Torsion-Effusion Technique for Studying the Kinetics of Gas-Forming

KINETICS OF GAS-FORMING REACTIONS

1079

Torsion-Effusion Technique for Studying the Kinetics of Gas-Forming Reactions

by Charles L. Rosen and Alvin J. Melveger

Downloaded by UNIV OF CALIFORNIA SAN DIEGO on September 10, 2015 | http://pubs.acs.org Publication Date: May 1, 1964 | doi: 10.1021/j100787a018

Research and Advanced Developntent Di,uiswn, Avco Corporation, Wilmington, Massachusetts (Received November 7, 1963)

The torsion-effusion technique has been applied to the study of the kinetics of thermal decomposition. An apparatus which includes a thermocouple as an integral part of the suspension system is described. The decomposition of polytetrafluoroethylene (Teflon) was studied and found to obey first-order kinetics with an activation energy of 76.7 f 7.3 kcal./mole in the temperature range 544 to 590'. The first-order rate constant, k (set.-'), was found to obey the expressionlog k = 17.27 - 16.66 X 103(l/T). The molecular weight of vaporizing species was calculated and found to be 100.0 jl 6.

I. Introduction The kinetics of reactions that involve the irrever8iblle formation of volatile species have usually been studied by techniques involving weight change or pressure change observations.l I n most weight change and pressure change experiments that have been reported , the integral amounts of sample weight or system pressure were measured a t given times. However, the information most frequently desired is the rate of reaction as a function of time a t various temperatures. These isothermal rates can be derived from the integral values. This paper will show the applicability of the torsioneffusion method to the study of reaction kinetics of irreversible gas-forming reactions. The torsion-effusion method permits pressure rate data to be obtained directly and in addition, if the weight change rate data are available, the molecular weight of the vaporizing species may be determined. The desirability of this method which measures the reaction rate directly rests upon its being an extremely rapid and relatively accurate procedure requiring only small quantities of rnaterial and an apparatus that is _ _ easy to construct. The torsion method was first used by Volmer2 for the measurement of vapor and this has . . pressures remained its main use. However, in addition to vapor pressure measurements, the torsion-eff usion technique has been used to measure the rate of evaporation and

the rate of growth of single crystals.s I n the usual experimental arrangement, a condensed phase is enclosed in a reaction crucible and the vapors which are formed upon heating this condensed phase are allowed to effuse through one or more orifices. It has been shown that in the molecular flow region, the force of the issuing vapor beam depends directly upon the number of molecules leaving the crucible per unit of time.4 This force, due to the transfer of momentum from the escaping gaseous molecules to the crucible, may be determined by allowing the, vapor to flow through crucible orifices that are eccentrically located with respect to a suspension wire calibrated in terms of force per angular displacement and measuring the displacement produced. Thus the angular displacement is actually a measure of the number of molecules leaving the crucible per unit of time and as will be shown, under certain conditions, the rate of reaction. For vapor pressure measurements, the effusion rates are kept as low as possible by using large evaporating to orifice area ratios in order to ensure that the vapor pressure above the condensed phase approaches, as closely as practical, the equilibrium vapor pressure. (1) (a) c. D. Doyle, J. A p p l . Polymer Sci., 5 , 285 (1961); (b) S. L. Madorsky, V. E. Hart, and S. Straw, J. Res. Natl. B U T .Std., 569343(1956). (2) M.Volmer, 2.physik. Chem., 863 (1931). (3) V. J. Clancey, Nature, 166,275 (1950). (4) R. D. Freeman and A. W. Searcy, J . Chem. Phys., 2 2 , 762 (1954).

Volume 68,Number 6 M a y , 1964

CHARLES L. ROSENAND ALVINJ. MELVEGER

1080


11. Theoretical Discussion The mathematical equations for the application of torsion-eff usion are well known.2J The applicability of these equations to the determination of the kinetics of irreversible gas-forming reactions will be demonstrated. The equations to be discussed are applicable only in the molecular flow region where from kinetic gas theory the rate of weight loss from the reaction crucible can be shown to be5

where dw is the loss of weight from the crucible; dt is the time interval during which the weight change occurs; f is the force of the effusing beam; M is the molecular weight of the vapor species; T is the absolute temperature; and R is the gas constant. The force exerted by the effusing beam on the crucible can be expressed as

f = DO (2) where f is the force, D is the torsional constant of the suspension wire, and 0 is the angular deflection of the suspension. A combination of eq. 1and 2 gives (3) Equation 3 shows that for a given torsion wire, the angular deflection is dependent only upon the rate of weight loss from the crucible, the temperature, and the molecular weight of the effusing vapors. If the residence time of a molecule in the crucible is short compared to the apparatus response time, then the rate of weight loss from the crucible equals the rate of formation of gaseous molecules. Thus, the angular deflection a t any time becomes proportional to the reaction rate. The average residence time of a molecule under molecular flow conditions will be estimated. Intermolecular collisions may be neglected in this flow region. The total number of collisions of vapor species with the walls of the crucible during time t can be expressed as6 (4)

where 2 is the total number of collisions with walls; C is the average velocity of the molecules; AT is the total area of the crucible walls; t is the time during which collisions occur; n is the number of molecules present; and V is the volume of the crucible. The Journal of Phgsieal Chern&y

If it is assumed that any molecule colliding with a n effusion hole leads to effective removal from the crucible, then the number of molecules removed from the crucible in time tis 1 n Z - -CAtl - 4 V

(5)

where 21 is the number of collisions with effusion holes and A is the area of effusion holes. If one considers a molecule having an average velocity, C, then the time necessary for it to make a collision leading to effective removal is

t = -41' CA Under the conditions of a typical experiment, the values of V , C, and A are such that a molecule is removed in the order of milliseconds after its formation. Therefore, within this time resolution, the angular deflection at any time is directly proportional to the rate of reaction. Implicit in the assumption of molecular flow is the occurrence of a cosine law effusion of molecules from the orifices. Corrections for the existence of nondiffuse effusion should be made in certain case^.^,^ This correction may be important when comparing the results from orifices of different geometry. It should be emphasized that although eq. 3 reveals the independence of angular deflection and orifice area, this only applies to irreversible reactions and/or cases where the orifice area is not a limiting factor in vapor removal. In reversible zero-order reactions, such as vapor pressure determinations, the amount of material effused per unit of time, and hence the angular deflection, is directly proportional to the orifice area as long as the rate of vapor removal through the orifice is small in comparison to the total rate of evaporation within the crucible. Even though the deflection has been shown to be independent of orifice area, the orifice area does determine the maximum rate of molecular effusion that can be maintained in order to remain in the molecular flow region.

111. Experimental The usual torsion-eff usion assembly has been modified to permit accurate temperature measurement of the decomposing specimen. The uncertainty associated with temperature measurements has been a factor limiting the accuracy attain( 5 ) J. L. Margrave, J . Chem. Phys., 27, 1412 (1957). (6) I. Langmuir, J. Am. Chem. Soc., 35, 931 (1913). (7) P. Clausing, Ann. Physik, 12, 961 (1932).


KINETICS OF GAS-FORMING REACTIONS

able in torsion-effusion experiments. The nature of the torsion-effusion assembly has, in the past, appeared to preclude the insertion of a thermocouple directly in the sample without introducing an extraneous torque. The usual procedure has been to place a thermocouple close to, but not in contact with, the effusion crucible and to calibrate this thermocouple against readings of a t h e m ocouple placed inside the cell during a ‘idurnmy’’run without a sample!. Figure 1 is B schematic diagram of the apparatus used in our laboratory. It has the advantage of allowing direct temperature monitoring of the evaporating system, thus helping to eliminate a major source of uncertainty in torsion experiments. A chromelalumel thermocouple is an integral part of the apparatus; yet it introduces, for our purposes, negligible Interference to the angular deflection of 20.2 in. long, 0.003 or 0.005 in. diameter tungsten torsion wire. A two-hole quartz torsion crucible fitted with a standard taper joint Connected to twin bore quartz capillary tubing is suspended from the torsion wire. The

A0005 INCH

SHEET METAL DAMPING VANE DAMPING OIL CONTAI 0.125 INCH ALUMINUM ROD

MIRROR

ALUMINUM SET SCREW COUPLING FOR DISASSEMBLING SYSTEM

THERMOCOUPLE WIRE

THERMOCOUPLE WIRE

--

0.005 INCH THERMOCOUPLE WIRE IN OUARTZ TUBING

SHIELDING TWO HOLE OUARTZ CAPILLARY TUBING

STANDARD TAPER JOINT TORSION CELL

THERMOCOUPLE-JUNCTION

Figure 1. Torsion suspension and damping system.

1081

capillary tubing is mechanically coupled to an aluminum rod which, in turn, is coupled to the torsion wire. Five-mil chromel-alumel thermocouple wire is fed through the quartz twin bore tubing and terminates in a ceramic-coated junction inside the effusion cell. The upper end of the capillary tubing contains tWQ holes from which the insulated thermocouple wires may be removed and tightly wrapped and cemented about the aluminum rod. The ends of the thermocouple wires are attached to small clips to which 0.0005in. diameter tungsten wire is connected and allowed to hang loosely. These very fine tungsten wires are led through the vacuum system by means of metal-ceramic seals and terminate a t a recorder that is used for monitoring the sample temperature. The stability of the torsion constant of a 0.003-in. diameter suspension wire was determined with the thermocouple and fine tungsten wires in place. This was done by measuring the period of oscillation of the system over the range of angular deflection 2-40’ of arc under simulated experimental conditions. I n 25 determinations over a l-week interval, the deviation of the period from a mean value of 28.22 sec. was less than 0.5% with a confidence level of 90%. The maximum spread of these determinations was 1.4%. These results indicate that the torsion constant determined with attached tungsten wires remains constant during normal experimental operation. The success of this method appears to depend upon the use of loosely hung wires and the coupling of the wires as close to the center of rotation as possible, thereby reducing extraneous torques. A possible source of error in temperature measurement with the described apparatus is the presence of tungsten-chrome1 and tungsten-alumel junctions in the temperature measuring circuit. The temperatures of these junctions were measured during sample heating and found to remain a t ambient temperature. As long as such conditions can be maintained, it is felt that this method is more reliable than the use of “dummy” calibrations. Although the described apparatus can be used only below the softening point of quartz, modification of the torsion crucible and the capillary tubing materials can extend the usable range of the apparatus to higher temperatures. I n order to make the technique practicable, the apparatus must employ a method for critically damping the system so that the angular deflection reaches its steady-state value during the characteristic time of a measurement. The suspension system employs an oil damping arrangement. Two damping vanes shown In Fig. 1 are attached to the rigid part of the suspension Volume 68,Number 6

May, 1964

CHARLES L. ROSENAND ALVINJ. MELVEGER


1082

system and dip into the oil, thus serving to damp out any extraneous oscillations and any overshooting while the torsion system's motion is being monitored. The amount of damping may be varied by increasing or decreasing the depth of immersion of the vanes in the oil. This can be achieved by either adding or removing damping fluid or by raising or lowering the entire suspension system by means of the screw assembly a t the top of the torsion system. In any given experiment the damping was adjusted to what was considered the critical amount. This was determined by imparting various torques to the system and monitoring the decay time to reach its equilibrium value. The amount of damping was then adjusted to make this decay time as short as possible. The system's motion was then found to be smooth and regular without any apparent overshooting that one would expect in an underdamped system. I n choosing a damping fluid, it was important to consider both its viscosity and vapor pressure since the system was operated under vacuum. n/Iotor oil was found to meet these requirements for our system. The actual measurements of angular deflection were made by reflecting a light from a mirror mounted on the suspension system onto a scale placed at a distance of 9 ft. from the axis of rotation of the system. The scale was calibrated in degrees of arc.

IV. Results The decomposition of polytetrafluoroethylene (Teflon), which has been studied previously, was used to test the method and the apparatus. Madorsky and co-workers,* by isothermal weight loss and pressure rise methods, reported that the pyrolysis of polytetrafluoroethylene in vucuo followed a first-order rate law between 480 and 510' with an activation energy of 75 f 4 kcal./mole. Andersong determined by thermogravimetry that in the range 450 to 550' the pyrolysis of Teflon in vacuo obeyed a first-order rate law with an activation energy of 80.5 kcal./mole. From eq. 3 it can be seen that the rate of material loss is proportional to the angular deflection a t constant temperature and constant molecular weight. Since a simultaneous determination of weight loss and angular deflection was not made, it was assumed that the average molecular weight of the effusing molecules remained constant during the course of an experimental run. Thus if the decomposition of material A (condensed phase) to some vapor phase follows a firstorder relation, then one may write -dA ~- ICA= dt

The Journal of Physical C h a S e t r y

ve

(7)

41

t

-3.0 -3.4

1

1.14

I

1.~16

1

I

i.is 1.20 i/~xioa.

I

i

1.22

1.24

Figure 2. Arrhenius plot for decomposition of polytetrafluoroethylene.

where -dA/dt is the reaction rate, k is the rate constant, and k' is a proportionality constant between the rate of reaction and angular deflection. It can be shown that after suitable integration of eq. 7 one may write

where A. is the original concentration of A. Thus, for a first-order reaction a plot of log 0 vs. t yields a line with a slope equivalent to -k/2.303. Values of log k a t various temperatures can now be determined and plotted against 1/T according to the Arrhenius expression &

2.303RT

(9)

where E is the activation energy and ko is the Arrhenius constant. The slope of such a plot yields the value - E/2.303R from yhich the activation energy, E , can be determined. DuPont Teflon which was cut into small shavings or powdered from a piece of the pressed material was used for the experiments. Sample weights of 50, 100, and 150 mg. were used. It was found that the results were independent of sample weight or form. The torsion crucible was placed in a vacuum resistance furnace and when ready was brought up to temperature as rapidly as possible and maintained a t temperature for the duration of the experimental run. The temperature indicated by the thermocouple (8) S. L. Madorsky, V. E. Hart, S. Straus, and V. A. Sedlaok, J . Res. Nail. Bur. Std., 51, 327 (1953). (9) H. C. Anderson, Makromol. Chem., 51, 233 (1962).

1083


KINETICS OF GAB-FORMING REACTIONE

was displayed on a Sargent strip chart recorder. The temperature range studied was 544 to 590'. There seemed to be some indication of anomalous behavior during the initial pyrolysis before the sample reached its final temperature and usually before 10% of the sample had vaporized. Only those readings of the deflection taken after the attainment of isothermal conditions were used. A series of 19 experiments was performed in the temperature range indicated. It was assumed that slight temperature changes during any run would be averaged out. Temperature fluctuations were usually kept to within 2'. For each isothermal run, values of log 6 us. time were plotted and a least-squares fit was made of these data to determine k . The logarithms of these values of k were then plotted against 1/T to evaluate the activation energy of the decomposition. Such a plot gave a straight line, shown in Fig. 2, which obeyed the equation log k

=

17.27 - 16.66 X 10" (1/T)

(10)

where k is the first-order rate constant in see.-', and T is the absolute temperature. The activation energy was then determined to be 76.7 f 7.3 kcal./mole with 90% confidence, which agrees with previous workers. An average molecula,r weight for the effusing vapors was determined by using the integrated form of eq. 3

(My2

=

W ( 2aR T )"* 20

6dt

(11)

The molecular weight was assumed to be constant during an experimental run in making this calculation. The value of 6dt was evaluated graphically from plots of e us. t . The total weight loss of sample in an experiment was used as the value for W . The torsion constant, D , was callculated from a knowledge of the modulus of rigidity of the 5-mil tungsten torsion wire and its length. Molecular weights which were determined on the basis of the calculated torsion constant were then corrected by means of an experimentally determined instrument calibration factor. Zinc metal which vaporizes into atomic Zn having a molecular weight of 65.4 and ammonium chloride which decomposes to NH3 and HCI with an average molecular weight of 26.8 were the calibrating substances used. By use of eq. 11 the molecular weights for the calibrating substances were calculated and found to deviate from their true value by the factor 1.37 f 0.05. All molecular weights determined for Teflon were then multiplied by this apparatus constant. I n calculating the molecular

weight of the decomposing Teflon, no correction was made for the fact that part of the effusion occurred before the sample reached its nominal temperature. Values for the molecular weight of Teflon determined in the above manner are listed in Table I. The mean value is 100.0 with an associated mean deviation error of approximately 6%. The estimated error includes the uncertainty associated with the experimental determination of the apparatus calibration factor. Table I Sample weight, mg.

Temp.,

99.6 99.9 101.0 99.9 98.5 99.4 99.4 100.5 100.4 99.7 99.7 100.7

817 846 829 840 833 834 842 824 819 854 854 819

96.9 106.3 115.2 95.1 98.1 97.7 96.3 106.2 100.0 87.3 104.3 104.3

50.3 50.2 51.0

853 856 855

94.3 99.7 95.6

150.3 150.0 150.4 149.4

817 819 819 833

101.1 101.2 99.3 101.1

J:

Mol. wt.

OK.

Mean

100.0 f 6

These results indicate that the average molecular weight of Teflon degradation products as determined by this technique is fairly constant and independent of sample size and temperature within the range studied. In order to investigate the possibility of changes in the molecular weights of the vapors over the duration of the experiment, one would need simultaneous angular deflection and weight loss data.

V. Summary The torsion-effusion technique has been shown to be applicable to the study of thermal decomposition reactions involving the formation of a gas phase. The method allows for the direct measurement of the rate of formation of a vapor phase using small samples and should be applicable to the study of kinetics in both organic and inorganic systems. Volume 68,Number 6 May, 1964

D. BURGREEN AND F. R. NAKACHE

1084

Acknowledgment. The authors wish to thank Mr. Robert Holmes for his effort in carrying out the experi-

ments, and Mr. M. J. Massa for his aid In making the statistical analysis of the data.


Electrokinetic Flow in Ultrafine Capillary Slits'

by D. Burgreen and F. R. Nakache Deaelopment Diuision, United Nuclear Corporation, White Plaine, New YorB

(Received November 9, 1963)

This paper contains an analytical study of electrokinetic flow in very fine capillary channels of rectangular cross section. It is a natural extension of the general theory of electrokinetic flow which heretofore was limited to channels of large electrokinetic radius or to interfaces exhibiting low source potential. The practical implications of the results of the study are explored.

Nomenclature

U

cross section area of capillary channel

uo

M 2io2~ / K

U,

ion concentration in moles per liter dielectric constant of fluid applied axial voltage streaming potential elliptic integral of second kind elliptic integral of first kind parameter plotted in Fig. 6 half of distance between plates current in external circuit electroosmotic conduction current = KOAY O electroosmotic transport current lumped conductivity (fluid path plus external path) = KO L/2hRo = K O L/rro2R0 specific conductivity of fluid Boltemann constant length of capillary passage mobility = & D / 4 ~ por fD/47rp average number of positive or negative ions per unit volume average number of ions of ith kind per unit volume number of ions of ith kind per unit volume preesure in fluid Reynolds number resistance of external circuit internal or fluid resistance radius of tube wetted perimeter of capillary channel absolute temperature

+

The Journal of Physical Chemistry

+

UP Ur

V VP

V, We WP

X

Y

YO Y* Y," Y 2

ZI

velocity a t a given point in capillary channel velocity a t center of channel electroosmotic velocity pressure-induced velocity retarding flow component volumetric flow volumetric pressure-induced flow volumetric retarding flow electrokinetic pumping energy mechanical pumping energy axial distance along capillary channel axial electric field = dE/dx applied axial electric field = dEo/dx dE,/dx = streaming axial electric field unreduced streaming potential distance measured from capillary wall valence of ions when one kind of salt is present and dissociates into two equal and oppositely charged ions valence of ith type of ion

Greek symbols LY

ai

7

e eo

ionic energy parameter = ez$o/kT ionic energy parameter = ezi$o/kT rectilinear coordinate measured from center of channel in flow between plates sin-' [cosh (~~$,/2$~)/cosh (a$/2$0)1 sin-' [cosh (a$c/2$o)/cosh (or/2)]

(1) Work performed for Aeronautical Systems Division, AFSC, ASRFS-2, Wright-Patterson AFB.

Torsion-Effusion Technique for Studying the Kinetics of Gas-Forming

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