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AFML-TR-65-246SPART II

THERMOGRAVIMETRY OFPHENOL-FORMALDEHYDE POLYCONDENSATES

PART II -EMPIRICAL KINETIC PARAMETERS

R. IV. FARMER

TECHNICAL REPORT AFML-TR-65-246, PART II

MARCH 1967

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AIR FORCE MATERIALS LABORATORYRESEARCH AND TECHNOLOGY DIVISION

AIR FORCE SYSTEMS COMMANDWRIGHT-PATTERSON AIR FORCE BASE, OHIO

107106711" Op ( .",,f I r! p) JUN 9 19672.!

73

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500- April 1967 - C0192 - 29-698

AFML-TR-65-246PART 11

THERMOGRAVIMETRY OFPHENOL-FORMALDEHYDE POLYCONDENSATEI!

PART II- EMPIRICAL KINETIC PARAMETERS

R. W. FARMER

Distribution of this document is unlimited.

k

AFML-TR-65-246

Part II

ABSTRACT

Empirical kinetic parameters for pSnol-formaldehyde polycondensate materials weresurveyed for general application to Air Force interests. The ranges of n, A, E for the empiricalkinetic "_rodel

-(dw/dt) = wn A exp' (-E/RT)

where n= 0-5, A = 2.x10-1 to 1.7x106 1/min, E = 3.7-72kcal/mole, where w normalizedweight, t =_ time, R _ gas constant, T - temperatu e. The mass spectrometry and thermo-gravimetry thermal analysis methods used both constant heating rate and isothermalapproaches.

Reexamination of data with anew computer program gave reduced variations:n = 1.56±0.07, A = 60.9+41.4, E = 10.38±1.20. The scopes of the comprehensive survey anddescriptive thermogravimetry computer analysis were: (22 constant rate + 3 isothermal) vs 6consfant rate experiments by 8 vs 3 investigators using (5 cured + 7 vitreous fiber reinforced)vs 4 cured polycondensates.

Parameter inconsistencies for the survey were partially associated with an atypicalpolycondensate, laminate andpolycondensate particle or laminate powder samples, or a reducedpressure atmosphere. Calculated parameters apparently dependent upon the two latter aspectswere not averaged with other values. Small curve-fitting and other errors potentially enhancefurther disagreement as they often gave large parameter variations.

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AFML-TR-65-246

Part i

FOREWORD

This report was prepared by the Thermally Protective Plastics and Composites Section,Plastics and Composites Branch and initiated under Ptoject No. 7340, "Nonmetallic Com-posites and Materials," Task No. 734001, "Thermally Protective Plastics and Composites. "This report was administered under the direction of the Nonmetallic Materials Division, AirForce Materials Laboratory, with Mr. R. Farmer acting as project engineer.

The contributions of Mr. G. L. Denmanin supplying samples, Mr. W. E. Huebner in assistingwith computer programs, Mr. A. Oliver for computer programming, and Mr. N. J. Olson formany candid technical criticisms are acknowledged with appreciation.

The materials described herein were not formulated for the thermal treatments reported.Results and conclusions should not be misconstrued as reflecting on t'he characteristics ofthese materials in different form or under other environmental conditions.

This report covers work conducted from May 1965 to September 1966. Manuscript releasedby the author September 1966 for publication as an RTD Technical Report.

This technical report has been reviewed and is approved.

R. G. Spain, Acting ChiefPlastics & Composites BranchNonmetallic Materials DivisionAir Force Materials Laboratory

ii

AFML-TR-65-246

Part R

TABLE OF CONTENTS

SECTION PAGE

I INTRODUCTION 1

H EMPIRICAL KINETIC PARAMETERS 2

A. EMPIRICAL MODEL 2

B. EVALUATION METHODS SURVEY 2

C. PHENOL-FORMALDEHYDE MATERIALS SURVEY 3

III EXPERIMENTAL MATERIALS AND METHODS 5

IV EMPIRICAL KINETICS COMPUTER PROGRAMS 6

A. THEORY 6

B. RESULTS 8

V TYPICAL APPLICATIONS OF EMPIRICAL KINETIC PARAMETERS 12

A. EMPIRICISM OF n, A, E 12

B. RELATIVE THERMAL STABILITY 12

C. HYPERTHERMAL ABLATION 12

D, MECHANICAL PROPERTIES 13

VI SUGGESTIONS FOR FURTHER WORK 14

APPENDIX I - GENERAL THEORY 15

APPENDIX II- COMPUTER PROGRAMS OUTLINES 17

REFERENCES 23

V

AFML-TR-.65-246

Part I1

TABLES

TABLE PAGE

I Approximate Ranges of Literature Empirical Kinetic Parametersfor Phenol-Formaldehyde Polycondensate Materials 27

II Some Literature Empirical Kinetic Parameters for Phenol-FormaldehydePolycondensate Materials 28

EII Some Literature Kinetic Methods for Constant Heating RateThermogravimetry 31

IV Experimental Materials 33

V Empirical Kinetic Parameters for a Phenol-Formaldehyde PolycondensateMolding Powder at Three Heating Rates Using Three Computer Programs 34

VI PRIM Empirical Kinetic Parameters for a Phenol-FormaldehydePolycondensate Molding Powder at Three Heating Rates 35

VII PRIM Empirical Kinetic Parameters for Pure and Glass FabricReinforced Phenol-Formaldehyde Polycondensate Powders 36

VIIl Summary of Results for Rerence 53 Phenol-Formaldehyde PolycondensateMaterials 37

IX Miscellaneous PRIM Results for Phenol-Formaldehyde PolycondensatePowders 38

X Estimated Overall Accuracy and Precision 39

XI Some Physicochemical Kinetic Relations and Mechanismis 40

XII Some Additional Literature Empirical Kinetic Parameter' for Phenol-Formaldehyde Polycondensate Materials 41

XIII Some Probative Kinetic Experimental Ranges for Polymers andReinforced Plastics 42

XIV Some Probative Kinetic Relations for Empirical Investigation 43

vi

vi

AFML-TR-65-246

Part H

ILLUSTRATIONS

FIGURE PAGE

1 Flow Diagram for the Maximum Rate Experimental Method(MAXRAX) Computer Program 44

2 Flow Diagram for the Transfer Resolution Integal Method (TRIM)Computer Program 45

3 Flow Diagram for the Parabola Resolution Integral Method(PRIM) Computer Program 46

4 Flow Diagram for the Thermogram Construction Subroutine 47

5 Thermograms for Phenol-Formaldehyde Molding Powder 48

6 PRIM Parabolic Error Plots for Phenol-FormaldehydeMolding Powder 49

7 Thermograms for Phenol-Formaldehyde Polycondensate Samples 50

8 Conversion Diagrams for (1 - wo) to w 51

9 Relationship Between the Integral Parameter K And The Active WeightFraction 52

10 Relationship Between the Terms X, p(X) and r 53

11 A Typical Temperature Distribution in Nylon Phenolic for Steady SurfaceRecession Rate 54

12 Reduced and Calculated Thermograms for CTL-91LD/Glass Fabric 55

13 Tensile Strength at 450 to Fabric Warp versus Active Weight Fractionfor CTL-91LD/Glass Fabric 56

14 Strength and Weight Retention for 100-Hour Air Aging of CTL-91LD/GlassFabric 57

15 Some Polymers for Future Study 5

vii

AFML-TR-65-246

Part II

SYMBOLS

SYMBOLSYMBOL DEFINITION UNITS

$

A empirical kinetic parameter* 1/min

c system concentration

C solid specific heat at constant pressure kcal/gm/°K

e base of natural logarithms dimensionless

E empirical kinetic parameter kcal/gm-mole

exp exponential function to the base e dimensionless

f function

AH normalized heat of reaction kcal/gm

k empirical kinetic parameter* 1/min

K integral parameter dimensionless

L thickness cm

In( ) logarithm to the-base e

1Og 0 ( ) logarithm to the base 10

m series term dimensionless

n empirical kinetic parameter dimensionless

P pressure atm

R gas constant kcal/gm-mole/%K2

S surface area cm

s ) error variance of estimate2

Sp( ) population error variance estimate

T temperature, degrees absolute* OK

TS(45°) tensile strength, 450 to fabric warp percent

w reactant (residue-free) weight fraction dimensionless

wo aggregate sample weight fraction dimensionless

x reactant (residue-free) weight gm

viii

AFML-TR-65-246Part 11

SYMBOLS (CONT'D)

SYMBOL

SYMBOL DEFINITION UNITS

z oxygen mole fraction dimensionless

a thermal diffusivity cm 2min

ale increment dimensionless

e temperature 0C

SUBSCRIPTS

SYMBOL DEFINITION

c calculated

i initial

i,j,k iteration value

I isothermal

m maximum rate, maximum value

p,q limiting value (q span)

r,s limiting value (s span)

r residue

1,2 singular value

SUPER13CRIPTS

SYMBOL DEFINITION

minimum n error

mean

(") d( )/dt

(-)T d( )/dT

ix

/

AFML-TR-65-246Part I!

FUNCTIONAL SYMBOLS

SYMBOL

SYMBOL DEFINING EQUATION UNITS

a logl 0 r(AR/ET) dimensionless

A! WTmW-nT exp (Xm) 1/min

a1 -v= kwn exp -(a1 - a 2 /L)] dimensionless

cmna

2

a 3 -v = k exp [-a 3 (1 - w)] dimensionless

b -E/(R In 10) K

c, c 2 TS(45) = c 1 exp (c 2w) dimensionless

g=a n2 + n+c dimensionless

2 2

G L(aCE/A HRL)n+l cmn+2/min n' l

g X(Woe _ w0)2 dimensionless

6pi1 p ck e +1-8 C

6q+1 q 0

p(X) xeX - dimensionlessx

q (e -9)/j+1 C Cp q

r x 2 eX p(X) dimensionless

s (e -8 9)/k + 1 00

s 2(a) S2(wo)/q dimensionless

2 2s e (b -ew/-(1/T - IT) O

so(w) g'/(q .. 2) dimensionless

s <Wo> [(W --w> 2 ]/(q- 1) dimensionless

x

AFML-TR-65-246

Part II

FUNCTIONAL SYMBOLS (CONT'D)

SYMBOLSYMBOL DEFINING EQUATION UNITS

w x/x i = w o - Wr)/(Woi Wr dimensionless

X E/RT -dimensionless

y log 10 (K/T 2 )

z l/T 110K

a A= aT 1/(min-(*K)p)

/dimensionless

SE= + T kcal/ gm-mole

kcal/gm-mole/OK

xi =

/"

AEM L-TR-65-246

Part II

COMPUTER PROGRAM DIAGRAMS

CALCULATE,

SUBSTITUTE

<DECI SIONI

READ,WRITE

SUBROUTINE

TITLE

*Different units for a symbol are noted with that symbol.

xii

AFML-TR-65-246Part II

SECTION I

INTRODUCTION

Part I of this report considered procedural variables in the constant heating rate thermo-gravimetry of phenol-formaldehyde polycondensates (Reference 17). The best sample wasan adequately cured and dried molding powder free of any postoure surface product. Powdersieve distribution, pressure or weight effects were small to 500°or 600C for runs in heliumpurging flow. Procedural interference increased thereafter to about 4 percent residual weightand 2500 near 9500. Fortunately, a change in a procedural variable magnitude gave nearlyparallel thermograms. Therefore, the residue-free thermograms were relatively free ofprocedural biasing. With this result a kinetic model based on a residue-free normalizedweight was adopted. Empirical kinetic parameters were calculated for several materialsusing two new and complimentary curve-fitting methods.

The residue-free thermograms and elemental compositions of five postcured polycondensatepowders were nearly identical from 300 to 8100 (Reference 37). The empirical kinetic modelproved representative for these experiments. Therefore it seemed reasonable that similarempirical kinetic parameters would be found for other polycondensates and fiber reinforcedpolycondensates. On this basis, a survey was made of previous constant heating rate andisothermal mass spectrometric and thermogravimetric thermal analysis studies.

The phenol-formaldehyde materials survey was disappointing in that the empirical kineticparameters were inconsistent (Table I). A systcmatic attempt was made to explain the largedifferences. First a survey was made of available curve-fitting methods for possible computerprogram use. Although no entirely satisfactory technique was found, a program was evolvedfor easy and precise curve-fitting using a dual method approach developed in Part I of thisreport.

General inspection of computer program or manual calculations for selected experimentsrevealed significant differences exceeding the normalizing ability of a residue-free basis.Troublesome aspects were reinforced laminate and polycondensate particle or laminatepowder samples, an oxidative atmosphere, reduced pressure, and unusual behavior of thesample. The data for some isothermal thermogravimetric and mass spectrometric studieswere unsatisfactory for manual calculations and were not amendable to the computer program.

Data clearly disagreeing with likely empirical kinetic parameters for a cured polyconden-sate powder or unmanageable data was rejected for this study. A computer program analysiswas then conducted for the remaining cases. This analysis involved six constant rate runs bythree investigators using four materials (Table IX). A markedly reduced spread in theempirical kinetic parameters was encouraging evidence that the simple kinetic model wasprobably valid for most curbd polycondensate powders and reasonable experimental proce-dures. Several cases of model inconsistency or significant procedural aberrations were alsodelineated as to probable causes.

Computer parameters were also found representative for seven other materials either byfurther calculations or residue-free thermogram analogy (References 4 and 37). Furtheraccepting these experiments, the survey and computer study scopes were then respectively(22 constant rate + 3 isothermal) vs 13 constant rate experiments by 8 vs 4 investigators on(5 cured + 7 reinforced) vs 11 cured polycondensate powders.

*All temperatures in 0 C unless noted as being 0 F, 0 K, or R.

/"


SECTION II

EMPIRICAL KINETIC PARAMETERS

A. EMPIRICAL MODEL.

Isothermal kinetic relations which empirically represent many physicochemical processeswere

k Aexp (-X) (2)

For a constant rate of heating '"

-WT = (Aw /f) exp(- X) (3)

B. EVALUATION METHODS SURVEY.

Numerous methods were available for extracting empirical kinetic parameters from experi-mental thermograms. Table III summarized a few examples for constant heating rate thermo-gravimetry with emphasis on thermosetting polymer studies. The approaches were categorizedinto first, one or more necessary heating rates and then residual weight, weight loss rate, or acombination of rate and weight as the major temperature (or time) dependent variable. Forexample, a rearrangement of Equations 1 and 2 gave a method using rate, weight, and animplicit value of n

log, 0 (- ;W-n) R-nE [:: + Iog10 A (4)l~gm-ww') -R In 10 T~ to

where E, A were respectively evaluated from the slope and intercept of a parametric plot of

logl 0 (- nw) versus 1/T. Other popular methods used a difference or ratio form of the above

equation, an integrated version of Equation 3 for a 1/T parametric plot, a maximum rateof weight loss theory. Frequently n could not be evaluated directly thereby requiring specialconsideration.

The precision and usage of the different methods varied considerably. Critical aspects havebeen described previously by other authors but will be briefly reviewed here. Multiple tem-perature point calculation methods had the advantage of being self-checking through visualinspection of a straight-line parametric plot. Unfortunately, such plots were often sensitive tosmall errors and thereby biased linearity judgment. This difficulty prevailed near the beginningand end of the thermogram. Measuring weight loss rate directly from the thermogram wasimprecise and tedious for rapid or slow rates. Aids as computer curve-fitting, electronicdifferentiation apparatus, optical devices, large and accurate records served to reduce errorand time. Integral weight methods, not requiring a rate input, had an advantage although it

- was usually necessary to determine n by separate means.

Multiple heating rate methods examined kinetics over a wide temperature and time spectrum.On the other hand, they required runs at different rates of heating. In addition, the calculationsproved time consuming.

The survey of analysis methods gave nine references for coherent evaluation of the throerate parameters n, A, E. One method required both rate and weight (References 22, 29 and 53).

2


In addition, the parametric plots were often difficult to interpret. Three other methods usedeither a computer program or complex manual calculations not otherwise available (References21, 36 and 44). The two remaining methods specified several rates of heating with a computerprogram being either necessary or desirable (References 2, 23 and 24).

For our work, no single method was entirely satisfactory for easy and precise curve-fitting.Therefore, three complimentary computer programs based on the Part I theory were developedfor this purpose. A maximum rate experimental method (MAXRAX) used data at the point ofmaximum rate of weight change. This program yielded n and a first estimate for A, E. Anintegral method program- (TRIM) used corresponding values of weight and temperature fromthe thermngram. A n value was transferred from MAXRAX. This requirement was avoidedfor the third program (PRIM) where a best apparent value of n was calculated to correspondto the minimum of an overall error term parabolic fit as a fur,ction of n (Reference 36). Twoadditional PRIM features were a comparative pseudo-variance analysis and two temperaturespans for A, E evaluation.

C. PHENOL-FORMALDEHYDE MATERIALS SURVEY.

Approximate ranges of experimental conditions and empirical kinetic parameters for thesurvey were summarized in Table I with detailed results in Table II. In most constant ratework, 5-400 mgm of a fine powder sample was run in a porcelain crucible to about 9500 at30 - 10 / m i n. Bulk material was frequently pulverized under liquid nitrogen to reduce frictionheating. A purging flow of inert gas was generally use' with a few moderate and high vacuumexperiments being reported. Available thermograms and commercial processing suggesteda desirable minimum cure or posteure temperature of about 1250 with temperature being moreimportant than time for thermogravimetry.* Therefore, the maximum processing temperaturewas indicated as a crude thermal history index.

The empirical kinetic parameters for constant heating rate thermogravimetry of cured andvitreous fiber reinforced materials overlapped. The higher n, A, E parameters were forreinforced samples. The largest set of values were designated temperature-dependent andvaried with each of three curve-fitting methods.

The parameter E for the single isothermal thermogravimetry source for a cured poly-condensate was comparable to an isothermal mass spectrometric analysis result, with n = 0in both cases. Constant rate mass spectrometric thermal analysis E values were temperature-dependent, ranging from 16 up to 48 kcal/mole, the highest reported for a cured polycondensate.The parameter n was zero; unfortunately, A results were not given for this study.

The empirical kinetic parameters for the survey were somewhat mutually compensating fordifferent experiments. For a given n, an increase in A gave an increase in E for ea '. investi-gator with only four close exceptions. For a given n and experimental set, an increase in Twas consistent with an increase in both A, E with only one minor exception.

For two sets of A, E and with constant n, T identical values of w would correspond to

(r A E )/(r 2 A2E1 ) = (, /T.) exp [(E -E )IRT] (5)

For T = T2 there was a single intersection of th. two thermograms and large differences

were suggested elsewhere. The low precision at hand, however, let sets of A, E and

*Unpublished work by the author.

3

it I . . . .


especially n, A, E approximate the same thermogram. Thus various parameter sets weredependent upon curve-fitting sensitivity. The same effect clearly existed for different heatingrates. This mutual compensation tendency dictated a new and precise curve-fitting technique forthe reanalysis of previous data.

A factual heating rate or temperature dependence of A, E was reported by a number ofinvestigators. This was believed to be due in part to mutual compensation from inaccuratecurve-fitting as further illustrated in a subsequent section of this report. In a formal senseEquation 3 was invalid for temperature dependent empirical kinetic parameters. The use -ofthis relation and associate curve-fitting techniques gave pseudo-values although the errorsinvolved were probably small. Although at least one partial solution for temperature dependentvalues of A, E has been obtained, no suitable evaluation method could be derived in detail(Reference 20). eurther factual dependence cfthe empirical kinetic parameters of the invariantmodel on such procedural aspects as ambient pressure, sample form and weight, and so forthwas a major consideration in the reexamination of thermograms using a new computer program.

4


SECTION III

EXPERIMENTAL MATERIALS AND METHODS

Table IV summarized the major materials for this report. Molding and other samples ofMonsanto R14009 commercial phenol-formaldehyde polycondensate were previously examined(Reference 17). The remaining materials were identical to those of either isothermal thermo-gravimetry or thermal expansion study (References 12 and 17).

A polycondensate casting and molding were pulverized under liquid nitrogen with a jewelers'cutter (moly-steel 10,000 rpm) and sieved to a standard particle distribution. A reinforcedlaminate powder was prepared in a similar manner but using a hole saw (moly-steel, 3/4 inchdiameter, 780 rpm). Integral glass fabric reinforced samples about one inch square by1/8 inch thick were used for isothermal air aging.

The modified Aminco Thermo-Grav recording thermobalance and experimental methods forconstant heating rate thermogravimetry were described in Part I. Laminate plate agingexperiments were conducted in a forced-air convection oven from 300 -800 F (about 150 -430 C) to 1000 hours. The procedures and mechanical property evaluations have been furtherdetailed or referenced elsewhere (Reference 19).

5

A FM L-TR-65-246Part II

usually agreed with the "best" n value. Small analytical and perhaps experimental errors atthe ends of the thermogram severely affected A, E results as the w, K values were especiallysensitive here. This was further illustrated by Figures 8 and 9.

The parametric study further suggested that visual inspection of data point deviations froma mean line for a parametric plot was not reliable for the precise evaluation of empiricalkinetic parameters. The third computer program PRIM was designed to provide other meansfor proving reliability.

For PRIM, six incremental values of n were chosen around the MAXRAX n result. Essential-ly, TRIM was then repeated for these six values. An overall error term g was calculated foreach case

g (Wo- Wo )2 (12)

A best value n' was then computed as a minimum for an approximation to g dependence uponn using a parabolic method of least squares

g a on + bon + c(3)

Then the result n' was used for calculating corresponding values of A, E using TRIM.

PRIM used two temperature spans. The first or q span was primarily for securing thebest value of n. The second or s span was used for calculation of A, E for the entire thermo-gram. The s range was a- compromise between available data and likely pyrolysis, 140' -10100 in 30 increments. The q span, which also used 30' increments, was roughly chosen foreach case using results from an initial -parametric study

(Wop, W0 q) 2 (0.98, 0.52) (14)

(Wp, Wq) - (0.95,0.05) (15)

(0 G ) Z (3200,880) (16)

A feature of PRIM was evaluation of four indices of conformance for the calculated andexperimental "thermograms. One was g' and a second was ,(Woe - wo)m, this value times

100 giving the maximum sample weightpercenterror for the s temperature span. Comparative2 2pseudo-variances- s (a), s (b) were calculated assuming that Equation 11 was valid for ae e

least mean squares analysis (Reference 42). These parameters were respectively indicativeof the deviations of A, E and E from a mean (Appendix II).

Absolute methods were not available for either the linear or parabolic approximating leastmean squares cases. As the pseudo-methods could fail, several checks were made. Acoefficient A' was calculated by an independent relation to confirm the value of A from Equation10. Several conformance indices were also calculated for the parabolic pseudo-method asfurther discussed in Appendix H.

The programs were written ;n Fortran IV for an IBM 7044/7094 system. Depending uponthe program, from 2-10 punched input cards were necessary. Only descriptive outlines weregiven herein as several sets of symbols were used and the programs were not optimized forminimum running time.

7


SECTION IV

EMPIRICAL KINETICS COMPUTER PROGRAMS

A. THEORY.

The general theory for the computer programs, developed in Part I, was also reviewedherein as Appendix I for reference convenience. Sequential steps for the three programs anda thermogram construction subroutine were summarized using flow sheets (Figures 1-4)and outlines (Appendix II).

The maximum rate experimental program MAXRAX essentially solved four equationsusing an iterative procedure and two tables

In r(n- 1) + In + I (6)

In wm

A wM (TXl nT)m e x p (Xm) (7)

E - T R(nT,/W) (8)

r = X e X m p(.Xm (9)

The necessary input data were evaluated at the thermogram maximum rate of weight loss.This point and the associate heating, and weight loss rates were visually estimated using astraight edge and an optical device based on the alignment of two partially reflected imagesof the curve.

The second computer program TRIM solved

log (K/T 2 ) R E + Ogor(AR/ET) (10)

which was derived from the integrated solution of the constant rate kinetic equation: Otherthan experimental data, the inputs n, r were from MAXRAX and the approximation T = Tmwas made.

For TRIM, the -parameters A, E were calculated for an ideal equation

y bz + a (II)

by the standard linear method of least squares. This was an approximating pseudo-methodas all terms were interdependent, experimental precision was variable and the term r slowly

decreased with increasing temperature (about +2 percent maximum).

Thermograms for -325 sieve molding powder at three heating rates were fairly smooth and

consistent excluding the final three percent of weight loss above 700 (Figure 5). A slight

discontinuity near 4000 for the T /min runwas also ignored. Using TRIM, systematic variationsof n, A, E and the temperature span were used to study these thermograms. The "best"

values of A, E for minimum error between calculated and experimental thermograms

6


separation by a constant sample weight difference with a small erroir occurring at intersections.Thus, inspection of Figure 7 revealed a residue-free resemblance to about 5000 with similarityfor powder samples to 9000. A particle was an unsatisfactory geometry in agreement withother results (Reference 18). Reference 10 further notes that complete drying would probablyhave given better agreement to 5000; smaller errors to 9000 would also result. The lowtemperature weight losses also suggested too low a processing temperature with some solventretention. The small thermogram fluctuations were abnormal and could have been due to aninstrument artifact, replotting, or other unknown factors.

PRIM empirical kinetic parameters for polycondeneate casting and glass fabric reinforcedlaminate powders were not the same (Table VII). The laminate powder sample was more stablefor a residue-free basis. This apparent stability was believed primarily due to glass particlesintering at the higher temperatures with encapsulation of otherwise decomposable material.For example, a glassy residue with brownish inclusions was found when the laminate powderhelium residue was rerun in air. Differences in resin contents calculated for the casting andlaminate powders in helium (19.4%), laminate powder in air (24.3%), and a laminate plate(27.0%) were not uhreosonable in that any encapsulated material would be ultimately weighedas "glass" and encapsulation would piz-bably be least effective in air. A plate resin contentof 27.0 percent was a moisture-free normalized value for long time burnout in air at 5400(Reference 6). Previous results with an uncured resin and heat cleaned 18!-"E" glass powder(50/50 mixture, -400 sieve) also suggested encapsulation at temperature above about 5000(Reference 18). The helium residues near 9500 were 59.5 percent for the mixture versus 56percent for the polymer alone.

It proved necessary to "dry" the casting and laminate powders prior to thermogravimetry(Table VII). The conditions were 1200 for 25 minutes, which gave an average stabilized weightloss of 1.45 percent. About 25 minutes were used for heating to 1200.

Empirical kinetic parameters were calculated for phenol-formaldehyde polycondensatepowder and sized glass fabric reinforced laminate samples (Table VIII). The powder samplewas more stable than the plate for both helium purging flow and a moderate vacuum. The spreadin A, E was fairly small for all four experiments with n values being similar for plate samplesbut depending upon environment for powders. Enhanced stability was found under vacuum forboth materials. This has been attributed to an increase in pyrolysis product fragmentation withincreasing pressure and may be associated with inefficient removal of pyrolysis gases by apurging flow (Reference 18).

PRIM and Reference 53 parameters were not the same for a powder and plate under vacuum(Table VIII). The thermogram error indexh(w oc - wo)m suggested that PRIM was more repre-

sentative for the powder with PRIM superiority being conclusive for the plate. There wereconsistent parameter variations for a polycondensate powder versus a plate geometry ascompared to a powder versus'a laminate powder (Tables VII ard VIII). Plate pyrolysis hasbeen suggested to be influenced by catalysis, geometry, glass fabric f.inish, or possibly othereffects (Reference 53). Polycondensate and laminate powder differences were believed primal -ily due to particulate glass sintering.

Five alkaline catalyzed polycondensate powders have undergone similar gravimetricpyrolysis once curing was complete (Reference 37). PRIM parameters for a sample codedB-C were comparable with other results (Table IX). The necessary thermogram was con-structed from tabulated e - wo values and extrapolated to 9500 (Reference 37). As nearly

identical residue-free thermograms were reported for these materials, the sample B-Cparameters were also representative for all five. They included three catalyzed by Ca(OH) 2

(P/F ratios of 0.36, 0.42, 0.50) and the commercial products CTL-91LD and SC1008.

9

/

AFM L-TR-65-246Part 11

PRIM curve-fitting indices and empirical kinetic p rameters were averaged for sixexperiments using an inert gas purge (Table IXK: A dpf:idtive pseudo-variance analysis wasintended to aid the selection of experiments mut could not be completed for this report.Qualitative results follow:

(a) Molding powder (Tables V and VI). The spread in MAXRAX and TRIM n, A, E valuesfor three heating rates exceeded the spread of the reference set. For PRIM, the 3a/minparameters were adjudged the best of the reference set. The 9°/min results gave upper A, Elimits for the reference group although also giving a good calculated-experimental thermogramfit.

(b) Pure polycondensate and glass fabric reinforced powder samples (Table VII). Thepolycondensate values were used for the reference group subject to being the lowest E case.The high n, A, E laminate powder results were questionable even in view of an excellentoverall fit resulting in the lowest conformance indices of any run.

(c) Pure polycondensate powder and glass fabric reinforced plate samples (Table VIII).The helium purge powder parameters were adjudged satisfactory for the reference set. Thevacuum results were marginally withheld due tohighn, low A values as well as a poor overallfit. Although similar, the plate sample values forboth helium and vacuum were not acceptablebecause of a low n and poor fit.

(d) Polycondensate powder (Table IX). The parameters for the only laboratory synthesizedmaterial were used in the reference set subject to being the maximum overall fit error case.

(e) Reference set materials (Table IX). There was still a tendency for mutual compen-sation of the parameters, especially for A, E between experiments. There were no consistenttrends for n, A, E with a change in T. There was a tendency toward higher values of g',

s 2(a), s 2(b(or average error) but not±(w - w )m (ormaximum error) atthe highervalues ofT.e e oc om

Within the limited spectrum of experimental conditions, no consistent dependence of the con-formance indices or parameters upon other variables as grinding method, sample weight, andso forth was evident. Although the spread in the parameters was low, especially when comparedto the initial materials survey, fair errors resulted if one thermogram was predicted usingeither the reference set parameters or results for another experiment. Rough estimatesimplied *(w - w ) of about 0.03-0.06 over a narrow temperature range with up to 0.03

cc 0omaverage error. 'Ihe qualitative selection of experiments for averaging and the averaged setwas biased by both low overall accuracy and PRIM limitations to the degree that all observa-tions in the above paragraphs were tentative and subject to future revision.

The residue-free weight w for the empirical kinetic model

w = ( w° - wr ) / ( w o i - w r) (17)

was for a continuous thermogram. The rate -T could approximate either zero at two points*oTor one maximum, but could not be a minimum. These rules permitted quick rejection ofnoncomforming thermograms. For multi-step thermograms (with -*oT approaching zero at

more than two points) the initial unity value of w . would have become wr for each successive

step. Equation 17 in a different form permitted easily constructed conversion diagrams forgraphical calculations or rapid estimates (Figure 8). General effects of n, w upon K wereoften pronounced (Figure 9). K values were insensitive to n but strongly dependent upon w forw O.8. This portion of the thermogram was limited for n, A, E evaluation and was unfairly

10

AFML-TR-65-246Part 1I

biased by small errors. For a w of less than about 0.2, K was strongly dependent upon bothn, w. Althoilgh perhaps attractive for n evaluation, small errors a!so exerted an unfair weight-ing here.

Accuracy and precision levels for constant heating rate thermogravimetry were reevaluatedand the new results summarized as Table X (Reference 17). In addition, slightly reved- Wrdata were used for some PRIM calculations (Table V).

MAXRAX reflected both experimental and model fitting errors as primarily compared toan overall model error for PRIM. A *(woc - wo) difference between the two was therefore

roughly the experimental weight error at the point of maximum rate. Calculated values werereasonable and varied up to twice the estimated experimental precision (Table X). Anargument similar to the one above was possible to show that the difference between A, A'approached the error in A associated with the experimental error at the point of maximumrate. In most cases, this difference was encouragingly small (for example, see Table VI).

The program and past studies revealed a variety of troublesome aspects in the evaluation ofconsistent empirical kinetic parameters for phenol-formaldehyde polycondensate materials(References 17, 18 and 20). Specific examples exceeding the normalizing ability of residue-freeempirical kinetics were:

(a) Critical curve-fitting aspects for a single thermogram or similar set including -

1. Data point spacing, reaction rate, or temperature range incorporation and possiblemagnification of errors (especially near thermogram ends).

2. Improper use of the invariant model in evaluating temperature dependent parametersor thermograms with more than one maximum rate of weight loss, and so forth.

3. Mutual compensation of different sets of parameters permitting approximate -

representation of a single thermogram.

4. The very flexible nature of the kinetic model for approximate representation ofdifferent thermograms.

(b) An oxidative or reduced pressure atmosphere.

(c) Reinforced laminate or polycondensate particle, laminate powder, or polycondensatefilm samples.

(d) Samples contaminated with postcure surface product or solvent, inadequatelycured or dried, or too large.

(e) Two, three, or occasionally many stepped thermograms. This atypical behaviorappeared pronounced for large sample particles and perhaps minute thermobalance oxygencontamination; low inert gas flow rates could have resulted in either contamination or ineffi-cient pyrolytic gas removal. Stepping was perhaps accentuated to varying degrees by (b)-(d)items as well as the lack of pressure during sample polymerization.

11 .

/°


SECTION V

TYPICAL APPLICATIONS OF EMPIRICAL KINETIC PARAMETERS

A. EMPIRICISM OF n, A, E

The kinetic parameters were strictly empirical. There was no factual significance interms of classical physicochemical mechanisms (Table XI). Attempts to assign primarygoverning mechanisms could not resolve complex intra-relations between the sample,experimental method, and possible large numbers of chemical reactions and physical processesduring pyrolysis. The kinetic model undoubtably grossly represented a variety of complexmechanisms.

B. RELATIVE THERMAL STABILITY

The empirical kinetic parameter E has often been used as an index of relative thermalstability. For example, this parameter was good for many thermoplastics with a n of a nearinteger and similar large A values. For thermosets with small values of A, E and high per-centage of final residue, the three parameters n, A, E proved closely interrelated. Moresuitable indices were the maximum rate loss rate and corresponding temperature. The

normalized weight at this point proved largely controlled by n, r at about 0.5. For a knownn, A, E, t, the maximum rate indices were only available by interpolation or trial and errorcalculation

-2 n-1Tm = nwm (AR/ET} exp(-X M ) (18)

Km= (AE/RT)p(X m ) (19

-WlTa Wm(X/nT)m (20)

C. HYPERTHERMAL ABLATION

Kinetic models similar to the current one have been used extensively for hyperthermalablation calculations and computer programs. Three regions were used in one descriptivechar-formation ablation analysis (Reference 49). These regions were a carbonaceous charlayer, a reaction zone, and the virgin material. A char-reaction zone interface recession ratefor the interface temperature was*

n+2 2n+1 -2(n+l) -X(L) AGn!(I-w.) X e (21)

)n+1

G L(aCE/AHRL) (22)

For a given G, the lowest recession rate would result for a large E, wr and a small A, T.

Clearly, small uncertainties in the parameters could give a large L error. Some typical para-meter values and results from another computer study were summarized by Table XII andFigure 11.

*This derived form uses the reasonable approximations: 1<<AHRX; T-0 asL-o; (wall/pyrolysis) mass flux = (1 - wr). Typically, << 1.

12


This application of empirical kinetic parameters to a complex environment appearedprimarily because of inadequate experimental methods. The simple thermogravimetry ex-periment for an isolated, nearly isothermal sample was extrapolated to an internal pyrolysiszone subject to intense and rapidly changing catalytic, compositional, pressure, stress,thermal, volumetric and other gradients. For example, the time for the receding steady tem-perature distribution of Figure 11 to traverse a pyrolysis zone thickness of about 0.35 mmwould be 1.4 second, correspondingto an "average" heating rateof 18,5000/min. In other cases,especially at low heat flux, the heating and recession rate, and temperature distribution wasless abrupt with a resultant thick pyrolysis zone. Excluding limited high heating rate and hightemperature work, no definitive empirical kinetic model or parameters could be found for thiscomplex environment or a fair experimental simulation.

D. MECHANICAL PROPERTIES.

The use of empirical kinetic models and parameters for the analysis and correlation ofmechanical properties has been limited (Reference 16). In one study with this intended goalthe present model failed to represent the air aging weight changes of CTL-91LD/Glass Fabric(Figure 12, Reference 19). The isothermal thermograms for this and similar materialssuggested two gross controlling mechanisms. There has been evidence for the predominanceof diffusive effects at the shorter times and oxidation for longer aging periods with completeoxidative control at the higher temperatures (References 15 and 18).

An encouraging correlation was found for the tensile strength at 450 to the fabric warp for

CTL-91LD/Glass Fabric (Figure 13). The empirical result was

TS(45) = c1 exp (c2w) (23)

A strength retention of only about 10 percent of the average room temperature control(25,260 psi) existed for w = 0.8. The empirical coefficients and other results have beensummarized elsewhere for CTL-91LD/Glass Fabric and a second material (Reference 19).Other attempts at mechanical property correlations were not satisfactory if the strengthincreased with an increase in either temperature of time. Correlations may have been possibleover restricted temperature or time regions as suggested by the similarity of the plots ofFigure 14.

Other isotherma.l air aging kinetic experiments for aCTL-91LD polycondensate powder andCTL-91LD/Glass Fabric were informative. A -325 sieve, 100 mgm powder sample had alife-time of two hours at 600 0F. The life-time for a -325 sieve 100 mgm laminate powdersample was 48 hours, implying a glass shielding effect. A 100 hour life-time of a 1/8 inchthick laminate plate was undoubtably associated with surface area and/or volume influences.These results suggested a need for a flexible empirical kinetic model properly accountingfor surface area, thickness, two controlling mechanisms with a transition region, and probablycatalysis, oxygen concentration, and weight. An established model would be necessary priorto any serious attempt to use this approach for the analysis and correlation of the mechanicalproperties of reinforced laminate plates during long-term air aging.

13

/"

AFML-TR-65-246

Part II

SECTION VI

SUGGESTIONS FOR FURTHER WORK

Additional work seems necessary to establish ranges of environmental validity for theempirical kinetic model. Particularly questionable aspects include heating rate extremes,isothermal thermogravimetry, micro size powder and large laminate plate samples, purgingflow through a powder sample, and reduced and high pressure (Reference 27). Currentapplications for hyperthermal ablation computer programs, mechanical property correlations,vacuum life-time predictions make realistic environmental simulation an essential need. TableXIII summarized some conditions pertinent to the two above requirements yet within practicalexperimental capabilities in the near future. Improvements in experimental accuracy of upto an order of magnitude better than for the accuracy values of Table X were desirablealthough by and large beyond the immediate state of the art of thermogravimetry.

Improved computer programs appeared desirable prior to further study. One outstandingapproach gave best empirical kinetic parameters in a least mean squares sense (Reference 43).Additional empirical kinetic models appeared necessary for some critical cases as an oxidativeenvironment or sample other than a fine polymer powder (Table XIV). Particularly dasirablefeatures for future computer programs included: (a) constant heating rate and isothermalversions, (b) evaluation of n, A, E in a least mean squares sense, (c) evaluation of confidencelimits, variances, and significant digits, (d) experimental corrections, (e) statistical data pointweighting for the entire thermogram, and (f) temperature variance options for n, A, E, eithersingularly or in any combination.

There were a variety of polymers for which definitive kinetic data could prove helpful inablative, coating, structural, and other aerospace uses. Polymer classes of special interestwere summarized by Figure 15. A future goal was kinetic information on the base polymers aswell as materials using such reinforcing agents as fibrous carbon, glass, graphite, and silica.

14

14J

AFML-TR-65-246

Part II

APPENDIX I

GENERAL THEORY

The constant heating rate kinetic relation

T= (wnA/i) exp (-X) (1-)

was rearranged as

K JW w-ndw = (A/) fT d (I- 2)I 0

for the assumption of a zero rate at zero degrees. K, a convenient index, became

K = (I- w) for n = 0, (1-3)

= -Inw = , (1-4)

= (w-n-1)/(n-I) : 0,1 (1-5)

Integration of the other side of Equation 1-2 by parts in two different ways gave

K = (AE/Rf)p(X) (-6)

pMX= X- eI X fX e Xdx (I -7)

K (AE/Rt) I (-I)m+1 X- (M+ 1)X -

For m = o, a relative error r was defined as

r = X2e p(X) (I-9)

Therefore

K = .r (AE/Rt)X-2 e - x (-10)

Figure 9 presented K = f(n, w). Figure 10 depicted p(X), r = f(X).

The maximum rate occurred when

d(-,)/dt = d(-')/dT = d(- )/dw = 0 (I-I1)

Differentiation of Equation I-1 with respect to time gave

n wn-1 + (f/T) W X] 0 (1-12)

The maximum rate followed as

-Tm w m (X/nT)m 1-13)

15


AlsoI-n . X

km Wm (X/nT)mT Ae - m 1-14)

where n cannot be zero.

The two principal relations for the maximum rate method came from rearrangements ofEquations 1-13 and 1-14

E ; -Tm nR(T /w)m (1-15)

1-n Xm

A Wn (TX/nT)m (1-16)

The third necessary relationship for n resulted from a comparison of Equations 1-10 and 1-14

K rw n n (1-17)m m

For n = 1

w = e-r (1-18)

and for n 0, 1

m = r(n - - ) +)1/(n-I) 1-19)

It should be noted that Equation 39 of Reference 17 is in errQr and should be identical toEquation 1-19 above.

16


APPENDIX H

COMPUTER PROGRAMS OUTLINES

I. Maximum Rate Experimental Method (MAXRAX). See Figure 1.

A. Read input: R, Tm , t, "m, Wmw oi, -W Tm Wr

B. Read tables:

rj,k fl (X )

2. Wm f2 (ni , ri) (11-2)

C. Read integral values of ni, r. for w from table.11 m

D. Calculate n.3

In[r(n'- -I) + +n'k I m + I ('rr-3) -

jk In wM

(ni,j,k 40 1) (11-4)

E. Calculate E, X

E -TmnjkR(T/w)m (I-5)

Xm E/RTrm (1-6)

F. Read rj from table.

G. Calculate nk from Equation 11-3.

H. Calculate E from Equation 11-5, Calculate A

A m ("X/nkT)m exp(Xm) ('n-7)

I. Write output:

1. Run identification.

2. n,A,E,r j , X m ,'T m

J. Construction subroutine

II. Transfer Resolution integral Method (TRIM). See Figure 2.

A. Read input:

n~,,m , TM' win Woi' -WTm'r

£7

/


B. Read table:

W = f, () with e. q. (1"-8)

C. Calculate T

T e + 273.16 (H1-9)

D. Calculate w

W (wo - wr)/(woi wr) (I-10)

E. Calculate K

K (I - w) for n 0, ("-II)

- nw = I, (1-12)

=(.1-n -l)/(n -1)9 0,I M]-1:5)

F. Calculate y, z

y Iog1 0 (K/T 2 ) (OE-14)

z = I/T (-5)

G. Calculate A, E by linear pseudo-method of least squares

y = bz + a (11-16)

H. Calculate A'

A' = -WTmWm-n m exp (Xm) (,1-17)

I. Write output:

1. Run Identification.

2. n, A, E, r, k, A'

J. Construction subroutine.

Uli Parabola Resolution Integral Method (PRIM). See Figure 3.

A. Read input: n, r, R, T ,T, Tm ,wm woil-WTm' Wr

B. Read tables:

01. w = fl() withep : <eq (H-18)

2. n1, n2 . . . ni, with i 6 maximum. (H1-19)

C. TRIM subroutine.

18


D. Calculate g

g = 7X(w e -WO) 2 (11-20)

E. If g = 0, n = n'. Proceed to item (I). (1-21)

F. Calculate a, b, c by parabolic pseudo-method of least squares

g = on + bo n + c (r-22)G. If a :5 0, designate. Proceed to item (V). 71-23)

H. Calculate n'

n -b /2a0 01-24)

I. TRIM subroutine.

J. Calculate g'

S0 )2 (1-25)

K. Calculate 7-0

0wo W0 /[ M o'.-26)

L. Calculate s 2 (we os (WO ) =g,/(q -2) (Ir- 27)

M. Calculate s 2(Wp 0

-2 21O) (Wo _ W;)2] /q

N. Calculate F(wo)

F(w o ) S, 1-29)0. Caiculate a, b

a logic r (AR/ET) (31-30)

b -E/(R InI0) (11-31)

P. Calculate l/T

lI/ i/t /q (1T_32)2

Q. Calculate s e(a)

2(0) S 2s(Wo)/q

19

AFML-TR-65-24 6

Part II

R. Calculate s2 (b)e(b) s (wo)/I(I/T- l/T) (11-34

S. Construction subroutine.

T. Substitute s temperature span for q temperature span with

e, e e(U35)

U. Repeat items () through (S) for s temperature span.

V. Write output:

1. Run identification.

2. For the q temperature span: n', A, E, R, T, A', g', Vo

s2 (wo) , s2 (wo), F(w ), a, b, l/T, 17T, s2 (a), s2 (b);

eo p o e e

Woc = Y(8) (Mr-36)

3. Item (V.2) for the s temperature span.

IV. Construction Subroutine. See Figure 4.

A. Read input: n, A, E, r, R, T, im' Woi' Wr

B. Read table: p(X) = fl(X) (2-37)

C. Calculate K

K = (AE/RT)p(X) (31-38)

D. Calculate w

w= I - K for n 0, ('1-39)

Kexp(- K) ( 1 (-40)1/0 -n)

K(n-, + 1I/ 0,1 (1 -41)

E. Calculate woc

WOC W(Woi r) + Wr (3-42)

F. Calculate 8

6 T - 273.16 (3E-43)

G. Write output: woc = f2 () with 8r <_ e _e5 s . (3:-44)

20


V. General Notes.

A. Numerical values for this report were:

1. J=k=30° (Ir-45)

2. E =S = 0.001. (Z1-46)

3. Woi 1 (71-47)

4. 0 p, 0q were for the J increment nearest to w p 0.95, w 0.05, (31-4L

respectively. See Equations 14-16.5. e r = 1400, 0s = 10100. (11-49)

B. The following was omitted for brevity:

1, Standard tests for avoiding In 0, In (-number), etc.

2. For MAXRAX,

a. Subscript m omitted for n.

b. Subscripts m, i, j, k, omitted for A, E, Xm

c. A manual test assuming n = 1 if nJk < 0. (E-50)

d. A test to insure that

ij i ,k-1) +l #0 n_ (11-50)

was positive.

e. Rules for choosing + e or - e.

f. -* Tm' wm calculated manually.

3. Linear least mean squares pseudo-method subroutine forTRIM with output A, E.

4. For PRIM,

a. Parabolic least mean squares pseudo-method subroutine withoutput n, g, go, ao bo ,co, (gc - g)mr s 2 (g) , 2 ()2p 2)

0 e p

b. Output: ii, A, E and w = f(0) as an option for each n value. (I1-52)

c. Equations 11-26 through II-21 for the flow diagram.

C. For TRIM:

1. n = n (MAXRAX), n = ni (PRIM), or n = n' (PRIM).m

2. r= rm (MAXRAX), and T = m unless noted.

21

/


D. For Construction Subroutine:

1. Run identification and n, A, E, r, Xm, T included in outputwhen run separately. m

2. s temperature span except as a special case for PRIM.

E. Symbols f and symbols using subscripts i, j, k usually uniquemfor each program outline.

22

AFML-TR-65-246

Part II

REFERENCES

1. H. C. Anderson, "Order of Polymer Pyrolysis by Thermogravimetric Cycling Experi-ments," J. App. Polymer Sci. 2, 115(1964) Polymer Letters, Part B, No. 6, February.

2. H. C. Anderson, "New Thermogravimetric Relationships for Studying the Pyrolysis ofPolymers," USNOL, White Oak, Maryland, Report NOLTR 63-113(8 July 1963).

3. H. C. Anderson, "Kinetics of Pyrolysis of Epoxide Polymers," Kolloid-Zeitschrift und

Zeitschrift fur Polymers 184, 26(1962).

4. H. C. Anderson, "Pyrolysis of Phenolic Polymers," SPE Transactions2, 202(1962).

5. H. C. Anderson," Pyrolysis of Polytetrafluoroethylene: A First Order Reaction," DieMakromolekulare Chemie 51, 233(1962).

6. 'ASD Thermal Composite Specimens: Preparation and Physical Test Data," H. I. Thomp -son Fiber Glass Company, Gardena, California, Final Report And Acceptance Data(July 1963). AF Contract No. AF 33(615)-11164.

7. N. Beecher, R. E. Rosensweig, "Ablation Mechanisms in Plastics with InorganicReinforcements," ARS J. 31, 532(1961).

8. M. D. Bowen, et al, "Antiballistic Missile Sheath and Wake Study Report," MartinCompany, Orlando, Florida, Report OR 3874(April 1964).

9. G. W. Briendley, et al, "Limitations of Dynamic Methods for Kinetic Studies of SolidState Reactions," Materials Research Laboratory, Pennsylvania State University,University Park, Publication, Appendix L

10. G. P. Brown, et al, "Synthesis and Evaluation of Thermally Stable Polymers," GeneralElectric Company WADD TR 61-255(June 1961). AF Contract No. AF 33(616)-7076.

11. W. Chang, "A New Method of Determining the Order of Reaction and the ReactionConstant from Kinetic Data," J. Phy. Chem. 61, 819(1957).

12. G. L. Denman, "Thermal Expansion of Reinforced Composites - Thermal HysteresisEffects," Wright-Patterson Air Force Base, Ohio, AFML-TR-65-279(March 1966).

13. C. D. Doyle, "Integral Method of Kinetic Analysis of Thermogravimetric Data,"Makromolekulare Chemie 80, 220(1964).

14. C. D. Doyle, "Kinetic Analysis of Thermogravimetric Data," J. App. Polymer Sci. 5,285(1961).

15. C. D. Doyle, "Logarithmic Thermal Degradation of a Silicone Resin in Air," J. Pol.Sci. 31, 95(1958).

16. C. D. Doyle, "Application of the Superposition Principle to Data on Heat-Aging ofPlastics," Modern Plastics, 141(1957)July.

17. R. W. Farmer, "Thermogravimetry of Phenol-Formaldehyde Polycondensates," Wright-Patterson Air Force Base, Ohio, AFML-TR-65-246(January 1966). AD 646 897

23

/

AFML-TR-65-246

PartlII

REFFRENCES (CONT' D)

18. R. W. Farmer, "Procedural Variables in the Thermogravimetry of Plastics," Wright-Patterson Air Force Base, Ohio, ML TDR-64-133 (April 1964).

19. R. W. Farmer, "Isothermal Thermogravimetry of Reinforced Plastics," 19th RPD SPIProceedings, Chicago, Illinois (4-6 February 1964).

20. R. W. Farmer, "Thermogravimetry of Plastics. Part I: Empirical HomogeneousKinetics," Wright-Patterson Air Force Base, Ohio, ASD-TDR-62-1043, PartI(February1963).

21. F, E. Freeburg, "Effects of Crystal Defects on Thermal Decomposition Reactions

Studied Thermoanalytically," Fairleigh Dickinson University, Madison, New Jersey,4th Thermoanalysis Institute Lecture(21 June 1965).

22. E. S. Freeman, B. Carroll, "The Application of Thermoanalytical Techniques to ReactionKinetics. The Thermogravimetric Evaluation of the Kinetics of the Decomposition ofCalcium Oxalate Monohydrate," J. Phy. Chem. 62, 394(1958).

23. H. L. Friedman, "Kinetics of Thermal Degradation of Char-Forming Plastics fromThermogravimetry. Application to a Phenolic Resin," J. App. Polymer Sci., 183(1964)Polymer Symposia, Part C, No. 6.

24. H. L. Friedman, "The Kinetics of the Thermal Degradation of Charring Plastics. I.Glass Reinforced Phenolformaldehyde," General Electric Company Report No. R61SD145(August 1961).

25. H. L. Friedman, "The Ablation of Plastics During Hypersonic Re-Entry. II. ChemicalReaction Rates from TGA Data," paper in, Wright-Patterson Air Force Base, Ohio,WADD TR 60-101(September 1960).

26. R. M. Fuoss, et al, "Evaluation of Rate Constants from Thermogravimetric Data,"J. App. Polymer Sci. 2, 3147(1964).

27. P. D. Garn, Thermoanalytical Methods Of Investigation Academic Press, New YorkCity, 1965. a

28. H. R. Gloria, et al, "Initial Weight Loss of Plastics in a Vacuum at Temperatures from800 to 500°F, ' ' NASA TN D-1329(December 1962).

29. H. E. Goldstein, "Pyrolysis Kinetics of Nylon, Phenolic, and Composites," LockheedMissiles and Space Company, Sunnyvale, California, TIAD 695 Indepartmental Com-munication(11 February 1964).

30. H. H. Horowitz, G. Metzger, "A New Analysis of Thermogravimetric Traces," Anal.Chem. 35, 1464(1963).

31. H. Hurwicz, "Aerothermochemistry Studies in Ablation," paper in, Fifth AGARDCombustion and Propulsion Colloquium, Pergamon Press, New York City.

32, T. R. Ingraham, "Making Decomposition Rate Measurements on Simple InorganicChemical Powders by TGA," Chemical Institute of Canada, Toronto, Canada, 1st TorontoSymposium on Thermal Analysis Proceedings (8 February 1965).

24

AFML-TR-65-246

Part II

REFERENCES (CONT'D)

33. K. M. Kratsch, et al, "Theory for the Thermophysical Performance of Charring OrganicHeat-Shield Composites," Lockheed Missiles and Space Company, Sunnyvale,California,LMSC 803099 2-60-63-7(October 1963).

34. H. T. Lee, et al, "Comparison of Kinetics of Thermal Degradation for a Series ofEpoxide Resins," Picatinny Arsenal, Dover, New Jersey, Technical Report 3197(December 1964).

35. H. T. Lee, et al, "Comparison of Thermal Degradation Behavior of a Conventional anda Fluorinated Epoxide Resin," Picatinny Arsenal, Dover, New Jersey, TechnicalReport 3194(May 1965).

36. H. H. Levine, "Reduction of Thermogravimetric Analysis Data for Establishing MaterialReaction Rate Constants," Avco RAD, Wilmington, Massachusetts, Report RAD-S230-HHL-645(23 July 1963).

37. H. W. Lochte, et al, "Thermogravimetric and Elemental Composition Studies of CharFormation for Phenol-Formaldehyde Polycondensates," Martin Company, Baltimore,Maryland, Report RM-182(Jilly 1964).

38. R. McGlothin, "Thermogravimetric Analysis of Some Ablative Materials," MartinCompany, Orlando, Florida, ML TR-64-146(15 May 1964).

39. S. L. Madorsky, Thermal Degradation of Organic Polymers, Interscience Publishers,New York City, 1964.

40. J. A. Magnuson, "Tabulation for Deriving Procedural Rate Constant from DynamicThermograms," Anal. Chem. 36, 1807(1964).

41. G. Metzger, H. H. Horowitz, "Application of Thermogravimetric Analysis to PetroleumChemistry: A Comparison of Approximate Integral Methods for Calculation of ActivationEnergies," ACS Division of Petroleum Chemistry New York City Meeting(8-13 Septem-ber 1965).

42. H. S. Mickley, et al, Applied Mathematics in Chemical Engneering, 2nd Edition,McGraw-Hill Book Company, New York City, 1957.

43. T. R. Munson, "Advanced Analytical Program for Charring Ablators," Avco SSD,Wilmington, Massachusetts, MPR RAD-CA-MPR10(1-28 February 1966). NASA ContractNo. NAS 9-4329.

44. T. R. Munson, "Thermal Decomposition Kinetics of Polymeric Materials," AvcoRAD, Wilmington, Massachusetts, Report RAD-TA-1057(2 April 1962).

45. H. Myers, D. B. Harmon, Jr, "Energy Transfer Processes in Decomposing PolymericSystems," paper in, High Temperature Resistance and Thermal Degr,,dation of Polymers,SCI Monograph No. 13, McMillian Cc..,pany, New York City, 1961.

46. J. A. Parker, H. R. Gloria, "The Kinetics of the Vacuum Weight Loss of a CompositeComprising a Subliming Solid in an Inert Polymer Matrix," NASA TM X-54030(January1964).

25

/"

AFML-TR-65-246Part I11.

REFERENCES (CONT'D)

47. Y. V. Polezhayev, "The Effect of the Rate of Thermal Degradation on the Process ofNon-Stationary Deterioration of Fiber Glass Reinforced Plastic," Akademiia Nauk SSR,157(1964). (USAF FTD Translation)

48. J. P. Redfern, "The Use of Thermogravimetric Data in Evaluating Kinetic Parameters,"SIMA Exhibition, Moscow, USSR(May 1965).

49. S. M. Scala, L. M. Gilbert, "Thermal Degradation of a Char-Forming Plastic DuringHypersonic Flight,"ARS J. 32, 917(1962).

50. S. M. Scala, E. J. Nolan, "Aerothermdynamic Feasibility of Graphite for HypersonicGlide Vehicles," General Electric Company SSL Report No. R60SD425(2 August 1960).

51. G. P. Shulman, H. W. Lochte, "Mass Spectrometric Thermal Analysis of Phenol-Formaldehyde Polycondensates," Martin Company, Baltimore, Maryland, ReportRM-193(April 1965).

52. H. G. Wiedemann, et al, "The Influence of Experimental Variables on the Thermo-gravimetric Determination of Activation Energies," ACS Analytical CIemistry andApplied Spectroscopy Division Pittsburgh Conference (21 February 1966).

53. H. S. Wilson, et al, "Analysis of Thermal Degradation of Glass Reinforced Phenolic andEpoxy Laminates," Wright-Patterson AFB, Ohio, ASD-TDR-62-939(July 1963).

2

26


0

r. 0

$, 0;4 4 0. .x

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A FML-TR-65-246Part 11

TABLE VII

PRIM EMPIRICAL KINETIC PARAMETERSFOR PURE AND GLASS FABRIC REINFORCED

PHENOL-FORMALDEHYDE POLYCONDENSATE POWDERS

A. Sample and Method

Atmosphere He purge He purgeCode A-4 Casting A-2 LaminateCrucible Coors 230 3/0 Coors 230 3/0

Grinding Method cutter; liquid N2 hole saw; liquid N2

Particle Size -325 sieve -325 sieve jPostcure Temperature, boC 178 178Resin Content, % 100 27.0Trade Name CTL-91LD CTL-91LDWeight, mgm 20 100

B. Empirical Kinetic Parameters

n .1.62580 1.73258A, min-1 24.234 201.572E, kcal/mole 9.18206 12.9362q span, *C 350-770 350-770rm 0.787766 0.845028t, *C/min 7.7 7.7Tr, °C 950 950wr 0.552 0.8888

C. Conformance Indices

g x 103 0,5973 0.05057

s2 (a) x 105 0.2667 0.02258es2 (b) x 102 -0.2347 -0.01987

±(Wo- w ) 0.009806(6200) 0.003142(6200)oc o m

a11 2-"h" glass fabric with Al100 finish.

bMaximum postcure temperature.

36


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A FM L-TR-65-246Part II

TABLE IX

MISC'LLANEOUS PRIM RESULTS FORPHENOL-FORMALDEHYDE POLYCONDENSATE POWDERS

A. Sample and Method

Atmosphere Ar purge Ar, le purgeCode B-C See Trade NamesCrucible porcelain Coors 230 3/0Grinding MethodLiquid Nitrogen cutter, drillRoom Temperature filing compaction, filing

Particle Size fine fine, -325 sievePostcure Temperaturea, OC 230 178,204,230Trade Name (Or Code) B-C B-C, CTL-91LD, R14009, SCI008Weight, mgm 200 20, 100, 200

B. Empirical Kinetic Parameters

n 1.61375b 1.55578±0.07002A, min - 51.5221 60.9338±41.3902E, kcal/mole 11.4162 10.38033±1.19827q span, °C 350-830 560 ±300

r m 0.780755 0.7924905± 0.0117355T, 'C/mmn 3.3 5.125±2.575Tr, 'C 815 882±68wr 0.555 0.577±0.025

C. Conformance Indices

g, x 103 0.6770 0.37462±0.30238

s2(a) x 105 0.2351 0.14589+0.12081es2(b) x 102 -0.2115 -(0.128635±0.106065)e-(Woc - W0)m 0.01694(4400) 0.011148±0.005792

D. Reference Lochte, et al (37) This Reportc

aMaximum processing temperature.

bApproximate estimates for q span, r_, wr. wo values from a smooth curve from tabulateddata extrapolated graphically to 950 . A' was not calculated accurately.

CAverages from Tables VI (30, 6', 9*/min), VII, VIII and IX.

38


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A FM L-TR-65-246Part 11

7AX RAX

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A,EUBROUTINE

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45

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AFML-TR-65-245Part if

READ INPUT,TABLES

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54o-------------------

Geometry Weight, mgm

0-250 Sieve 200

20 -- - 250 Sieve 60A-Particle 200

Heating Rate- 30C/rnin

10 Nitrogen Purging Flow

0 I I I I100 200 300 400 500 600 700 800 900

FURNACE TEMPERATURE, -C

Figure 7. Thermograms for Phenol-Formaldehyde Polycondensate Samples

50

'1t

AFML-TR-65-246Part If

0.90j

0.80 _ _ _ _ _ _ _ _ _

070

O.6C (-w)

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Figure 9. Relationship Between the Integral Parameter K And The Active WeightFraction

52

AFML-TR-65-246Part Il

co 0 co Nl ODm0) ODCD)l

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AFML-TR-65-246

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20.5 0.6 0.7 0.9 0.9 1.0

ACTIVE WEIGHT FRACTION

Figure 13. Tensile Strength at 450 to Fabric Warp versus Active Weight Fractionfor CTL-91LD/Glass Fabricj

56

J 4

. .. .. . +. 70 0 F

AFML-TR-65-246Part If

TEMPERATURE, OF

00300 350 400 450 50 550...

zwol0

w

w

2 0

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a.

I Curve Property

41 20 A Tensile Strength (450 to Warp)B Compressive Strength

C Tensile Strength (00 to Warp)2D Flexural Strength

a: OI E , Residue,.- Free Weight160 I80 200 220 240 260 280 300 320

TEMPERATURE,-C

Figure 14. Strength andi Weight Retention for 100-Hour Air Aging of CTL-91LD/GlassFabric

57


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58L.... I.n-_ i

UNCLASSIFIEDSecurity Classification

DOCUMENT CONTROL DATA- R&D(Security cIAl.cIt.81 of titto, body of abstract and Indexing annotation must be entered .on !he ov.atll report I. classiled)

ORIGINATING ACTIVITY (Corporate author) 2.. RF.PORT SECURITY C LASSIFICATION

Air Force Materials Iboratory I UnclassifiedResearch and Technology Division .2b.Wright-Patterson AFB, Ohio ___

3. REPORT TITLE

THERMOGRAVIMETRY OF PHENOL-FORMALDEHYDE POLYCONDENSATES Part HEmpirical Kinetic Parameters

4. DESCRIPTIVE NOTES (Typo of report and Incluelve date.)

May 1965 to September 1966S. AUTHOR(S) (Last name, first name, Initial)

Farmer, R. W.

6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF RCFS

February 1967 72 538a. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUM9$R(S)

b. PROJECT NO. 7340 AFML-TR-65-246, Part II

Task No. 734001 Sb. OTHER IPORT NO(S) (Any other numor that.may be asined

d.

10. A VAIL ABILITY/LIMITATION NOTICES

Distribution of this document is unlimited

1I. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Air Force Materials Laboratory(MANC)Research and Technology DivisionWrigbt-Patterson Air Force Base. Ohipc _

13. ABSTRACT

Empirical kinetic parameters for phenol-formaldehyde polycondensate materials weresurveyed for general application to Air Force interests. The ranges of n, A, E for the empiricakinetic model '-r,:" •-)

-(dw/dt) = Wn A exp (-E/RT)..1" 16" '

were n = 0-5, A ="_ X----to -7x-t0 1/min, E = 3.7-72kcal/mole, where wi\normalizedweight, tlE time, R- gas constant, T4*\temperature. The mass spectrometry and thermo-gravimetry thernial analysis methods used both constant heating rate and isothermalapproaches.

Reexamination of data with a new. computer program gave reduced variations:n = 1.5 07, A = 60.9 1.4, E = 10.38I4;.20. The scopes of the comprehensive survey anddescriptive thermogravimetry computer analysis were: (22 constant rate + 3 isothermal) vs 6constant rate experiments by 8 vs 3 investigators using (5 cured + 7 vitreous fiber reinforced)vs 4 cured polycondensates.

Parameter inconsistencies for the survey were partially associated with an atypical

polycondensate, laminate and polycondensate particle or laminate powder samples, or a reduced

pressure atmosphere, Calculated parameters apparently dependent upon the two latter aspects

were not averaged with other values. Small curve-fitting and other errors potentially enhance

further disagreement as they often gave large parameter variations.

DD 1JAN 1473 UNCLASSIFIEDI T Security Classification

/

UNCLASSIFIEDSecurity Classificatiou _

14.... "INK A LINK 9 LINK C/-,KFY WORDS nOLlE WT PtOL.E WY ROLE WT -

AblationKinetics

Phenol-formaldehyde Polycondensates,PolyersThermal AnalysisThermogravimetry

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UNCLASSIFIED

AFLC-WPAFB-JUL 66 3M Security Classification

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