L RD-ft,62 429 TIE-TE PERIITURE-TRRNSFORNTI N (TTT) CURE DIAORRNS:

1/1RELRTIONSHIP BETMEE..U U) PR1INCETON UNIV NJ DEPT OFCHEMICAL ENGINEERING X PENG ET AL. DEC 85 TR-5

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TECHNICAL REPORT NO. 5

00TIME-TEMPERATURE-TRANSFORMATION (TTT) CURE DIAGRAMS: k..

RELATIONSHIP BETWEEN Tg AND THE TEMPERATURE AND TIME OF CURE

_ FOR EPOXY SYSTEMS

Sby

X. Peng and J. K. Gillham

for oublication in

The Journal of Applied Polymer Science DTICPRINCETON UNIVERSITY " DEC 111985

Polymer Materials Program "E 1 19&1zDepartment of Chemical Engineering

Princeton, New Jersey 08544 LDecember 1985

Reproduction in whole or in part is permitted forany purpose of the United States Government

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Principal InvestigatorJohn K. Gillham

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Time-Temperature-Transformation (TTT) Cure November 1984-Diagrams: Relationship Between Tg and theDembr18Temperature and Time of Cure for Epoxy Systems. sPRFORMN ORG. REPORT N.ME[ .No

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9 KEY WORDS 'Continve on, raeor..r aide Of necessary and Identify by block numbe,

Cure KineticsEpoxies Time-Temperature Transformation Cure DiagramsVitrification Vitrification%Glass Transition

20 ABSTRACI (Centin.,r on rere side if neceecar) and Identify by block number.'

A procedure is provided for estimating the time to full cure versusisothermal cure temperature for vitrified epoxy systems. An equationrelating the glass transition temperature of vitrified epoxy systems tothe time and temperature of cure is developed./ *

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.. . . . . .

TIME-TEMPERATURE-TRANSFORMATION (TTT) CURE DIAGRAMS:

RELATIONSHIP BETWEEN Tg9 AND THE TEMPERATURE AND TIME OF CURE "

FOR EPOXY SYSTEMS Accesion For

NTIS CRA&UTIC TAE3

Xiseng Peng* and J. K. Giliham L1no~ie

X i n sh Ju tlfcationPolymer Materials Program _ _ . . ..

Department of Chemical Engineering By..........

Princeton University Di--t ibitionPrinceton, New Jersey 08544, USAAv1LiyCce

Av.aiiL; P V ~or

Dist o

SYNOPSIS /-

A procedure is provided for estimating the time to full cure versus

isothermal cure temperature for vitrified epoxy systems. An eauation relating

the glass transition temperature of vitrified epoxy systems to the time and

temperature of cure is developed.

*Present address: Changchun Institute of Applied Chemistry, Chinese Academy

of Sciences, Changchun, Jilin, People's Republic of China. IS~r

INTRODUCTION.

The glass transitior temperature, T9, of a thermosetting system is

observed to be higher than the temperature of cure, Tcure, after prolonged

isothermal cure below the system's maximum glass transition temperature, Tg--

(1-7). This implies that the cure reactions proceed after Tg has risen to

Tcijre (i.e., after vitrification). It is therefore important to investigate

the cure behavior after vitrification. This communication is concerned with ,

the relationship between Tg, Tcure and time of isothermal cure for two epoxy

systems cured to beyond vitrification. The conclusions apply to both systems.

Linear T - Tcure relationships were obtained after cure at different

temperatures for fixed times. The temoe-atures of cure for lull cure to occur

in the same fixed times could be obtained by extrapolation of the appropriate

Tg - Tcure relationships to To. The time to full cure versus Tcure is ore-

sented in a time-temperature-transformation (TTT) cure diagram together with

the times to gelation and to vitrification (1-7). An empirical Ta - Tcure

time eouation is also developed. The two epoxy systems investigated were a L-4

difunctional and a trifunctional epoxy resin each cured with the same tetra-

functional aromatic diamine.

. .-...

... 2.

EXPERIMENTAL

Materials -

The difunctional eooxy was a diglycidyl ether of bisphenol A (DER 331,

Dow Chemical Co.), the trifunctional epoxy was the triglycidyl ether of

tris(hydroxy phenyl)methane (XD 7342.00, Dow Chemical Co.), and the curing

agent was trimethylene glycol di-p-aminobenzoate ("TMAB", Polacure 740M,

Polaroid Corp.). Stoichiometric formulations were prepared on the basis of

one eooxy grou1, per amine nyarogen.

Cure, T ano T Measurements

The eooxy resi- systems we-e cured isothermally at different tern-

Deratures in a flowing atmosphere of dry helium in a torsional braid analysis

(TBA) chamber (1). Each specimen was orenared using a Ta')tifilamented heated-

cleaned glass braid imoregnated with a solution of the reactants (! g. solild'l

ml methyl-ethyl ketone). Changes due to cure were monitored as a function of

time by measuring the frpiniirnry (~ 1 Hz) and decay of intermittently induced

free oscillations; the times to gelation and to vitrification were located by

maxima in the logarithmic decrement plots. Each specimen was cured for a pre-

selected time, which was longer than the time to vitrification, at the tem-

perature of cure, Tcure. After isothermal cure, dynamic mechanical spectra ~-

1 Hz) of the sDecimens were obtained on cooling from Tcure to -180C and then

on heating, to 2400C for the DER 331/TMAB system and to 280°C for the XD/TMAB

system, at a rate of 1.50C/min. Spectra were then obtained on subseouent

->.;-

"-4 "

• " -> >,--i ;." S-.}.L. L.>,-.,.. ,.I;,.;>;L............................................................... -.-..-..'.-,.,-.,.----..-,.

- . -.- _. . . - r ;. - L. r r w w- r .r - r.Jt . . -. -. . ... : .- - .-.. + - . . . - - .- .

3.

cooling. The glass transition temDerature, Tg, was identified by the tem-

Perature of the principal maximum in the logarithmic decrement Dlot during the

heating scan. The maximum glass transition temoerature, Tg(, was identified

as the glass transition temperature during the subseauent cooling scan (from

240*C for DER 331/TMAB and from 280*C for XD/TMAB).

The data for Tg versus Tcure for different cure times were compared

(not shown). A small increase in Tg,, with increasing temperature of isothermal

cure for DER 331/TMAB was observed. This behavior is attributed to the cure

not being completed by heating to and cooling from 2400 C after the isothermal

cures. The Tg,, data for the XD/TMAB system followed a trend in which the

higher values of Tg. were obtained with high cure temoeratures for short cure

times, low cure temoeratures for long cure times, and intermediate cure tem-

peratures for intermediate cure times. This behavior could be attributed to

the competition between cure (which increases Tg) and thermal degradation

(which decreases Tg) at the high temperatures which are necessary for curing

this high Tg,. system. Average values of Tg=, were used for the calculations in

this paper: 1680C for the DER 331/TMAB system (range 166 to 170*C), and 268*C

for the XD/TMAB system (range 261 to 278*C).

RESULTS AND DISCUSSION

Tgvs. Tcure

The data for Tg vs. Tcure for the DER 331/TMAB and XD/TMAB systems for

different times of isothermal cure are given in Tables I and 2, and are

plotted as Tg vs. Tcure in Figures 1 and 2. A set of aooroximately parallel

• . .. . . . . . . . . . . . . . . . . . . . . . . . . . .-.

.,-...-,..

'-nes we'-, obtained for each system. Each line represerts a lin(-s rela-

tionship between T. ano "cure for the same cure time (which was io,':,et tnan,

the time to vitrification). Therefore "'" -',

Tg= A + BTcure () -

where A depends on, and B is independent of, the cure time. The values of A

and B for different cure times for the DER 331/TMAB and XD/TMAB systems are

presented in Tables Ill ano IV. The average values of B are 0.98 and 1.24 for ."-

the DER 331/TMAB. system and the XD/TMAB system, respectively (ratio 0.79).

Also, the apparent activation energies, AE, for full cure are 71.6 and 92.7

kcal 'mol for the DEP 331 'TMAB and the XD/TMAB systems, resoectively (ratio

0.78) (see later, Table 7). It is oossible therefore that the sloDE, B, is

related to the activation energy and hence to the reaction mechanism. Since

t e- cure reactio,! for the XD/TMAB system has the higher activation energy

after vitrification, the effect of increasing Tcure 0r g (which increases

with the extent of cure) is greater for the XD/TMAB system than for the DER

331,'TMAB system.

T vs. Time to Full Cure

cure

Assuming that the materials are fully cured when Tg reaches Tg, the

temDerature for full cure to occur in a specified time, T,,(t), was determined

by extrapolation of the Tg Tcure relationship line for the same cure time to

Tg ,, using equation 1. For examole, since for the XD/TMAB system Tg = -2.67 +

1.20 Tcure focr the sixty mlnute cure timpe. then when Tg Tg, 268PC, T cure =1 . 2 0 . . .. .

T,(60) 226°C. In other words, the time to full cure at the cure temoerature

of 226°C, t ,,2 2 6 ), should be 60 minutes. Times to full cue, t,, at d 44feren+

cure temperatures were calculated in this manner. They are presented in Table

5.

For testing the extrapolated conditions for obtaining full cure shown in

Table 5, the DER 331/TMAB system was cured at 148 0C/1440 min, 146°C/2880 min,

and 1410C/8640 min, and the XD/TMAB system was cured at 211°C/1440 min, and

207°C/2880 min. The corresoonding values of 7. obtained from these cure con-

ditions for the DER 331/TMAB system were 165 0 C, 166 0C, arid 166°C, and for the

XD/TMAB system were 2680 C and 265 0C (Figures 1 and 2). They are close to, but

in general below, the averaoe values of T,,. for the DER 331/TMAB system

(168 0 C) and for the XD/TMAB system (2680C).

:f the e traoated data for Tcure versus time to full cure (Table 5) M.-

are plotted as Tcure vs. loo time of cure, a new line results which is

des'arated the full cure 7ire on a Time-Temoerature-Transformatiori (TTT) cure

diagram (Figure 3). The gelled glass region ir the TTT diaora,o is Givided ..-.

into twn Darts by the full cure line. In the absence of decraoatior (Figure

3, devitrification and char formation), the too and lower parts could be

designated fully cured gelled glass (gel glass) and undercured gelled glass

(sol/gel glass) regions, respectively. The TTT diagrams w'th the full cure

lines for the DER 331/TMAB system and for the XD!TMAB system are shown in

Figures 4 and 5, respectively. These lines appear to be linear, which can

therefore be expressed by

-- 7. . -

F. •-.-~ . -- -.___ _.-.-.__ __ __

F.

- C-c t (2)

Knere - ana t are tht- temoerat. ure arC , Pe to fu1' c e resnertively. The

irterce-ts (a) an,. sc-'; (:) 4or the two systems are provided in Table 6. .

-he full cure line should be useful for designing cure processes which lead to

full cure. Selection of the temoerature or time of cure gives thc- time or

temoerature, respectively, to full cure.

The data fo-- tr:. e, traoolated time to full cure versus tem nepature of

isothermal cure for' the two systems are plotted in ar, Arrheniu , maaner as the

logarithmic time versus l/T(K) in Figure 6, which also includes corresponding

data for gelation ar. vltrificat~on. The activation energies for full cure

(after- vitrification), gelation, and vitrification for the DER 331./TMAB and

the XD.'TMAb systems are oresented in Table 7. Trhat the act-vation eneray for

full cu-e is much highe" tha, .- -at 'or celat*or, is a result of the cure reac-

tions being controlled bv nhvsic;1 relaxations in the alass'v state (wh. 4ch

themselves nave similarly high activation eneraies.). "-%"-

T - - Timf- Eauai ora . cure

An eauation relating Tg, Tcure and time of cure can be derived from

eQuatorl, I and 2. From equatior, 1, with Tg g,. and Tcure

T = A + R T (3)

Fo- cure in the same time period, subtracting equation 1 from equation 3

res: l's in

I%

'.r... °.. . . .... . -

- curL'

Subst tutir, 1c, 7 eauation 4 in terms of time using eauation 2 gives

g. Tg B(a + b log t, Tcu"e) (5)

where t, could te any time, t.

Therefore eQuation 5 can be rewritten as

Te 7, -8fa + b Iont - Tcure) (6)

-,e T of the material cured at temoerature Tcure for time t carn be calculated

us1.C tthis T r - time equation.

Th. rA-t-cu ,. ecuaton's fnr the DER 331/TMAB and the X,'7MAB systems

e. e {ormuarec by substituting values for lo, B, a, ard b r ecuat ;cv 6 with .-.-

( e ,o - a..) es 3-6. Fo< 11,e DEP 331,'7MA5 system,

- f.' ioc t 0.9S T - n (7)

- .9 cure

avr ;: r the XD T t~ sytt,,

'a = 14.4P log t + 1.24 Tcu, - (6)

t -s rn- ute,, and Tcure and T are in degrees centigrade.

sy ,em3s,te To calculated (Tg cal) by equations 7 and 8 are included

- -2- t ter with the corresponding experimental values for Ta.

arueenet -oord.

- a- a,-. _ calculation of To from Tcure and curC time for the

V t T . vs. Tcure lines for two sDecified cure times are

. . . . . . . . . ..

. . . . .. . .-.- '.-.-

needed if Tg is knov,,. The r,;; er 6, a a'na -- eouj;i.ic,,, C cF&, be derived

from, thesE- two 1ir-s. J Pced ur E7 a s mE- ore- iaininc hfe rela-

tionshio between Tg' Tcure ana time of cure.

Cor'-ection of Cure Time

The relationship between T 9 and Tcure for the same isothermal cure time

observed in this work is for cure behavior after vitrification since the cure

behavior after vitrification, where the cure reaction oroceeds in the glassy

state, should be different from that before vitrification where the cure

reaction occurs in the liauia and rubbery states. This suggests that the time

of cure should be measured from the vitrification time and that the time of

cure in this work should be corrected by subtractir the vitrification time.

For example, when the DEP 331'TMAR system was cured at lower temoeratures, the

j data points dev iated f rom the st -ao:ht ine (rf~e~ resufrab y for shorter

time'r the data wo,76 a&sf de-cia-zr fror ner y They would be exo~ected to

be Cl-oser tC t :~ . w the t rnes of cure were corrected. For the

XD/TMABR system, thep prrnr-' Were 'eSS because tne timne tO Vitr-ificatiori for the

XD'TMAB system was shorter than for the DER 331/TN AS system. Similarly,

correctina the time ue would be exnerte to reduJce tne difference between

the test values of Tg and the average value of Tg,,(Figures 1 and 2). As a

quantitative example, a sample of the DER33l/TMAB system was cured at 165"C

for 39 minutes which according to equation 2 should give f uil cure. The

Pobserved Tg9 of 117*C was mich lower than Tg,,, (1686C). However, the observed

Twas 167*C when cure at 165*C was for the time to vitrification (351 minu-

tes) plus 39 minutes.

9.

CONCLUSIONS

Analysis of the relationships between the time and temperature of cure

for two epoxy systems has led to the following conclusions for both systems.

1. A linear Ta - Tcure relationship for isochronal cure was observed.

2. The cure temperature for full cure to occur in a given cure time ca-

be determined by extrapolation of the appropriate Tg - Tcure line to T g-. A

plot of Tcure versus log time of cure to full cure yields a new

line, the full cure line, on the time-temoerature-transformation (TTT) cure

diagram.

3. The apparent activation energies for full cure, and for gelation and

vitrification, were obtained from their Arrhenius relationships. The activa-

tion energy for full cure is much higher than those for gelation and vitrifi-

cation as a consecuence of the cure reactions being controlled by physical

relaxations in the glassy state.

4. An empirical Tg - Tcure -time eauation for cure in the vitrified

state has been developed which permits computation of the glass transition

temperature from the temperature and time of cure.

ACKNOWLEDGMENTS

This research was supported in part by the Office of Naval Research.

V.

10.

REFERENCES

1. j. K. Gilihan, "Torsional Braid Analysis (TRA) of Polymers", inDevelopments. in Polymer Characterisatior-3. J. V. Dawkins, Ed. , ApplieGScience Publishers, London, 1982, Ch. 5, pp. 159-227.%

2. J. K. Giliham, "The Time-Temprerature-Tr'ansformation (TT) State Diagramand Cure", in The Role of the Polymer Matrix it) the P'-ocessinc a-dStructural Properties of Composite Materials. J. C. Se-reris and L.Nicolais, Ed., Plenum Press, New York, 1983, po. 1?7-145.

3. J. B. Enns and J. K. Gillham, "Torsional Braid Analysis:Time-Tempoerature-Transformation Cure Diagrams of Thermosetting Epoxy/AmineSystems", in Polymer Characterization: Soectroscornic, Chromatocraohir,and Phys icall Instr-umental Methodls.- C. D. Craver, Ed. , American ChemicalSociety, Advances in Chemistry Series, 1983, No. 203, pn. 27-63.

4. J. B. Enns and J. K. Gillham, "The Time-Temp~erature-Trrnsformation (TTT)Cure Diagram: Modeling the Cure Behavior o f Thermosets", Journal ofApplied4 Polymer Science, Vol. 28, pr). 2567-?Sql (1983).

5. L. C. Chan, H. N. Nat- an~d J. K. Gillham, "Time-Temoeratuire-Transformation(T7T) Diagrarns of High Tg Eooxy Systems: Competition Between Cure andThermal Degradation", Journ;-- of Applied Polymer Science, Vol. 29, Do.3307-3327 (1984).

6. L. C. Chan, 2.K. G llham, A. J. Kinloch and q. J. S~."b&-oieEpoxies: Cure, Transitions, and -o&~i~,~Rtw VoditiEc 71-,p-c, set1Resins. C. K. Riew and Ji. K. Gillhar., Fd. , Amc- ica! CIE--V-ica. So(tyAdvances in Chemistry Series, 1984, Nc.. 208, un. 235-260.

*7. J. K. Gillham, British Po'ymr Journal, 17, 224-220 (1985)

A

TAPUKE CAPTIONS

fr . _,

1. T0 V". -cure for Soe(.ified Times of Cure for, the DER 331/TMAB System.

1", ,.. .

V2. Tc vs. Tcure for Spec-fied Times of Cure for the XD/TMAB System.

3. To A + B Tcure: Value*, of A and P for the DEP 331 /TMA8 System.

4. Tg A -4 B cure- Values of A and B for the XD/TMAB System.

5. Time to Full Cure versus Cure Temoerature for the DER 331/TMAB

and XD/TMAB Systems.

*6. T,,= a + b loo t : Fu',' Cure Lire D;-ameters for, the DFD 3i/TMAB and

the XD/TMAB Systems.

7. Apparent Activation Energies for the isothermal Transformations of the4

DEP 331 'TMAF. and the XKTMAB Systems.

. . .- a . . . .. * r .. . - . . * ' ° ..

. . . . . . . . . . . . . . . . . . . . . . . . . .. . .

- a . .

12. -.- I

FIGURE CAPTIONS

1. To vs. Tcure for the DER 331/TMAB System for Preselected Times of Cure

(Solid Lines):

(7) 720 min, (0) 1440 min; (0) 2880 min; (0) 5760 min; (A) 8640 min; (o)

23040 min. Extrapolated values to Tg,, of T vs. T (,). Also:

experimenta7 test values of Tg (0,0, and A) from the extraoolated values9

of Tcure (see text). Also included is the line for the average value of

Tg,, and the Tg Tcure line (whic:1 is not for constant t:mE).

2. Tg vs. Tcure for the XD/TMAB System for Preselected Times of Cure

(Solid Lines):

(V) 60 min; (3) 300 min; (0) 1440 min; (0) 2880 min; (A) 5760 min; (o)

14440 min. Extrapolated values tc. Tgx. of Tg vs. Tcure (.). Also:

exnep'rrertal test values of To (1 andO)) from the extraoolated values of

Tcure (see text). Also included is the line for the average value of 17--0

and the To Tcure line (which is not for constant time).

3. Schematic Isothermal Time-Temoerature-Transformation (TTT) Cure Diagram

Disolaying TemPerafure of Cure, Tcure, vs. Times to Gelation,

Vitrification, Full Cure and Char Formation. The full cure line (Tg =

Tg,.) is constructed so as to connect the ohysical1y controlled

relationsFKp in the glassy state with the chemically controlled rela-

tionship above Tg+ .

4. TTT Cure Diagram for the DER 331/TMAB System: (S) Gelation

(exoerimental); (o) VitriFicatior; (exoerimental); (A) Full Cure

(calcula~ed, see tex"..

.. . . . . . . . . .. [-

r> %'

13.

*5. 7-1 Cure Diagram for the K)ITMAC, System: (U) Gelation (exoerimental); (o)

Vitrification (exoerimental); (A) Full Cure (calculated, see text).

*6. Ln Time (min) vs. 1/T(K) for the DER 331/TMAB System: (V) Gelation; (U)

Vitrification; (0) Full Cure. Also Ln Time (min) vs. l/T(K) for the

XD/TMAB System: (0) Gelation: (&) Vitrification; (o) Full Cure.

Activation energies were obtained from the regions of linear data (solid

1lines).

14.

LA COI..O-

F E

4- acccc

L N LO L

0M CO

H~ 0 N Ncc. C7 0

0 Cs Cs

Cs1

C CL

4-' 4-J~

u 0

L~ 4) L ~ ' ..

15.

0 c~ cc

Cm ccNN N~ C14

U), 14 Cf C

co o

*4- a, LO U'

0 c NC Ct

-4 N C U14

'4-

00

CD c N t - c

L) E1 m Nl N

c ell. C'.

04 04 C

C, ccccN 0f -4 V -0

C O c') C')

L E

0

04 (D ( cc C ko cc

4). N 4 N co U) M) 0)L CNj

u c~OD tot

(Ci C1 --

a) UF- cc

M0 E 0 S L

U a)) 4)

4) ..- ..- V

16.

TAB.E 3. 7 A + B T7u~e: Valties o' A ' t fot tt ' 33 AB Sysfe, DEE

720 min 1440 min 2880 min 5760 min 8640 m4 n 23040 min

A 13.40 21.70 34.09 26.49 30.36 35.50

Ba 1.01 0.99 0.92 1.00 0.98 0.98

rb 0.99 0.99 1.00 1.00 1.00 1.00

a Average value of B = 0.98

b Corre 7ation coefficient

TABLE 4. To A + B Tcure: Values of A and B for the XD/TMAB System

CureTime 6G min 300 min 1440_min 2880 min 5760 min 14400 min

A -2,67 -2.56 9.27 11.01 15.45 15.84

BC 2D 1. 24 1 .-22 1.24 1. 2Z 11.27 "- -

rd i.0 1.00 -.00 1.00 1.00 1.00

c Averaae value of B = 1.24

d Correlation coefficient

. . A.

,.-',...-

-.:

..............

17.

TAB',E 5. 7iriu to Full Cure versi.s 'c'~r ~,rDEP 331 'TMAS and XO/TMA6 Systems.

System DER 331/TMAS (Tg(,, 1 68*C) XD/TMAS (To, 268*C)

Tcure, 00 152 148 146 142 141 136 226 218 211 207 203 'qf

1/Txl000,0 K 2.35 2.38 2.39 2.41 2.42 2.45 2.00 2.04 2.07 2.08 2.1C 2.12

t~ m r 720 1440 2880 5760 8640 230zn 60 300 14, 2880 5760 7~40"

TABLE 6. T, a + b log t : Pul2l Cure Line Param'pte-s for the

DER 331 /TMAB and the XDJ<TMAB Systems

Cor-e at ion-System Intercent (al S 1OoeJb', Coefficient I

*DER 331!/TMAB 181.47 -10.39 0.99

XD/TMAB 247.11 -11.68 '.00

17,~ C

18.

TABLE 7. Apparent Activation Energies fo-' Isothermal Transformationsfor DER331'TMAE and the XD!/TMAB Systems

AE1 &El 2 E

System Gelation Vitr.4lication Pull Cure

bDER331/TMAB 13,6 9.2 71.6

XDITMA3 13.7 10.9 92'. 7

1) AE in kcal/mcloe.

2) A~E for vitrificaticr determined 'ram thr, liinear region ofvitrificatior curve (Fia. 61

040T-* *4 0

oo 14 oDV t C'O)

aI 0C4 %EE

CO~C 10- o

0 14

CDC

o V 0

C...

040N

N %

E E 0

a 0 0

S EE co

E? 040

to 0

x co

0 0 0U.U

0

I- 0

0 0 0 0 0 0N m N

(3)l

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TE . IC, FEOC.E 7 C:S7. :E c' 7,.; , LIST, GEN

No. C.Copies CC

Office of Naval Research 2 Dr. David Young .Attn: Code 413 Code 334800 N. Quincy Street NOP..;

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Defense Technical Information Center 22 Mr. John Boyle 1E 'd - - , Ca- e -M .- , Materials Bran hA'eY2En:-i, Vircinia 222-i Naval Ship Ercinee~inc Ce-tr -

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Dr. William TollesSuperintendent -

Chemistry Division, Code 6100Nave? Rese--ch La5t:atcrvWashincton, D.C. 20375.

. . . .....

T =a 4 b log t, (2)

wnere ano t, are the temoerature and time to full cure, resoectively. The

intercepts (a) anc slopes (b) for the two systems are provided in Table 6.

The full cure line should be useful for designing cure processes which lead to

full cure. Selection of the temperature or time of cure gives the time or

temperature, respectively, to full cure.

The data for the extrapolated time to full cure versus temioerature of

isothermal cure for- the two systems are plotted in an ArrheniuS manner as the

logarithmic time versus l/T(K) in Figure 6, which also includes corresoonding

data for gelation anr. vitrificat'on. The activation energies for full cure

(after vitrification), gelation, and vitrification for the DER 331/TMAB and

the XD/TMAB systems are oresented in Table 7. T hat the act'vation energy for

full cure is much higher tha-, -k ai 'or celatior, is a result of the cure reac-

tions being controlled by nhy-ic l relaxations in the alassy state (which

themselves have similarly high activation eneraiec'.

T - T - Tim(- Eaua" or,_g cure

An eauation relating Tg, Tcure and time of cure can be derived from

equations I and 2. From equation 1, with Tg =T- and Tcure =T.,

T = A + B T (3)

For cure in the same time period, subtracting equation 1 from eauation 3

results in

~~~~........ ............................... ............. .........::: ::..... . :::...............:":,. . . ... ..... .. . . . . . . .. . . . . . .. .: : .. .,,. . .-. .-... .. : - .- : : : : -- : . . .: , :

V-

, . ( T , Tcure) (4)

Substituting for T -n eouation 4 in terms of time using eauation 2 gives

T T1,- Tg = B(a + b log t, - Tcure) (5)£

where t, could be any time, t.

Therefore equation 5 can be rewritten as

T= To, -B(a + b lo t - Tcure) (6)

The Tg of the material cured at temoerature Tcure for time t can be calculated

usina this Tg - Tcure - time eauation.

The Parzicular equations for the DER 331/TMAB and the XD/TMAB systems

were formulated by substituting values for Tg... B, a, and b ir eauation 6 with

the data in Tables 3-6. For- the DER 331/,TMAB system,

T 10.18 loc t 0.98 T 10 (7)9

and for the XD/TMA6 systeoi,

Tg = 14.48 log t + 1.24 Tcur e -a (8)

where t is in minutes, and Tcure and Tg are in degrees centigrade.

For both systemsthe Tg calculated (Tg cal) by equations 7 and 8 are included

in Tables i and 2 together with the corresponding experimental values for Tg.

The agreement is good.

For an approximate calculation of T0 from Tcure and cure time for the

epoxy systems, only two Tg vs. Tcure lines for two sDecified cure times arec-

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