - s - ) Fi. 8. Calculated Θ as a function of Π at different heatin rates. For each heatin rate, 0 sets of data of ρ o, h c, and L, and δ were randomly enerated. Havin in mind that equals to / e for small values of Π, we used a polynomial expression to best fit the data in Fi. 8. After trial-and-error, we obtain the followin expression: e 0. (9)

10 which ivens an excellent areement with the calculated data as shown in Fi. 8. Note that q. 9 takes into account both the equipment and material parameters, and as a result it is valid for all cases. Consequently, it can be used to determine equipment or material parameters based on the TGA measurements, such as the heat transfer coefficient and the heat of pyrolysis. ffects of reaction order For simplicity, we have assumed that the deradation of material follows a first-order Arrhenius expression, which would not be the case for most practical materials. For enerality we assume that the dx reaction rate of a iven material can be approximated as: X Ae, where λ is the reaction order, which can be considered as a material constant and obtained numerically by fittin the mass loss curves at different heatin rates in the TGA apparatus. In order to verify that q. 9 is valid for any reaction order, we repeated the calculation as for Fi., however, the reaction order of PMMA was artificially varied between 0.5 and. The results in Fi. 9 shows that with an increase in the reaction order, there is an increase in the sold temperature at which the MMLR occurs (T ) and thus the reaction rate. The normalised MMLR,, can, however, be expressed as the same function of Π usin q (K - s - ) = Numerical results q (K - s - ) Fi. 9. ffect of reaction order on the dependence of the dimensionless MMLR, Θ, on Π Application to PA6 and PBT In order to further validate q. 9, we performed numerical calculations for two polymers, PA6 and PBT, for which we have conducted measurements in TGA at different heatin rates (,, 5, 0, and 0 K/min). The thermal properties were deduced by inition tests at different heat fluxes in the cone colorimeter whereas the kinetic parameters are obtained usin the thermokinetic software by Netzsch, which are summarized in Table. h c = 5000 W/m K and δ = 0. mm were used for all calculations. The results are shown in Fi. 0. Table. Thermal and kinetic parameters of PA6 and PBT. ρ c p L A λ (k/m 3 ) (J/k K) (J/k) (J/mol) (s - ) PA PBT

11 0 K/min (K - s - ) 0. K/min 0.0 PA6 PBT q (K - s - ) Fi. 0. Calculated Θ as a function of Π for PA6 and PBT at different heatin rates. Because a hiher value of h c was used, the data is mostly within the reion of small values of Π, where we have verified that Θ is proportional to Π. More importantly, althouh there are lare differences in the thermo and kinetic parameters for PA6 and PBT, the calculated normalized MMLR Θ still follows the same function iven by q. 9. This fiure, alon with results in Fis. 7 9, demonstrates that the validity of q. 9 for materials with different thermal properties and/or kinetic parameters. XTNSION TO THRMALLY THICK SOLID XPOSD TO CONSTANT HAT FLUX When a thermally thick solid is exposed to a constant heat flux, the conduction equation overnin the heat transfer inside the solid is: T T c p k m ( t) L (0) t x where, m is the volumetric mass loss rate, which can be calculated as assumin first-order reaction: m Ae / () The boundary conditions on the front and back surfaces are iven by qs. a and b respectively: T k x x0 4 4 T T h T T q (a) ext s c s T k 0 (b) x xl where x = 0 represents the top surface which recedes durin pyrolysis. The mass loss rate is related to the Arrhenius expression at steady state by: A q net / e dx H 0 (3) 343

12 where H is the total heat of pyrolysis, consistin of both the latent heat of pyrolysis, L, and the sensible p Ts T 0,where T s is the surface temperature. heat, c From q. 3, an asymptotic expression can be derived for lare values of / if we know the temperature radient at x = 0. In the thin reaction reion close to the expose surface, the reaction layer conduction is balanced by the reaction term at steady state (note that outside the reaction zone conduction is balanced by convection for a stationary front): d T k dx / ALe (4) By multiplyin q. 3 by /dx and interatin, the radient /dx varies sinificantly inside the reaction layer except if the latent heat of pyrolysis is zero. Asymptotic analysis shows that the followin relation is valid: Ae s s q net kh L fcn( H ) (5) This equation for the surface (pyrolysis) temperature in the cone calorimeter is similar to the relation for the temperature in the TGA (see q. 9) but with an effective heatin rate, q / kh, which depends on several material parameters includin the conductivity of the material. The function on the RHS of q. 9 is s one for L 0. This is verified numerically in Fi. 0, where the LHS term, Ae net, at steady state is q net plotted aainst for different heat fluxes for PMMA (0 cm), where the latent heat of s kh pyrolysis was set to zero. The other properties and parameters used in the calculations are the same as those used in the TGA. For the rane of heat fluxes considered, there is an excellent areement between the two sets of data. It has also been proposed in Ref. [3] that the HRRs of various materials in the cone calorimeter are proportional to a heat release capacity, H c / e. This conclusion was reached by the observed empirical relation of the MHRR in the TGA with the heat release rate per unit area in the cone calorimeter for thermally thick samples. To verify this findin, we conducted calculations with different values of activation enery (ranin from 4 to 9 kj/mol) and the calculated steady HRR is plotted in Fi. versus the heat release capacity determined from the TGA at a heatin rate of 0 K/min. In Fi., temperature, T s, in the ordinate is the surface temperature of a thermally thick sample in the cone calorimeter, whereas the temperature, T, in the abscissa is the temperature at which the imum MLR occurs in TGA.It appears that there exists a linear relation between the HRR in the cone calorimeter and the heat release capacity in the TGA as suested by Ref. [3]. However it should be emphasized that the relation is not universal but depends on the material properties such as the conductivity and latent heat of pyrolysis as shown in Fi., where the conductivity and latent heat of pyrolysis were set to half/ twice of their oriinal values. The chane in the latent heat of pyrolysis has a fundamental effect on the HRR whereas the effect by chanin the conductivity is marinal. 344

13 kw/m Ae / (s - ) kw/m s q net s kh (s - ) Fi.. Calculated Ae q net as a function of for different external heat fluxes at steady s kh state of a PMMA (0 cm) in the cone calorimeter by settin the latent heat of pyrolysis equal to zero. Steady HRR, (kw/m ) H q c ext T L c T T p s 4 s k=0., L=0.86 k=0.05, L=0.86 k=0.4, L=0.86 k=0., L=0.46 k=0., L=.66 =9 kj/mol Heat release capacity, increase H c / =4 kj/mol (J/-K) Fi.. Predicted steady HRR with different values of activation enery in the cone calorimeter aainst the heat release capacity in the TGA at a heatin rate of 0 K/min. We show and propose here that the chane in the HRR in the cone calorimeter with the heat release capacity in the TGA is primarily related to the chane of surface temperature. As the surface temperate is nearly proportional to /R (based on q. 9 or q. 5), an increase of activation enery,, will result in an increase of surface temperature but a decrease of the heat release capacity in the TGA ( H c / e ) (assumin the heat of combustion does not chane). The increased surface temperature has two effects on the mass loss rate in the cone calorimeter: a) decreased net heat flux owin to an increase of surface reradiation losses and b) increased sensible heat. Both factors contribute to the decrease of the MLR, where estimates and numerical results show that the former is the primary cause. 345

14 CONCLUSIONS Numerical calculations and analytical solutions have been performed to derive the imum mass loss rate (MMLR) in the TGA apparatus (the heatin rate increases at a steady rate with time) for finite rates heat transfer. The main conclusions of this work are: At the MMLR, the time derivative of the solid temperature is equal to the heatin rate. The temperature at which the MMLR occurs is independent of equipment and material parameters but depends only on the heatin rate and kinetic parameters. Present result verified that the MMLR relation in Ref. [3] is valid only for infinite fast heat transfer, or when a characteristic parameter C hc L is lare, where h c is the total heat transfer coefficient, ρ the sample density, L the heat of pyrolysis, and δ the characteristic size of the sample. For small values of C, the MMLR is a function of C as indicated by q. 9 with symbols defined in the nomenclature. Application of the numerical model to the TGA data of two polymers, PA6 and PBT, verified that this function is also independent of the heatin rate or the kinetic parameters. For thermally thick materials exposed to a constant heat flux in the cone calorimeter, the pyrolysis temperature (q. 5) is similar to the one in the TGA (q. 9), but additionally it depends on the ratio of the latent heat of pyrolysis and total heat of pyrolysis. When this ratio is small, the steady pyrolysis rate can be calculated usin q. 5. We have concluded that the proposed empirical relation in Ref. [3] that the HRR in the cone calorimeter is proportional to a so-called heat release capacity ( H c / e ) is not fundamentally appropriate. Althouh our results showed that there is a nearly linear relation between them, this relation is not universal but depends on the material properties such as the conductivity and latent heat of pyrolysis (see Fi. ). The chane in the HRR in the cone calorimeter with the heat release capacity was mainly due to the chane of sample surface temperature. The present methodoloy can also be used to check and optimise the operational characteristics of the DSC, e.. by chanin the as flow rate and hence the heat transfer coefficient. RFRNCS [] Inuilizian, T.V., Correlatin polymer flammability usin measured pyrolysis kinetics, Masters Thesis, University of Massachusetts (Amherst), January 999. [] Lyon R.., A Microscale combustion calorimeter, Office of Aviation Research, Washinton D.C. 059, DOT/FAA/AR-0/7, 00. [3] Lyon R.., (000) Heat release kinetics, Fire and Materials 4: [4] Lyon R.., Heat Release Capacity, Fire & Materials Conference, San Francisco, CA, January -4, 00, pp [5] Ralston, A. and Wilf, H.S, Mathematical methods for diital computers, Wiley, New York / London, 960, pp [6] Ralston A., (96) Rune-Kutta methods with minimum error bounds, MTAC, 6: [7] Stoliarov S.I. and Walters R.N., (008) Determination of the heats of asification of polymers usin differential scannin calorimetry, Polym. Derad. Stab. 93: [8] Vovelle, C.D., Delfau, J.L., Reuillon, M., Bransier, J., and Laraqui, N., (987) xperimental and numerical study of the thermal deradation of PMMA, Comb. Sci. Tech. 53: