jAD

US ARMYMA7ER1EL

* COMMAND

TECHNICAL REPORT BRL-TR-2741

-. U

O-.ELECTRICAL CONDUCTANCE OF LIQUID

PROPELLANTS: THEORY AND RESULTS

John A. VanderhoffSteven W. Bunte

Philip M. Donmoyer DTIC- l EC T E I I

JU 29 686,June 1986

APPROVED FOR PUBLIC RELEASE; DISTRIUTON UNUITED.

US ARMY BALLISTIC RESEARCH LABORATORYABERDEEN PROVING GROUND, MARYLAND

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The use of trade names or manufacturers' names in this reportdoes not constitute indorsement of any commercial product.

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Technical Report BRL-TR-2741 fllji? I_ ___________

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FinalELECTRICAL CONDUCTANCE OF LIQUID PROPELLANTS: ______________ -

THEORY AND RESULTS 6 PERFORMING ORG. REPORT N,.mBER

7. AUTOR(*)S. CONTRACT OR GRANT NUMBER(&)

John A. VanderhoffSteven W. BuntePhilip M. Donmoyer*

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US Army Ballistic Research LaboratoryARAa0R(UINMERATTN: SLCBR-IB IL161 102AH43Aberdeen Proving Ground. MD 21005-5066 ______________

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*Summer student from University of Maryland, College Park.

19. KEY WORDS (Continue on reverse aide it ne.cessary and identify by block number)

Liquid Propellant Electrical ConductanceIon-PairingConcentration DependenceTemperature Dependence

20. AStR ACT rCom~finje pere.m s.f It nime.eary md Identify by block nmtber) me g

An overview of the development of the theory of electrical conductance ofelectrolytes is presented. Conditions where ion-pairing can occur isemphasized. Electrical conductance versus both concentration and temperatureis reported for aqueous hydroxylammonium nitrate (HAN) solutions. Electrical 5conductance versus temperature is reported for liquid gun propellantsLGP 1845 and LGP 1846. Possible local molecular structure consistent withthe observed data is discussed.--

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TABLE OF CONTENTS

Page

LIST OF FIGURES ...... o .................... s .................. 5

I I INTRODUCTION ........................................... .. 7

II. EARLY WORK ................................. .. . ................ 9

III. IONIC INTERACTIONS ........................ . ............ ... .11

IV. ION-PAIRING ..................... ............ .... ........ .. .14

V. TEMPERATURE ..................................................... 15

VI. EXPERIMENT ...................................................... 16

VII. RESULTS AND DISCUSSION ....g ..... ... ......... ...... c... . ...... 16

VIII. SUMMARY .................................... . ........ ........ ... 21

REFERENCES ...................... ........ .................. 27

DISTRIBUTION LIST ............................................... 2 9

Accesion For

NTiS CRAiDTIC TAB 13UnannouncedJustif ication ........ ......... . ......

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Avail andforDist Special

p4-i ITHIS DOCUMENT CONTAINEDBLANK PAGES THAT HAVE

BEEN DELETED

3

LIST OF FIGURES

1 Picture of Ion Model for the Debye-Hckel Theory ................ 12

2 Specific Conductance of HAN as a Function of Concentrationin H2 0 at -12, 20, and 40°C ..................................... 17

Equivalent Conductance of HAN as a Function of Concentration

at -12, 20, and 40°C ........................................... 18

4 Fit of Equivalent Conductance at 20°C With Wishaw-Stokes

Equation, Data 0 , Fit --- Without Viscosity Correction,Fit -With Viscosity Correction ............................... 19

5 Equivalent Conductance of HAN as a Function of Concentration

in H20 and in H2 0-CH3 OH Mixtures at 20 and 40°C ................. 21

6 Specific Conductance of 11 M HAN, LGP 1845, and LGP 1846 asa Function of Temperature. Data areQ] , 0, A. Solid Linesare Polynomial Fits ............................................ 22

5

I;- ~ ~ ~ ~ ~ ~~~' L ... RV w tVL 17

LIST OF TABLES

Table Page

1 Critical Distance for Monovalent Electrolyte Ion-Pairingat Various Temperatures and Dielectric Constants ................ 15

2 Ionic Separations for Monovalent Electrolyte Solutions atVarious Concentrations.......................................... 15

3 The Specific and Equivalent Conductances of Aqueous HANas a Function of Concentration for Three Temperatures;

-12.2 0 C, 20.0 C, and 40.0 C ..................................... 17

4 Viscosity of Water and Aqueous HAN as a Function of j "

Concentration at 20 C ........................................... 20-1

5 Specific Conductances of 11 M HAN as a Function ofTemperat ure ..................................................... 23 P:"

6 Specific Conductance of LGP 1845 as a Function ofTemp=rature...................................................... 24

7 Specific Conductance of LGP 1846 as a Function ofTempe rature ..................................................... 25

8 Polynomial Coefficients Used for the Best Fit of theTemprature Dependent Conductance Data for 11 M HAN,LGP 1845, and LGP 1846 .......................................... 25

7.

.'.

7

- 4 ' - , =.-V ~ ~ ~ ~ ~ ~ . .. - "' .o "% "" J" .,1, . P"%.:! '

I. INTRODUCTION

Candidate liquid gun propellants generally fall into the category ofconcentrated aqueous salt solutions. The most promising candidate containshydroxylammonium nitrate (HAN) and triethanol ammonium nitrate (TEAN). In aneffort to enlarge the data base for these solutions, measurements of the

electrical conductance were performed. These measurements can be of greatpractical value in the design of electrically initiated liquid propellantcombustion systems; moreover, the variation of the electrical conductance withparameters such as concentration, temperature, and solvent can provideinformation about the fundamental behavior of these materials. Definitions ofelectrical conductance and a simple, almost universal, a.c. circuit used in

making conductivity measurements were introduced in a prior report.1 Theimportant parameters to be considered in producing a proper conductivity celldesign were also discussed in detail. Some initial data on the conductance ofaqueous HAN as a function of concentration were also presented.

This report contains data on the conductance-concentration dependence of

aqueous HAN and the conductance-temperature dependence of aqueous HAN and twoliquid gun propellants, LGP 1845 and LGP 1846. Both LGP 1845 and LGP 1846

-. consist of mixtures of aqueous HAN and TEAN. In addition, the report begins

with a review of the historical development of the conductance theory ofelectrolytes. This review is included to aid the reader not familiar with thedetails of physical chemistry. Ion-pairing and conductance equations aredeveloped in this review and are subsequently used in the interpretation of

the data.

II. EARLY WORK

An electrolyte is a solute, which upon dissolution into a solventproduces a solution which conducts current. Whether the electrolyte is

considered as being strong or weak depends upon its degree of dissociation.Strong electrolytes are almost completely dissociated. In practice,conductance measurements involve very simple circuits. The properties ofconductance have been studied for over 100 years. One of the early

descriptions of electrical conductance came from the works of Arrhenius2 andOstwald.3 The dissociation equilibrium is written as

c +

AB+ A +B (1)

where AB is the undissociated molecule, and Kc is the equilibrium constant.Application of the law of mass action yields

[A+][B] =K (2)lAB] c

where the brackets denote the equilibrium concentrations of the enclosed

species. It follows that

[A+] [B-] = c y (3)

*..9

where c is the concentration of solute and y is the fraction of ions free tocarry current. Substitution of Eq. (3) into Eq. (2) results in the followingexpression

2 2c -Y Kc (4)

It was hypothesized that

T A (5)

A0

where A is the equivalent conductance of the solution and A is the equivalent

conductance at infinite dilution. Substitution of Eq. (5) into Eq. (4), with--. some rearranging of terms, produces the Ostwald dilution law for conductance;

1 i CA (6)

A A0 K A 2c o

This expression explained the electrical conductance of weak electrolyteswell, but was inadequate for describing the electrical conductance of strongelectrolytes. The reason for this being that ionic crystals are made upcompletely of positive and negative ions arranged in a periodic lattice, henceno dissociation of neutral molecules takes place. However, experimentalconductance data showed that the strong electrolytes produce some structure insolution which is non-conducting. From Eq. (6) a plot of I/A should be linearin concentration. This held true for some electrolytes, but certainly notall. During this time Kohlrausch 4 had developed a new technique for measuringthe conductivity; the use of alternating current. He made many detailedmeasurements of the conductance of electrolytes, and obtained an empiricalexpression to describe the behavior of the conductance of dilute solutions asa function of concentration. This expression

0 - Dc 12 (7)"A 0

was called the Kohlrausch square root law and gives a different concentrationdependence of the conductance than the Ostwald dilution law. At this pointthere was a dilemma. The prominence of Arrhenius and Ostwald made Eq. (6) thefavored expression. To resolve this concentration dependence question, ittook the development of an interionic attraction theory. Up to then, noconsideration of the ions influencing each other was taken into account.Nonetheless, Eq. (6) described fairly well the behavior of dilute solutions of

- weak electrolytes in water and of strong electrolytes in solvents of lowdielectric constant.

, , .

a-. ..

10

* A A*~.*.*' ~ A! . m !, t r k",%' *

III. IONIC INTERACTIONS

It was recognized that ionic interactions must be incorporated into thetheory to describe the variation in conductivity with concentration.Considerable work was expended in an attempt to express the electrostaticpotential as a sum over all pairs of ions, where each ion is considered as a

-.- discrete site of charge. This approach led to infinit sums and non-convergence. Instead of this method, Debye and Huckel considered all of theions, except a reference ion at the origin replaced by a continuous space

charge whose density is a function of distance from the origin. The model asV '. shown in Figure 1 is then a central ion of charge +e surrounded by an ion

atmosphere of charge -e. This ion atmosphere may be envisioned as a charged

spherical shell located at a distance a + 1/k I from the center of the ion.The calculation is performed by combining Poisson's equation of electrostatic

theory with Boltzmann's distribution law. The end result is an expression forthe electric potential ip of the form

-k rAe 1,.- = ,(8)r

r where A and k, are physical constants which are completely determined from the

boundary conditions and known physical properties of the electrolyte. Thiswork was a major breakthrough, and equations for various transport properties

were derived shortly thereafter. A more complete mathematical discussion of

Z'.. the Debye and Huckel theory can be found in many texts; see for example Harnedand Owen. 6 The theory of Debye and Huckel does have limits of application for

several reasons. A point charge model is used which must necessarily fail atclose range due to the finite size of the ions. In addition, this range is

larger when considering asymmetrical ions. In the derivation of an analyticexpression for the electric potential, an exponential is expanded and only twoterms retained. The necessary condition for neglecting the rest of the seriesis that ZeX<<kT, where Z, k, and T are the ion charge multiplicity,Boltzmann's constant, and the absolute temperature, respectively. Physicallythis means that the theory will break down more easily for multivalent ions,and values of $ must be kept small by large separation of ions (dilute

solutions).

The transport property of concern here is the electrical conductance, A.

One of the first analytic expressions which used the electric potential ofDebye and Huckel appeared in the work of Onsager. 7 Two main effects wereconsidered in the interaction of the ions with an external field. First, an

electrophoretic effect arises from the interaction of the spherical shell ion

atmosphere with an external electric field. This field causes the shell andsolvent molecules to move in one direction, while the central reference ionmoves in the opposite direction, similar to swimming upstream. The othereffect is the relaxation effect. When the external field is applied, the ions

move and if the response were instantaneous then spherical symmetry would be

preserved. However, frictional forces cause a time lag and an asymmetry

arises. This asymmetry induces an internal field that opposes the externalfield and lowers the conductance. In light of these effects, Onsagerdeveloped the resultant expression

A,

%-..4%

A = A - (1 + B)c/2 (9)0 0

where a and 6 are physical constants that are completely determined from thephysical properties of the electrolyte. Here the aA c term arises from therelaxation effect, and the Bc/2 term is due to the electrophoretic effect.Onsager's equation is not strictly an equation for the conductance, but ratherthe equation for the tangent to the conductance curve in the limit of zeroconcentration. This result, and an earlier approximate result obtained byDebye and Huckel, showed that the equivalent conductance at low concentrationis proportional to the square root of the concentration. These theoreticalresults were in exact agreement with the empirical square root law determinedby Kohlrausch.

/< /;ii ,-e N

l:,

Figure 1. Picture of Ion Model for the Debye-Htickel Theory

A subsequent major step in the improvement of the equation forconductance at higher concentrations was attributed to Falkenhagen, et al. 8

They included the finite size of ions by not approximating the Debye-Hu'ckelexpression Eq. (8) for the electric potential. Here the physical constant Acontains a term

k1ael+k1 a1

which is only negligible at low concentrations. Falkenhagen, et al., retained. this term in calculating the relaxation effect. The resulting expression for' the conductance takes the form

12

S . . . . . . .- - - - -..- ,,,, . -. .-. . - o- . 'i ,. .- . ,, -. . - , ', ." - . '- , - / . . .: • .5..

1' 1/2 1/2FA tA c (10)

0, ' 1/2- I i /2(1+Bac 1 + Bac

where a and S are analogous to the constants of Onsager's limiting result.These parameters are conveniently expressed as

8.20xi0 5 82.5 50.29IeT 3/2 ' o = 1/2 3 and B = 1/2. (cT) n°(CT) (CT)11

0

where E and n are the dielectric constant and viscosity of the solvent,- .'[ respectively. The distance a used here is in units of centimeters and a =

a/10 8 . The term

exp (0.2929 k a) -1" F=F-="0.2929 k1a

is more conveniently represented by

F = e - where x = 0.2929 Bac1/2x

Equation (10) has a much larger applicable concentration range. However,

at concentrations exceeding several molar, certain salt solutions showsubstantial deviations. It has been found that these deviations at highconcentrations could be minimized by multiplying Eq. (10) by a relative

fluidity factor (n°/), where n is the viscosity of the solution. Equation(10) then becomes the well known Wishaw-Stokes9 equation. Although thisviscosity correction seems to work well, an assessment of the validity of thisfactor is complicated. A qualitative explanation of this correction is asfollows. The bulk viscosity is the force required to move layers of solution

with respect to each other. These shear forces are long range Coulomb forcesand short range ion-water forces. As a general rule, strongly hydrated ionscause large increases in viscosity, while unhydrated ions do not. The Coulombforces between ions have already been taken into account in the conductivityequation, thus it seems that only the short range forces have been neglected.Therefore, the viscosity should not be the bulk viscosity, but only a fractionof it. The justification for using the bulk viscosity is that the short range

forces dominate in the concentrated region, and depend approximately linearlyon the concentration.

The present state of the conductance theory for unassociated electrolytesis represented by Eqs. (9) and (10). The model from which these equations arederived fails at high concentration. However, no theory has been successfulin the description of the conductance behavior of concentrated solutions. Ithas been suggested1 0 that this description should properly start from a theoryof fused salts, where the distribution function is a periodic and dampedradial function. This function must approach the Debye-Huckel function in thelimit of low concentration.

, 13

IV. ION-PAIRING

Up to this point, we have only discussed unassociated electrolytes;however, for the cases under consideration, namely nitrate salts, it ispossible that ion pair formation occurs in regions of highest concentration.

For the present purpose, ion association is divided into two generalclasses. In the first class, the solid molecules do not completely dissociateinto ions when dissolved. This is a property of weak electrolytes. In thesecond class, i.e., strong electrolytes, the jolid phase ions exist in theform of a periodic lattice structure, and upon dissolution, become mobile.These ions in solution can then form some aggregate structure, where the net

charge on the structure is zero, thus giving no contribution to theconductance. The simplest structure of this type is an ion-pair, which is theassociation that is of concern for the solutions studied here. There is adistinct difference in the non-conducting structures of these two classes:the undissociated molecule is a number of atoms held together by electronicbonds, whereas the ion-pair is held together entirely by electrostatic Coulombforces, where neither the cation nor the anion lose their identity.

Early data clearly showed that some strong electrolytes must producestructures in solution which are non-conducting. In 1926, Bjerrum proposeda criteria for the formation of ion-pairs, which essentially equates thethermal energy with the electrostatic energy of two oppositely charged ions.From this, a critical distance b can be obtained

b = Z ( 1)

,,.-..2EkT

where for distances equal to or smaller than b, the ions are consideredpaired. This is a simple approximation of conditions necessary for ionpairing. Nevertheless, it is instructive in showing the dependence of ionpairing on the various physical properties. It is obvious that multivalentions have a greater tendency to ion pair. It is also evident from Eq. (11)that a decrease in the dielectric constant will increase ion-pair formation.Moreover it appears on the surface that decreasing the temperature increases

%" ion-pairing, however, the dielectric constant is also temperature dependent tothe point where increasing the temperature slightly favors ion pairing. Formonovalent ions in water at room temperature, the critical distance b is3.574. It is of interest to calculate critical distances for monovalent ionsas a function of temperature and dielectric constant, and then compare thesecritical distances with ionic separations which are predominantly a functionof concentration. Tables I and 2 contain these comparisons. The dielectricconstant was changed by using water and methanol as a solvent. Values for theionic separation were obtained from an approximate empirical relationship formonovalent ions in solution, 9.4 M-1 1 3 A. Here M is the concentration inmoles per liter. For methanol, it is seen that the critical radius is overtwice as large as for solvent water. Moreover, the ionic separation valuesare such that one would expect some ion-pairing for methanol and not forwater. Further discussion of ion-pairing in this context is given with theresults for the conductance of HAN in water-methanol solvent mixtures.

14

-- I U. %. W T - 71 1v _T:

Table 1. Critical Distance for Monovalent Electrolyte Ion-Pairing at

Various Temperatures and Dielectric Constants

Dielectric Critical Distance Dielectric Critical Distance

Temp. Constant, H 20 Solvent, H 20 ConFt, CH3OH Solvent, CH3 OH°C A A

-50 .... 49.5 7.7-25 .... 43.5 7.90 88 3.45 37.5 8.1

+25 78 3.57 32.0 8.7

Table 2. Ionic Separations for Monovalent Electrolyte Solutions atVarious Concentrations

Concentration Ionic SeparationM 9.4M -1 / 3A

6 5.179 4.52

11 4.2313 4.0015 3.81

V. TEMPERATURE

Another important variable that deserves comment is the large temperaturedependence of the conductance. There is nearly a five or six fold increase inthe conductivity of a strong electrolyte when increasing the temperature from

.r' 0 to 100°C. This increase in conductance is due, at least in part, to thedecrease in the viscosity of water. From Walden's Rule, An=const, where r isthe viscosity, it is observed that this product varies at most by 30% as afunction of temperature. This suggests that viscous forces are responsiblefor most of the resistance to the motion of ions in water.

.. A majority of the conductance data have been reported at a temperature of

25°C, thus, Campbell, et al.,1 2 have used the empirical relationship

,=At 2

At- = 1 + a(t-25) + b(t-25) 2 +... (13)A2 50

to fit the temperature dependence of the conductance for strong electrolytes.Here t is the temperature in °C and a and b are empirical constants. A formof Eq. (13) will be applied later to the temperature dependent data reportedhere.

15

.. .7 , .A

7

VI. EXPERIMENT

The measurement circuit and conductivity cell used to obtain theexperimental data were very similar to that described in the first report. 1

-* The only difference is that the U-tube Pyrex cell was slightly shorter, givinga cell constant of 137.6 cm- I . The cell constant was checked with both sodiumchloride and potassium chloride solutions. Current flowing through thesolutions of interest was kept well below one milliampere. An audio frequencyalternating current of I kHz was used for all of the data reported here, andall measurements were independent of frequency over the 500 Hz to 10 kHzrange. For the temperature dependent studies, the U-tube conductivity cellwas almost completely immersed in a Dewar filled with methanol or water. Thetemperature of conductivity cell was controlled manually with heating elements

and cooling with dry ice or ice while being continuously stirred. Thetemperature was monitored with a digital readout platinum resistancethermometer, which gave temperatures to the nearest 0.1°F. The temperaturecontrol was *0.1°F.

Reagent or research grade chemicals and distilled water were used forthis study. The preparation of 13 M HAN solutions, which were used as thestarting point for the various aqueous HAN solutions, were prepared byconcentrating high purity dilute solutions obtained from Southwest AnalyticalChemicals, Inc., Austin, TX. The liquid gun propellants LGP 1845 and LGP1846, are made of mixtures of HAN, TEkN and H2 0. LGP 1845 contains (weightpercent) 63.2' HAN, 20 TEAN, and 16.81 H2 0. LGP 1846 contains (weightpercent) 60.8V HAN, 19.27 TEAN, and 201 H 20.

VII. RESULTS AND DISCUSSION

The specific conductance and equivalent conductance of HAN as a function* of concentration in water for three temperatures, are shown on Figures 2 and

3, respectively. The data is tabulated in Table 3. Both the concentrationand temperature dependence of the conductance is typical of monovalent saltsdissolved in water. As shown in the first report, the conductance of NaNO3as a function of concentration in water is very similar to that of HAN. Itwas observed that the specific conductance of HAN starts decreasing atconcentrations greater than about 7 M at 200C, whereas most other saltssaturate in this concentration region. However, if these salt solutions areheated to increase the solubility limits, then the bending over phenomenon ofthe specific conductance is also observed. This decrease in the conductanceas more ions are added suggests that the mobility of the ions is substantiallydiminished and/or the ions form non-conducting species. Most of the

experimental data has been obtained at 20°C, so it is this data of Figure 3that we will attempt to fit with Eq. (10), the Wishaw-Stokes equation. Itshould be noted that most of these concentrations severely push the limits ofvalidity of this equation for concentration maximums; furthermore, not havingan experimentally determined value for Ao causes questions at the very lowconcentrations.

16

_.~~~" .. .. . -2-k . ..- ,*A.. .. .

SPECIFIC CONDUCTANCE OF HANAT -12.2 C, 20.0 C, AND 40.0 0C

0.28-10.26

" 0.24

c) 0.22-

0.20 )

LJ U.18C-) 1EENz 0.16 a .X N .

0}''"(- .1]4 - 20.0 X 1.

co:

C.

'. C C.:.

C 2 4 6 e 10 12

C UN.. NT IM- \ (MOLES/LITER)

Figure 2. Specific Conductance of HAN as a Function of Concentration

in H 20 at -12, 20, and 40C

Table 3. The Specific and Equivalent Conductances of Aqueous HAN as aFunction of Concentration for Three Temperatures; -12.2°C,

20.0°C, and 40.0°C

Concentration Sp. Cond. Eq. Cond. Sp. Cond. Eq. Cond. Sp. Cond. Eq. Cond.

M 1 cm-I cm2 R-1 -I C 1 i Q-1 Q c 1m- cm2 f

T = -12.2°C T = 20.0°C T = 40.0 °

0.1 ---- .00924 92.4 .0140 140

* 0.5 .0191 38.3 .0390 78.1 .0555 ill1.0 .0350 35.0 .0693 69.3 .0970 97.0

-. 3.0 .0825 27.5 .153 51.0 .206 68.6

5.0 .101 20.2 .189 37.8 .255 51.07.0 .0998 14.2 .194 27.7 .262 37.4

d' 9.0 .0802 8.91 .176 19.6 .244 27.1., 11.0 .0608 5.53 .144 13.1 .205 18.7

13.0 .0370 2.85 .105 8.08 .155 11.9

17

-:. EOUIVALENT CONDUCTANCE OF HANFT -12.2 C, 20.0 C, RND 40.0 0C

LEENrc 121

4--12. X 1.C-- c 2C.C X 1,0_- 40.0 X 1.0

CCD E-

L2

-. 3 o- C . "-I I

C 2 i E e 1C 12pC:\- 7KQ (CE/ATHz.)

Fizure 3. Equivalent Conductance of BAN as a Function of Concentrationat -12, 20, and 400 C

Normally A is determined from an extrapolation of extremely lowconcentration data using a form of Eq. (7). In our experiments only one cellwas used, which was tailored for accurate measurements of concentratedsolutions. This design does not work well for dilute solutions; thus, A hasbeen roughly estimated by analogy with other limiting conductances of sa~tsolutions, A can be written as Ao = Ao A, where A+ and A are the

souios 0. 0+ A0 0 0limiting equivalent conductances of the constituent cation and anion. For' .'-" NOR, Ao is 64 at 20C, however, a value for NH3OH has not been reported. WeN03, xo 3 ha o enrpre.W

could say it is similar to NH+ which is 65, or choose an ion of similarmolecular weight, say CH3NH3 , which has a limiting equivalent conductance ofabout 53 at 20°C. From these considerations, a reasonable value for A foraqueous PAN solutions is 64 + (5916) = 123 * 6 at 200C. 0

For an aqueous monovalent electrolyte at 20°C, Eq. (10) becomes

W1/2 1/253.48c 1 0.2269c F

0 1+0.3276ac ] 10.3276,cl/2.

xwhere c is expressed in moles per liter, a in angstroms and F = 1 where xis equal to 0.0959acl / 2. With the data being A and c, a least squaresanalysis of this equation was applied using A o and a as adjustableparameters. The resulting fit is shown as a dashed line on Figure 4. The fit

187:'

.. . . 1.- 7*1 77v *

is not good and the convergence values are physically unrealistic.Although A did not change appreciably from the estimated value, settling inat a value0of 122, the best fit occurred with an a value of 0.87A. This valueof the ion size parameter is too small since the estimated radius of the NO3anion is 1.8A.

FIT OF EOUIVRLENT CONDUCTANCE O7TO THE NiSH9W-STOKES EOURTION

100

CDC-80

(.2

-:

C~2

C% '

j, .,C. 2 41 " E. Z 1

CC

- .2

i-'-7

Figure 4. Fit of Equivalent Conductance at 20*C With Wishaw-Stokes

Equation, Data C , Fit --- Without Viscosity Correction,Fit- With Viscosity Correction

It was thought that a better fit might occur if we included a relativefluidity factor in the equation. However, there was no published data for the

4" vicosity of aqueous HAN solutions, so a Brookfield viscometer was obtained andthe viscosity of aqueous HAN measured as a function of concentration at20°C. The results are tabulated in Table 4. With the inclusion of the

. *. relative fluidity factor, the least squares analysis gives the solid lineshown on Figure 4. The best fit occurs with Ao = 112.3 and a = 3.13A. The a

-'- value is still a bit small, most monovalent aqueous salts fit to an a valuebetween 4-5A, however it is much more realistic than before. The limiting

.. equivalent conductance has changed by about 10% from our estimated value.This fit is better than the fit without the fluidity correction, but notgreat. Since Eq. (10) has been derived with approximations that are onlyvalid for dilute solution conditions, and then a semi-empirical modification(n°/n) applied to extend the concentration range, a precise fit is not to be

expected.

.4.

19

.5ILA

Criteria for forming ion-pairs have been discussed earlier. From TablesI and 2 it is seen that under simple approximations, smaller dielectricconstants favor ion-pairing. The numbers of Tables I and 2 suggest that ion-pairing is much more likely to occur in methanol than in water. To test thispossibility, we measured the equivalent conductance of 13 M aqueous HAN mixedwith various amounts of methanol. The concentration scale for the 13 M HAN-methanol mixtures is approximate since 13 M HAN was treated as pure HAN, thishowever, does not affect the qualitative behavior in which we are interested.The equivalent conductance of HAN in water and 13 M HAN in methanol as afunction of concentration at 20 and 40°C is plotted in Figure 5. Asignificant difference is observed; for most of the concentration region theequivalent conductance for the methanol solvent is much lower. This behavioris also observed for AgNO3 solutions in solvents of different dielectricconstant. The smaller the dielectric constant, the more pronounced isljhedecrease in the conductance. From these results and also Raman spectra, I

ion-pairs are presumed to be present in aqueous HAN-methanol solutions. Weplan also to investigate the Raman spectra of HAN dissolved in differentsolvents. Thus far, the conductance results are qualitatively analogous tothose found in AgNO 3 . This indicates that ion-pairing is occurring whenmethanol is used as the solvent. Ion-pairing is probably minimal in aqueousHAN solutions.

Table 4. Viscosity of Water and Aqueous HAN as a Function ofConcentration at 20°C. The Experimental Results are Obtained With a

Brookfield Viscometer Calibrated With Distilled Water, and a Brookfield

Standard Liquid of Known Viscosity

Species Viscosity (n) Viscosity CorrectionCentipoise Factor n°/n, no=1.002

12 0 1.002 1.000.1 M HAN 1.02 0.980.5 M 1.06 0.95

- 1.0 M 1.06 0.953.0 M 1.23 0.815.0 M 1.52 0.667.0 M 2.14 0.479.0 M 3.05 0.3311.0 M 4.80 0.2113.0 M 7.11 0.14

Finally the specific conductance of aqueous HAN and two candidate gun%- propellants, LGP 1845 and LGP 1846, has been measured as a function of

temperature over the range from -60 to +60°C. The data are plotted in Figure6 and tabulated in Tables 5, 6, and 7. Polynomial fits of this temperaturedata are also shown on Figure 6. Instead of applying the empiricalrelationship, Eq. (13), suited for 25°C conductance data, we chose a moregeneral form which is

V-0

20

%. % .

..V..

• 2 3a 0 + a+2t + a3t

and applied a least squares analysis to the data. The resulting fits are

quite good, and the best values of the coefficients are listed in Table 8.Again these three solutions studied have temperature dependences very similarto other common aqueous salt solutions.

ED- ' 'Qu'I K C2INLC7:,, OF HAN-H20 FINDr b -eH L CTI\S . T 20 3\Z 4c C

S160.

. ..._ '\ c- 22.S x i.-

7 1 , t. S :, .

\11

Figure 5. Equivalent Conductance of HAN as a Function of Concentration

in H2 0 and in H 20-CH 3OH Mixtures at 20 and 40°C

VIII. SUMMARY

A brief historical review of the development of conductance theory has

been reported and applied to the concentration dependent conductance datameasured for aqueous HAN solutions. Specific conductance a- a function oftemperature for 11 M HAN, LGP 1845, and LGP 1846 has been measured and

subsequently analyzed in terms of a polynomial equation. Two different

solvents, water and methanol, have been used in the studies of HAN to assess

the importance of ion-pairing. These data indicate that ion-pairing becomesmore important with decreasing dielectric constant; a result consistent with

the Bjerrum criteria and similar to previous results for other monovalent,alts.

21

•~ ,q

In general, the solutions studied here behave like most common monovalent-.; -salt solutions, with respect to the temperature and concentration dependence

of the conductance. No evidence has been founid for substantial ion-pairingfor these aqueous salts, however, should these salts be dissolved in solventsof lower dielectric constant, ion-pairing will increase.

c FE. IFIC CONDUCTFNCE OF 11iM-NLJ 1846

.} .., .. ,-- O .M E -

.- 0.24j*U

I 0.22-

C X

""-- "-' C.2-U C. _7 cC- 1 .% X 1 .9z,, -" I :-: . X 1.0

% U3" ',. 1I _j I

CD

" .- - 8 3 - 4 : - 2 : £ 2 4".-'..:t",rcRTURE fC)

~Figure 6. Specific Conductance of 11 M HAN, LGP 1845, and LGP 1846 asiiiiil a Function of Temperature. Data areQ- , 0, t5. Solid Lines

. are Polynomial Fits

'C

;2.,2

* -2 22

* C 2, 4.'.

..

,. ,:,,...,. ..v,.. .,,. ..:,.,. :.; .::,,?.:.:.:..-..? : , . . .: -i.:.. .-.- :.:.. . -i::--".. . ".: ..T. .. ,. . .::. .i . . ::.C )>i>?Fiue6 pcfcCnutneo 1MHN G 85 n G 86a

Table 5. Specific Conductance of 11 M RAN as a Function of Temperature

Temperature Specific Condyctance0C cm

-59.9 9.00 x 10 - 4

-59.0 1.03 x 10 - 3

-57.9 1.26 x 10 -

-54.4 1.91 x lo- 3

-52.9 2.41 x 103

-51.0 2.91 x 10 3

-49.2 3.36 x 10 3

-46.6 4.51 x - 3

-43.3 6.27 x 10 - 3

-40.7 8.07 x 10-37.7 1.05 x 10-2-34.2 1.38 x 10 - 2

-28.4 2.07 x 1o-2

-24.7 2.62 x 10-2-20.9 3.21 x 10-2-17.3 3.77 x 10-14.6 4.38 x 102-13.0 4.62 x 10 - 2

-10.0 5.26 x 10 - 2

-7.3 5.86 x 10-2

-4.1 6.58 x 10 - 2

-0.6 7.56 x 102

3.6 8.48 x 10 - 2

4.9 8.83 x 10- 2

13.8 1.19 x 10-16.6 1.28 x 10- 1

18.0 1.32 x 10-

20.6 1.40 x 10-121.4 1.44 x 1023.2 1.50 x 10-

24.3 1.54 x 1024.7 1.55 x 10- 1

26.4 1.61 x 10- 127.8 1.65 x 10-

30.7 1.75 x 10-

32.5 1.81 x 10 I

33.8 1.85 x 10-1

35.2 1.89 x 10-136.9 1.95 x 10-

39.2 2.03 x 10--141.6 2.09 x I043.5 2.16 x 10- 1

-146.0 2.25 x 1049.0 2.35 x 10-53.0 2.48 x 10-1

53.8 2.50 x 10-1

23

Table 6. Specific Conductance of LGP 1845 as a Function of Temperature

Temnpe:ature Specific Conductance Temperature Specific Conductance-C cm-1 °C 1 cm-1

-47.0 8.20 x 10- 4 5.2 3.98 x 10-2-44.9 9.54 x 10 - 4 6.3 4.15 x 10-2-42.5 1.42 x 10- 3 7.6 4.33 x 10 - 2

-40.9 1.73 x 10 - 3 8.8 4.56 x 10 - 2

-38.6 2.16 x 10 - 3 10.2 4.77 x 10 - 2

-35.9 2.98 x 10 - 3 11.5 4.98 x 10-2

-34.2 3.53 x lo- 3 12.7 5.17 x 10-2-30.3 5.03 x 10- 3 13.8 5.37 x 10 - 2

-28.7 5.76 x 10-3 14.9 5.57 x 10- 2

-26.9 6.67 x 10- 3 15.9 5.75 x 10 - 2

-25.5 7.41 x 10- 3 17.1 5.96 x 10-2-23.7 8.69 x 10 - 3 18.3 6.16 x 10- 2

-22.8 9.29 x 10- 3 19.4 6.37 x 10-2-21.8 9.97 x 10 - 3 20.5 6.55 x 10- 2

-21.2 1.04 x 10- 2 23.9 7.46 x 10 - 2

-29.7 1.08 x 10 - 2 31.8 9.06 x 10 - 2

-20.1 1.13 x 10 - 2 34.6 9.63 x 10- 2

-19.5 1.17 x 10-2 36.5 1.00 x 10- 12-.6 1.2" x 10- 2 37.6 1.03 x 10-1

-17.8 131 x 10- 2 39.2 1.07 x 10- 1"''-14.8 1.57 x 10 - 2 41.0 1.11 x 10 - I

-14.0 1.64 x 10- 2 43.0 1.15 x 10-1-12.R 1.77 x 10- 2 44.6 1.19 x 10-1-11.4 1.90 x 10- 2 45.0 1.20 x 10- 1

-10.0 2.06 x 10-2 46.2 1.22 x 10- 1-3.3 2.23 x 10- 2 47.9 1.26 x 10-1"-7. 2.3 x 0 49.7 1.30 x 10-5.9 2.50 x 102 51.8 1.35 x 10-1-4.7 2.64 x 10 - 2 54.3 1.41 x 10-1-3.7 2.77 x 10' 55.6 1.44 x 10-1

" -2.5 2.91 x 10 - 2 56.8 1.47 x 10- 1-0.3 3.14 x 10- 2 59.4 1.53 x 10 - 10.9 3.40 x 10 - 2

2.7 3.62 x 10- 2

4.1 3.82 x 10 - 2

eOq

-..

24

.... .. ......-.....................-.................-- ,

- w 4 - -C .- . 0- 4

Table 7. Specific Conductance of LGP 1846 as a Function of Temperature

Temperature Specific Conductance Temperature Specific Conductance°___Q- cm 1 °C - cm-

-60.1 1.96 x 10- 4 2.7 4.45 x 10- 2

-57.9 2.72 x 10-4 5.9 4.95 x 10- 2

-55.6 3.52 x 10- 4 8.3 5.37 x 10- 2

-52.9 5.27 x 10- 4 10.7 6.03 x 10- 2

-50.2 8.30 x 10- 12.9 6.19 x 10-2

-47.7 1.17 x 10- 3 15.1 6.59 x 10-2

-44.5 1.81 x 10- 3 17.4 7.07 x 10-

-41.1 2.67 x 10- 3 19.5 7.47 x 10- 2

-38.6 4.22 x 10- 3 21.8 7.97 x lo- 2

-36.1 5.14 x 10- 3 24.1 8.44 x 10- 2

-33.2 6.32 x 10- 3 26.2 8.94 x 10- 2

-29.9 8.19 x 10- 3 28.4 9.41 x 10- 2

-27.2 9.94 x 10- 3 30.6 9.79 x 10-2

-24.7 1.18 x 10- 2 32.8 1.03 x 10-1

-22.1 1.40 x 10- 2 35.2 1.08 x 10- 1

-19.1 1.67 x 10-2 36.9 1.12 x 10-I

-15.S 2.03 x 10-2 39.0 1.17 x 101

-13.1 2.31 x 10-2 40.9 1.22 x 10-I

-10.3 2.64 x 0- 2 42.6 1.25 x 10- 1

-7.0 3.08 x 10 - 2 44.5 1.29 x 10_I

-3.9 3.46 x lo- 2 46.7 1.36 x 10 -1

-0.6 3.94 x 10- 2 48.9 1.40 x 10-1

51.1 1.46 x 10-

53.4 1.51 x 10-1

55.6 1.57 x 10-1

57.8 1.65 x 10-1

60.0 1.71 x 10-1

62.2 1.77 x 10-1

Table 8. Polynomial Coefficients Used for the Best Fit of the TemperatureDependent Conductance Data for 11 M RAN, LGP 1845, and LGP 1846

a a1 ' a3 .-1 01 -o- cm1-12 -2 1 -[ -3

Species S cm Cm - _____________

11 M HAN 3.282xi0 - 2 1.385xi0 - 3 1.362xi0 - 5 -4.143x10- 8

LGP 1845 7.915x0 -2 2.670xi0 3 1.651x0 -5 -1.189xi0 - 7

LGP 1846 4.099xi0 - 2 1.495x0 - 3 1.244x0 - 5 2.418xi0 8

25

.4e

REFERENCES

1. J•A. Vanderhoff and S.W. Bunte, "Conductance Measurements ofHvdroxvlammonium, Nitrate," BRL Memorandum Report, in press.

2. S. Arrhenius, "Uber die Dissociation der in Wasser gelotsen Stoffe," Z.- ' Physik. Chem., Vol. 1, p. 631, 1887.

3. W. Ostwald, "Uber die Dissociations theorie der Elektrolyte," Z. Physik,Chem., Vol. 2, p. 270, 1888.

4. F. Kohlrausch and L. Holborn, "Das Leitvermogen der Elektrolyte,"

Teubner, Leipzig, 1916.

5. P. Debve and E. Huckel, "The Theory of Electrolytes. I. Lowering ofFreezing Point and Related Phenomena," Phyzik. Z., Vol. 24, p. 185, 1923.

6. H.S. Harned and B.B. Owen, The Physical Chemistry of ElectrolyticSolutions, 3rd Ed., Reinhold Publishing Corp., New York, NY, 1958.

7. L. Onsager, "The Theory of Electrolytes. II.," Physik. Z., Vol. 28,p. 277, 1927.

8. H. Falkenhagen, M. Leist, and G. Kelbg, "Theory of the Conductivity ofStrong, Nonassociative Electrolytes at Higher Concentrations," AnnalsPhysik, Vol. 6(11), p. 51, 1952.

9. B.F. Wishaw and R.H. Stokes, "The Diffusion Coefficients and Conductances

of Some Concentrated Electrolyte Solutions at 25°C," J. Am. Chem. Soc.,Vol. 76, p. 2065, 1954.

10. R.'I. uoss and F. Accascina, Electrolytic Conductance, IntersciencePublishers, Inc., New York, NY, 1959.

11. N.K. Bjerrum, Danske Vidensk. Selsk., Vol. 7, 1926, No. 9, "SelectedPapers," p. 108, Einar Muuksgaard, Copenhagen, 1949.

12. A.N. Campbell, A.P. Gray, and E.M. Kartzmark, "Conductances, Densities,and Fluidities of Solutions of Silver Nitrate and Ammonium Nitrate at35°C," Can. J. Chem., Vol. 31, p. 617, 1953.

13. W.E. Wentworth, "Rigorous Least Squares Adjustment: Application to SomeNon-Linear Equati-ns, I," J. Chem. Ed., Vol. 42, No. 2, p. 96, 1965.

14. G.J. J'nz, "Studies of Ionic Association and Solution with Raman LaserSpectroscopy," Electroanalytical Chemistry and Interfacial

Electrochemistry, Vol. 29, p. 107, 1971.

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2 Purdue University1 University of Minnesota School of Mechanical

Dept. of Mechanical EngineeringEngineering ATTN: N.M. Laurendeau

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I Rensselaer Polytechnic Inst.

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