Proceedings of the Eighth International Seminar on Fire and Explosion Hazards (ISFEH8), pp. 477-487 Edited by Chao J., Liu N. A., Molkov V., Sunderland P., Tamanini F. and Torero J. Published by USTC Press ISBN:978-7-312-04104-4 DOI:10.20285/c.sklfs.8thISFEH.048

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Study of Counterflow Flame of Ultrahigh-Molecular-Weight Polyethylene with and without Triphenylphosphate

Korobeinichev O.1,*, Gonchikzhapov M.1,2, Paletsky A.1, Tereshchenko A.1, Shmakov A.1,2, Gerasimov I.1, Karpov A.3, Shaklein A.3, Hu Y.4

1Institute of Chemical Kinetics and Combustion, Novosibirsk, Russia 2Novosibirsk State University, Novosibirsk, Russia

3Institute of Mechanics, Izhevsk, Russia 4State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei,

Anhui, China *Corresponding author email: korobein@kinetics.nsc.ru

ABSTRACT The structure of counterflow flames of air and ultrahigh-molecular -weight polyethylene (UHMWPE) with triphenylphosphate (TPP) added, and also without it, was studied at atmospheric pressure using the molecular-beam mass spectrometry (MBMS) with soft electron-impact ionization. The burning surface temperature and the temperature profiles in the condensed and gas phases were measured by a microthermocouple technique. The dependence of the regression rate of UHMWPE and UHMWPE+5wt.% TPP on the surface temperature was determined. Using the flame structure data, heat and radiation fluxes on the polymerʼs burning surface were calculated. Using the heat balance equation, the heat releases of chemical reactions on the polymerʼs burning surface were determined. To calculate the kinetic parameters for the rate constants of the degradation reaction for UHMWPE and UHMWPE+5wt.% TPP the formula for the propagation rate of the combustion wave in the condensed phase was used. Comparison of the data obtained on the degradation rate constants with the data previously obtained using the methods of thermal analysis allowed the Arrhenius dependence of the degradation rate constants to be obtained for a broad temperature range. In adding TPP to UHMWPE, widening of the flame zone, a decrease of the maximum flame temperature, its shifting from the burning surface, reduction of the heat flux from the flame to the polymer surface, and reduction of H and OH radicalsʼ concentrations were found. In addition, HOPO and HOPO2, the main products of TPP destruction, which catalyze the recombination of H and OH radicals, were found in the flame. Direct experiments conducted demonstrate that the action of a flame retardant in a polymer flame consists in its participation in chain-termination reactions.

KEYWORDS: Polymer burning, flame retardant, counterflow flame, flame structure.

NOMENCLATURE Cp specific heat capacity (J/(kg·K)) Ea activation energy (kJ/mol) k0 preexponential factor (s-1) Kp Planck mean absorption coefficient (-) Lg distance between nozzle and polymerʼs burning

surface (m) M mass flow rate of the polymerʼs pyrolysis

products from the polymerʼs surface (kg/(m2·s))

M1 total mass rate of the polymerʼs combustion (kg/(m2·s))

M2 mass dripping rate from the polymer surface (kg/(m2·s))

m atomic mass unit (amu) Qs heat release on the polymerʼs surface (J/kg) Q heat of reaction (J/kg) qr radiation heat flux from flame to polymerʼs

surface (W/m2) R universal gas constant (J/(mol·K)) S surface area of the polymer sample (m2) T temperature (K) Ts temperature of the polymerʼs surface (K) T0 initial sample temperature (K) U linear velocity of the polymerʼs combustion

(m/s) k rate constants for pyrolysis of polymer (s-1)

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Greek ε emissivity (-) ρc polymerʼs density (kg/m3) λ polymerʼs thermal conductivity (W/(m·K)) σ Stefan-Boltzmann constant (W/(m2·K4))

Subscripts FR flame retardant c condensed phase g gas phase r radiation s surface

INTRODUCTION

To understand the mechanism of combustion of polymer materials with flame retardants and without them and to develop the model of this process, it is necessary to know the physical and chemical processes occurring in the condensed phase and in the flame. Studying the counterflow flame of a polymer burning in air is one effective method of investigating the mechanism of a polymerʼs combustion. This method has been used earlier to study сombustion of some polymers [1, 2]. However, this method has practically not been used for studying the the flame retardancy mechanism for plymers. In this study, this method was used to investigate the counterflow flame of ultrahigh-molecular-weight polyethylene with and without triphenylphosphate.

EXPERIMENTAL

Materials

The specimens were pressed from UHMWPE powder with a grain size ~ 60 µm (MW ~ 2.5 × 106, Тmelt =142 оС) synthesized in the Institute of Catalysis (S.B., Russian Academy of Sciences), together with its mixture with TPP (crystal size ~ 40-60 µm, MW ~ 326, Тmelt = 40-50 оС, Aldrich, CAS number: 115-86-6). Mixture of UHMWPE + TPP 95/5 (wt.%) powders was used in the study and were prepared by mechanical mixing for 15-20 min. Specimens of UHMWPE and UHMWPE +TPP (14 mm diam. and 30-40 mm long) were prepared by hot pressing powders at 140 °С and a pressure of 100 atm. The density of the UHMWPE was 920 kg/m3; when 5 wt.% TPP was added, the density changed insignificantly to 940 kg/m3.

Experimental setup

The structure of a counterflow flame of polymer was investigated using a specially designed burner, similar to those used [1, 2] previously. The burner incorporated a mechanism for moving the specimen and a nozzle of a special shape, with which the flow of air was directed at the polymerʼs surface. A photograph of the burner and a schematic diagram of the setup are shown in Figs. 1 and 2. To provide uniform flow of oxidizer, a converging nozzle was used. The velocity of the air was in the range of 0.1-2 m/s; it was measured to an accuracy of 1%.

For this burner, two stepper motors were used, one of which served to rotate the specimen around its axis; the second one moved the specimen along the axis. The specimens were rotated with a frequency of ~1 Hz inside a thermostated metal cup. Rotation was required for uniform heating of the specimen, which was ignited with a glowing nichrome spiral. The upper part of the specimen (~4 mm) was insulated from the walls of the metal cup with a teflon ring, which prevented cooling of the upper melted layer of UHMWPE during burning. The distance between the nozzle and the polymerʼs surface was 14 mm. The experiments were conducted using two temperature values in the thermostat: 1) −70 оС; 2) −150 оС. In the first case, water was used as the working liquid, while the central was made of aluminium. The liquid layer of the polymer was dripping. In the second test, silicon oil was used as the working liquid, and a metal central axial rod was replaced with a Teflon one, to rule out overheating of the stepper motor. There was no rotation, as the specimen was originally heated to the melting temperature. Heating the polymer to the liquid phase allowed avoiding dripping during burning.

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Figure 1. Photographs of the burner and burner with flame.

Figure 2. Configuration of the experimental setup.

The air velocity and temperature (under normal conditions) at the exit from the nozzle varied to change the burning velocity and the polymerʼs surface temperature. The air flow rate was 44, 52, 60, 80 cm/s and was set with an MKS flow controller (Type 247, dev. 0.3%). The air flow temperature was 20 оС и 250 оС. The accuracy of measuring the air velocity was ± 0.13 cm/s. To adjust the air flow temperature, a heater was built in the nozzle. The air flow temperature was measured with a chromel-copel thermocouple at the nozzle exit. The temperatures of the gas in flame and of the polymerʼs surface were measured with a П-shaped Pt-Pt/Rh (10%) thermocouple with the arm length of 5 mm. To measure the temperature in the condensed phase, the thermocouple was embedded into the specimen, as shown in Fig. 3. For this purpose, holes of 0.5 mm in diameter were drilled in the specimen at angle of 150o; then a Pt-Pt/Rh (10%) thermocouple of diameter 5 × 10-2 mm was inserted into the channel. The channel was finally melted at the edges of the specimen to rule out any subsequent shifting of the thermocouple. A flame was stabilized by moving the specimen with the second stepper motor at a fixed velocity equal to the burning rate. Polymer combustion was investigated with vertical [3] and horizontal orientations of the burner. At the thermostat temperature of 150 оС, the studies were conducted only with the vertical orientation of the burner. Comparison of the species concentration profiles and the flame temperature profiles measured for both cases showed that the orientation of the burner in space did not exert any noticeable influence on the process of combustion and the results of the experiments. Species mole fractions in the flame were measured using the MBMS setup shown in Fig. 2. Detailed descriptions of the setup have been presented previously [4, 5]. The flame gases were sampled with a sonic quartz probe with an orifice diameter of 0.04 mm, wall thickness of 0.08 mm and an internal angle of 40o. The central part of the supersonic jet was extracted by a stainless steel skimmer and ionized in the ionization source of the mass spectrometer. The MBMS setup was equipped with a MS-7302 quadrupole mass-spectrometer with soft electron-impact ionization (spread in ionization energies of ±0.25 eV). The position of the burner relatively to the probe during an experiment was adjusted with a 3D-coordinate device and controlled using a cathetometer with an accuracy of ±10-2 mm. In order to minimize perturbations of a flame by the probe, flame gases were sampled at a distance of ~5 mm from the specimenʼs axis.

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Table 1. Measured species, their ionization potentials (IP), and energies of ionizing electrons (IE) used in experiment.

m Formula Species name IP, eV IE, eV

1 H Hydrogen atom 13.6 16.65

2 H2 Molecular hydrogen 15.43 20

17 OH Hydroxyl 13.02 16.65

18 H2O Water 12.62 15.4

28 C2H4 Ethylene 10.53 12.3

28 CO Carbon monoxide 14.01 14.35

32 O2 Oxygen 12.07 14.35

40 Ar Argon 15.76 16.2

44 CO2 Carbon dioxide 13.8 15.4

64 HOРO Phosphinic acid 10.7 12.8

80 HOРO2 Metaphosphoric acid 12.4 14.5

Table 1 summarizes all species, the mole fraction profiles of which were measured, along with their atomic mass units (m), ionization potentials (IP), and energies of ionizing electrons used for each species (IE). The mole fractions of most species were determined using the calibration coefficients (relative to argon) derived from direct calibration experiments with gas mixtures of known composition. Calibration coefficients for H and OH radicals were determined by applying a relative ionization cross-section (RICS) method described by Cool et al. [6] and used in our previous work [7]. The uncertainty of determining absolute mole fractions of the major flame products including: CO2, H2O, and O2, was estimated to be ±10% of the maximum mole fraction values, and ±20% for CO, H2, C2H4. Absolute mole fractions of H, OH and phosphor containing species were determined to within a factor of about 2.

RESULTS AND DISCUSSION

The temperature profiles in the flame and in the condensed phase/The polymerʼs surface temperature

The temperature of the UHMWPE burning surface in a counterflow flame was measured using two methods: (i) a thermocouple was moved through the flame until its junction touched the burning surface and (ii) a thermocouple was embedded in the specimen. The temperature corresponding to the moment the junction contacted the liquid was considered in the first case to be the surface temperature, when the thermocouple was enveloped with the molten layer. This moment was controlled visually. After that, the thermocoupleʼs movement was stopped. The thermocouple remained motionless for several seconds, and then it was moved in the opposite direction. To raise the measurement accuracy, the above procedure was repeated many times.

Whilst measuring the temperature with the thermocouple embedded in the specimen, the burning specimen was moved by a stepper motor without being rotated. The moment the thermocouple junction touched the burning surface was recorded with a Panasonic M3000 camera synchronized

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with the thermocoupleʼs data acquisition module. Fig. 4 shows the temperature profiles in the condensed and gas phases obtained by both methods of measurement at the flow rate of 0.44 m/s and the temperature of 20 оС. The temperature gradient in the condensed phase near the burning surface was equal to 1.3 × 105 K/m for UHMWPE and 105 K/m for UHMWPE +5 wt.% of TPP.

Figure 3. Embedding a thermocouple inside the

specimen. 1- thermocoupleʼs junction, 2- thermocouple leads.

Figure 4. The temperature profiles in the

condensed and gas phases in UHMWPE burning. solid line – UHMWPE, dashed line – UHMWPE

+5wt.% of TPP.

The temperature gradient in the gas phase near the burning surface was equal to 5 × 105 K/m for UHMWPE and to 4.3 × 105 K/m for UHMWPE +5 wt.% of TPP. The temperature measured with the embedded molded-in thermocouple was 550 оС for UHMWPE and 530 оС for UHMWPE +5 wt.% of TPP. The temperature of the burning surface measured with an embedded thermocouple (550 оС) slightly exceeded that (522 оС) measured with the thermocouple moved in flame. However, within the limits of accuracy (±15 оС) they are equal. One can also conclude that adding TPP to UHMWPE does not affect the temperature of the polymerʼs burning surface. The 14% reduction in the temperature gradient in the gas phase adjacent to the burning surface, when 5 wt.% of TPP was added to UHMWPE indicates a corresponding reduction of the heat flux from the flame to the polymer when a flame retardant is present. Adding 5 wt.% of TPP changed the structure of the UHMWPE flame. In accordance with the temperature profile (Fig. 4), adding TPP to UHMWPE resulted in an increase of the total width of the flame zone by ~1.4 times (from 3.7 mm to 5 mm), a shift in the temperature maximum from 1.5 mm to 2.2 mm, and a decrease in the maximum temperature of 150 °С (from 1380 °С to 1230 °С).

The structure of counterflow flame of UHMWPE with and without TPP

Figs. 5 and 6 show temperature profiles and concentration profiles for stable species in a counterflow flame of UHMWPE without and with 5 wt.% TPP, correspondingly.

Adding TPP to UHMWPE led to a change in the composition of the species in the flame, reduction of the maximum temperature, shifting its profiles from the burning surface, and the increase in the width of the combustion zone. In the flames studied, H atoms and OH radicals were identified, their concentrations and their concentration profiles were measured. In the flame with TPP additives HOPO and HOPO2, the main products of TPP destruction in flame, were identified, and their concentrations

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were measured. Shown in Fig. 7 are the concentration profiles of H, OH, HOPO and HOPO2 in the flames of UHMWPE without and with 5 wt.% TPP.

Figure 5. Temperature profile and concentration

profiles for stable species in a counterflow flame of UHMWPE.

Figure 6. Temperature profile and concentration

profiles for stable species in a counterflow flame of UHMWPE with 5 wt.% TPP.

It can be seen that adding TPP to UHMWPE results in reduction of H and OH radicalsʼ concentration by approximately 2 times, a shift of their maxima by 1 mm from the burning surface. It was shown earlier [8, 9] that reactions with participation of HOPO and HOPO2 are the key reactions in the catalytic cycle of recombinations of H and OH radicals:

2

2 2

2 2

2 2 2

H+PO +M HOPO+MHOPO+OH PO +H OOH+PO +M HOPO +MHOPO +H PO +H O

⇒

⇒

⇒

⇒

The maxima of the HOPO and HOPO2 profiles are shifted to the burning surface by approximately 1 mm versus the concentration profiles of H and OH.

The burning rate of UHMWPE and UHMWPE+5 wt.% of TPP

Fig. 8 presents data relating to the burning rate of UHMWPE and UHMWPE+5 wt.% of TPP solid and melted polymer specimens. In the case of the melted polymer, U is the burning rate, as calculated by measuring the length of the burnt specimen and the time of its burning. In the case of burning of the polymer specimen, the mass rate of the polymerʼs combustion (M1) and the dripping rate (M2) were measured. М2 was equal to the mass of dripping divided by the burning time. The mass flow rate of the polymerʼs pyrolysis products from its surface M was determined using the formula М=M1−M2. The linear velocity of the polymerʼs combustion was calculated using the formula U=M/(ρS), where S was the surface area of the polymer specimen and ρ was the polymer density.

Shown in Fig. 8 are the dependences of the polymerʼs regression rate on the temperature of its surface in Arrhenius coordinates. The polymerʼs regression rates for the polymer without an additive U and with a 5%TPP additive (UFR) may be approximated by the following Arrhenius dependences: U=U0exp(−E0/(RT)) and UFR=U0,FRexp(−E0, FR/(RT)) , U0 =10−0.05 m/s, E0 = 145 [kJ/mol] and U0,FR = 10−1.11 m/s, E0,FR = 173 kJ/mol. As can be seen, when TPP was added to UHMWPE, the polymerʼs regression rate decreased.

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Figure 7. The concentration profiles of H, OH, HOPO and HOPO2 in the flames of UHMWPE

without and with 5 wt.% TPP.

Figure 8. Dependence of the regression rate of UHMWPE and UHMWPE+5 wt.% TPP on the

polymerʼs surface temperature. Blue symbols refer to the tests with cold air, while the red ones refer

to the tests with hot air.

At the flow rate of 44 cm/s and the temperature of 20 оС, When TPP was added to UHMWPE, the width of the glowing zone increased from 1.3 mm to 2 mm, and the distance from the polymerʼs surface to the middle of the glowing zone increased from 1.7 mm to 2 mm. Previously [10], TPP vapors were identified in the flame during candle-like burning of UHMWPE+10 wt.% of TPP. It has been shown [11] that adding TPP to a methane-air flame reduces the concentration of OH radicals by accelerating the recombination of OH radicals, thereby inhibiting the flame. When 5 wt.% of TPP was added to UHMWPE, the burning rates, M1 and U, approximately halved. The mass burning rate M, related only to the products entering the gas phase, decreases much less (~1.4 times) than the burning rate U.

The rate constant of the polymerʼs pyrolysis in the conditions of combustion

To find the kinetic parameters of polymer pyrolysis from the data on dependence of the rate of linear pyrolysis of polymers on the surface temperature, it was proposed in [12] to use Merzhanovʼs formula [13] to determine the burning velocity of condensed species:

22

00

2 e* (( ) / )

Es RTs

c s p

RTU kE T T Q C

λρ

−=− ±

, (1)

where U is the burning velocity, λ is the polymerʼs thermal conductivity, R is the universal gas constant, ρс is the polymerʼs density, Ts is the temperature of the polymerʼs surface, T0 is the initial polymerʼs temperature Q is the heat release on the polymerʼs surface, Сp is the specific heat capacity of the polymer, k0 is the preexponential factor of the degradation rate constant, Ea is the activation energy of the degradation reaction.

Using Eq. (1), an expression was obtained for the rate constant k depending on temperature. The constants used in Eq. (1) are shown in Table 2.

Table 2. The numeric values used for Eq. (1).

T0 (K) Cp(J/(kg·K)) λ(W/(m·K)) Q (J/kg) ρ (kg/m3)

343 0.0025 [15] 0.21 [14] 0.13* 940 * According to DSC data for decomposition of UHMWPE.

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Shown in Fig. 9 are the Arrhenius dependences of the rate constants of pyrolysis of UHMWPE and UHMWPE+5 wt.%TPP, obtained using Eq. (1) and the data shown in Fig. 8. Fig. 9 shows data both for the case of liquid melted polymer and for the case of the original polymer.

The kinetic parameters of the zero-order reaction obtained previously by the TGA and DMSTA methods for pyrolysis of UHMWPE and UHMWPE+TPP, as well as those obtained in this study in the counterflow flame mode are shown in Table 3.

Shown in Fig. 10 are the rate constants for degradation of UHMWPE with TPP additive and without it, obtained by three methods: DMSTA, TGA, and the counterflow flame method (CFF). Two approximation lines are drawn for all the three methods: the solid line indicates pure UHMWPE; the dashed line stands for UHMWPE with TPP additive. In the case of approximating data for UHMWPE with TPP additive, the TGA data were not taken into account, as no TPP impact was discovered for slow heating. The rate constants for pyrolysis of UHMWPE (k) and UHMWPE with TPP additive (kFR) in a wide temperature range by the data of Fig. 10 show the following Arrhenius dependences k1=1015exp(−E1/(RT)) 1/s and kFR=1010.7exp(−EFR/(RT)) 1/s, where E1=246 kJ/mol and EFR=189 kJ/mol.

Figure 9. Dependence of the rate constant of

pyrolysis of UHMWPE (the solid symbol) and UHMWPE+wt.5%TPP (the empty symbol) in the

burning mode.

Figure 10. The degradation rate constant of

UHMWPE and UHMWPE+TPP in Arrhenius coordinates.

Table 3. Kinetic parameters of the zero-order reaction during pyrolysis of UHMWPE and UHMWPE+TPP in a counterflow mode.

lgk0, k0 (1/s) E (kJ/mol)

UHMWPE 8.36 143.6

UHMWPE+5 wt.% TPP 9.93 169.4

UHMWPE, DMSTA [16] 4.5 68

UHMWPE+10 wt.%TPP, DMSTA [16] 11.2 189

UHMWPE, TGA [16] 13.2 223

The heat release on the burning polymerʼs surface

In [2] the authors stress the importance of oxygen diffusion to the fuel surface and subsequent surface oxidation. In their evaluation, the enthalpy released by oxidising the polymer pyrolysed was twenty

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percent of the energy required for fuel pyrolysis. The remainder of the energy was delivered to the surface from the flame through heat transfer processes. We did such evaluation by using another approach based on the data presented in Fig. 4 for net polymer and for polymer with FR.

The amount of heat released on the polymerʼs surface during its burning was calculated by the thermal balance on the polymerʼs surface using the following relationship:

4d dd dg s c r s

g c

Т ТT q UQх х

λ εσ λ ρ − − + = −

, (2)

where gλ , cλ , qr, Qs, ε, σ, (dT/dx)g, (dT/dx)c are the polymerʼs thermal conductivity in the gas and condensed phases, the radiation heat flux from flame to the polymerʼs surface, heat release on the polymerʼs surface by oxidising the polymer pyrolysed, polymer surface emissivity, Stefan-Boltzmann constant, the temperature gradients on the polymerʼs burning surface on the sides of the gas and condensed phases. Thermal conductivity in the gas was evaluated to be 0.055 W/mK. The gas-phase radiation heat flux was calculated by the optically thin model [17]):

4

02 d

Lg

r pq K T xσ= ∫ , (3)

where Kp is the Planck mean absorption coefficient, calculated from the formula

( )ip p i

iK K T Y=∑ , (4)

where i= {CO2, H2O, CO}. For the ith component Yi is the volume concentration of the components determined experimentally.

ipK is the mean absorption coefficient set in accordance with the data from [18]. Thus, we obtain from Eqs. (3)-(4):

( )2 CO 2 H O CO2 2

4 4 4CO H O CO0

2 dLg

r p p pq Y K T Y K T Y K T xσ= + +∫ . (5)

There are no reliable data on literature on the emissivity of polymersʼ burning surface. Therefore calculations were made for εp = 1 and 0.3. The calculated gas-phase radiation heat fluxes with εp = 1 for the net polymer and for the polymer with FR were 1.43 × 103 W/m2 and 9.56 × 102 W/m2, accordingly, and with εp = 0.3 they are 4.17 × 102 W/m2 and 2.78 × 102 W/m2, accordingly. Using the literature and experimental data, Qs was calculated, using the Eq. (2). The calculated values Qs with ε = 1 were 2.68 × 106 and 2.64 × 106 J/kg for net UHMWPE and UHMWPE with FR, accordingly, and with ε = 0.3, they were 7.9 × 105 and 5.2 × 105 J/kg for net UHMWPE and UHMWPE with FR, accordingly. Taking the enthalpy of polymerʼs depolymerization to be equal to be 3.85 × 106 J/kg [2], we obtained that with εp = 1, Qs was about 70% the enthalpy of polymerʼs depolymerization, irrespective of the presence of FR. With εp = 0.3, Qs was 20% of the enthalpy of polymerʼs depolymerization for net polymer and 13% for polymer with FR.

ACKNOWLEDGMENT

This work was supported by the RFBR under grant #13-03-91164 and by the NNSF of China under grant 51120165001.

CONCLUSIONS

The structure of counterflow flames of air and UHMWPE with TPP added, and also without it, was studied at atmospheric pressure using the MBMS with soft electron-impact ionization. The dependence of the regression rate of UHMWPE and UHMWPE+5 wt.% TPP on the surface

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temperature was determined. To calculate the kinetic parameters for the rate constants of the degradation reaction for UHMWPE and UHMWPE+5 wt.% TPP the formula for the propagation rate of the combustion wave in the condensed phase was used. In adding TPP to UHMWPE, widening of the flame zone, a decrease of the maximum flame temperature, its shifting from the burning surface, reduction of the heat flux from the flame to the polymer surface, and reduction of H and OH radicalsʼ concentrations were found. Direct experiments conducted demonstrate that the action of a flame retardant in a polymer flame consists in its participation in chain-termination reactions.

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17. Yoshinaga, K., and Kobayashi, H. Numerical Study of Radiation Effects on Polypropylene Combustion Using High-Temperature Oxidizer Diluted with H2O and CO2, Journal of Thermal Science and Technology, 3(2): 167-178, 2008.

18. Zhang, H. M., and Modest, M. F. Evaluation of the Planck-Mean Absorption Coefficients from HITRAN and HITEMP Databases, Journal of Quantitative Spectroscopy and Radiative Transfer, 73(6): 649-653, 2002.