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The structure of gel and sol fractions of epoxy compositions
Structure of gel a n d sol fractions of epoxy compositions
1823
3. P. G. BABAYEVSKII and Ye. B. TROSTYANSKAYA, Vysokomol. soyed. 17: 723, 1975 4. V. I. KLENIN, S. Yu. SHCHEGOLEV a n d V. I. LAVRUSHIN, Kharakteristicheskiye funktsii svetorasseyaniya dispersnykh sistem (Characteristic Functions of Light Scattering of Dispersed Systems). Izd. Saratovskogo un-ta, 1977 5. W. HELLER, H. L. BHATNAGAR a n d M. NAKAGAKI, J. Chem. Phys. 36: 1163, 1962 6. W. HELLER a n d W. PANGONIS, J. Chem. Phys. 26: 498, 1957 7. B. SEDLACEK, Collect. Czeehosl. Chem. Commtm. 32: 1374, 1967 8. G. VAN DE HOLST, Rasseyaniye sveta m a l y m y chastytsami (Light Scattering b y Small Particles). Izd. inostr, lit., 1961 9. V. I. KLENIN and S. Yu. SHCHEGOLEV, Vysokomol. soyed. A I 3 : 1919, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 8, 2161, 1971) 10. D. A. KARDASHOV, Sinteticheskiye klei (Synthetic Resins). Izd. " K h i m i y a " , 1976 11. Ts. M. LEVITSKAYA, K a n d i d a t s k a y a dissertatsiya (Post-Graduate Thesis). L e n i n g r a d , IVS AN SSSR, 1970 f 12. T. E. LIPATOVA, K a t a l i t i c h e s k a y a polimerizatsiya oligomerov i formirovaniye polim e r n y k h setok (Catalytic Polymerization of Oligomers and Polymer Network F o r m a tion). Izd. " N a u k o v a d u m k a " , 1974 13. A.A. BERLIN, Sb. p r e p r i n t o v , D o k l a d y yubileinoi sessii po MMS, I K h F A N SSSR (Preprints) (Papers r e a d a t the J u b i l e e Session of ttMC, ICF, U S S R A c a d e m y o f Sciences), 1970 44. K. DUSEK, J. P o l y m e r Sci. C 16: 1289, 1967 15. S. F R E N K E L and V. BARANOY, Brit. P o l y m e r J., 228, 1977 16. T. L. HILL, Thermodynamics of Small Systems, W. A. Benjamin Inc. New Y o r k - A m sterdam, 1963 17. V. G. BARANOV and S. FRENKEL', 1976-th Prague Meeting on Macromolecules, p. 38 18. P. J. FLORY, J. Amer. Chem. Soc. 78: 5222, 1956
Polymer ScienceU.S.S.R. Vol. 21, pp. 1823-1829. Pergamon Press Ltd. 1980. Printed in Poland
0032-3950/79/0701-1823507.50/a
THE STRUCTURE OF GEL AND SOL FRACTIONS OF EPOXY COMPOSITIONS* V. A . TOPOLKARAYEV, L . A . ZHORIbTA, •. V. VLADIMIROV, AL. AL. BERIng, A. N. ZELENETSKII, E . V. ]:)RUT
and N. S. YESTIKOLOPYA:N I n s t i t u t e of Chemical Physics, U.S.S.R. A c a d e m y of Sciences
(Received 3 August 1978) A s t u d y was made of the clmmical structure of gel and sol fractions of solidified e p o x y compositions based on 4,4'-diaminodiphenylsulphone and resorcin diglycidyl ester. Decomposition of gel and sol fractions was carried out using a Soxhlet a p p a r a t u s and boiling acetone. The a m o u n t of unreacted e p o x y groups was determined in gel * Vysokomol. soyed. A21: N.o. 7, 1655-1659, 1979.
1824
V. A. TOPOT.~A~AYEV et al.
and the proportion of free dicpoxide, in sol. I t was shown that up to 50~/o diepoxide excess of the sol fraction consists mainly of free diepoxide. Results of experiments were compared with data concerning the statistic~al model of crosslinked polymer structure. A STUDY was made" o f t h e chemical s t r u c t u r e o f gel a n d sol f r a c t i o n s o f e p o x y c o m p o s i t i o n s b a s e d on 4 , 4 ' - d i a m i n o d i p h e n y l s u l p h o n e used as h a r d e n e r a n d resorcin diglyeidyl ester. This s y s t e m w a s selected for t h e q u a n t i t a t i v e a n d qualit a t i v e verification o f m o d e l theories concerning n e t w o r k f o r m a t i o n [11] for t h e following reasons: in spite o f t h e c o m p l e x i t y of t h e m e c h a n i s m of h a r d e n i n g o f e p o x i d e s b y a r o m a t i c a m i n e s [2-7] it was s h o w n t h a t p r a c t i c a l l y no s e c o n d a r y r e a c t i o n s t a k e place a t m o d e r a t e t e m p e r a t u r e s of h a r d e n i n g in t h e s y s t e m a n d n e t w o r k f o r m a t i o n is t h e result of t h e p o l y - a d d i t i o n of t h e N H g r o u p of d i a m i n e t o t h e e p o x i d e ring; initial r e a g e n t s b l e n d s a t i s f a c t o r i l y a n d during t h e r e a c t i o n t h e s y s t e m r e m a i n s fairly h o m o g e n e o u s ; t h e r i g i d i t y o f a d i a m i n e molecule arid t h e s h o r t c o n t o u r length of t h e e p o x i d e oligomer suggest t h a t t h e n e a r e s t a d j a c e n t links r e a c t d u r i n g n e t w o r k f o r m a t i o n , t h e r a p i d increase in t h e v i s c o s i t y o f t h e s y s t e m as a result of t h r e e d i m e n s i o n a l crosslinking c o n s i d e r a b l y r e d u c i n g molecular mobility. Chromatographically pure compounds were used: resorein diglycidyl ester (DE), (b.p. 170°/10 -z torr, M=222, epoxy number 37-8) and 4,4'-diaminodiphenylsulphone (DS), (m.p. 178 °, M=248). Initial substances were purified by standard methods. The degree of purity was determined from the melting point and by thin layer chromatography. Reaction components were mixed at 120°4~ntil the solution was fully homogeneous. Solidification was carried out in test tubes treated with an antiadhesive, dimethyldichlorosilane in a heal chamber at 150° for 5 hr. The samples obtained were ground to a finely dispersed powder. The powdered samples were extracted using boiling acetone in a Soxhlet apparatus and with dimethylformamide at room temperature. The solvent from the .extract (sol fraction) was distilled in vacuum using a rot.or type evaporator. Sol and gel fractions were dried at T = 20 ° under high vacuum to constant we.ight. To determine the molecular weight of the sol fraction a method was used which is based on the measurement of heat effects of condensation (MHEC). The composition of the gel fraction was analysed by thin layer chromatography. The amount of diepoxide in the mixture was determined by preliminary calibration ~/~' = k log c, where S is the area of the spot of the individual material on the chromatographic pattern (mm2), c, concentration of the solution applied in acetone (mole/1.), k, constant equal to 0.3 mole/1. The epoxy number in the gel fraction was determined by hydrochlorination in acetone or dioxane. Epoxy group content was determined from the relative band intensity at 910 cm -1, corresponding to bond stretching vibrations of the C--C bond in the epoxyring. The band at % / 770 cm -x corresponding to mixed vibrations of the C - - O - - C - - bond was used as inter/ \ nal standard. A UR-20 spe~tromv~er was used to obtain I R spectra. I n o r d e r to d e t e r m i n e t h e r a n g e of a p p l i c a b i l i t y o f t h o m o d e l p r o p o s e d for gel f o r m a t i o n [1], it wag of i n t e r e s t to c~rry o u t a s t r u c t u r a l a n a l y s i s b o t h bef o r e t h e gel p o i u t a n d in t h e region of th~ gel-like s t a t e w i t h h i g h d e g r e e s of con-
Structure of gel and sol fractions of epoxy compositions
1825
version of reaction groups. A s t u d y was made of compositions with different reagent ratios, which enabled the conversion of reaction groups to be varied within a wide range in the system. ridABLE 1.
EXPERIMENTAL
AND
THEORETICAL
TIOI~ O F D E
RATIOS
A1/A~
A1/A~
[E]:[A]
(exp)
( c o m b ) (sta$.mod)
0,2 0.15 0.125
4.9 5.95 7.5
Aj
• ~~-~x~
(A~/A2)
AND
(A,/A3) r ' o R
TEE REAC-
WITH m-P~ENYLENEDIANIINR
4.1 5.22 7.0
AI/A~ 5±0.5 5.7±0.5 6-3tl
A~/A8
AJA3
A,/Aa
(exp)
(comb)
(stat. mod)
3.6 5-3 --
4.1 4.5 6.0
3-3~0.5 5~1 --
A2 -'-
.A 3
In the range up to the gel point reaction products represent a soluble sol fraction which enables detailed chromatographic analysis to be made of the system and relative product concentrations to be calculated. This analysis was carried out previously [8] for epoxy compositions based on DE and m-phenylene diamine. The authors examined compositions with considerable diamine excess, [E] :[A]=0.125-0.2 and conversions of reaction groups much lower t h a n t h e critical, corresponding to the gel point (here and further [E], [A] are the molar concentrations of diepoxide and diamine). A numerical calculation was made o f relative concentrations of X-reefs formed during the reaction for the ratios examined in the study mentioned [8]. The calculation was based on an analysis of structural curves plotted using a computer. As a result the number of branched chains (i) of size x~ was calculated. Averaging was carried out in each case for four-five similar curves. Alternatives with different probabilities of monoeyclization were analysed. Most satisfactory agreement between numerical calculation a n d experimental results was observed with zero probability of monocyclization (Table 1). Analysis of structural curves indicates t h a t with such considerable
1826
V. fl-. TOPOLEARAYEVe~ al.
diamine excess branched chains are formed exclusively. The formation of closed cyclic mierostructures is unlikely. This rdsult confirms the assumption conrcening the absence of ring formation in combinatorial calculations [8]. Results of TABLE
2.
RESULTS
OF
ANALYSING
LIMITED
COI~VERSION
OF
]EPOXY GROUPS I N COMPOSITIOI~S W I T H ]~QUII~IOLECULAR RATIOS OF R E A G E N T S
Conditions of hardening time, hr 4 5 2
0/
13
Degree of conversion, % according to the epoxy according to number IR spectra
T, °C 150 150 139 150 130
]
95 96
. / I
96 96
90 92
calculation adopted from a previous study [8] are given in Table 1. Satisfactory agreement is observed (within the framework of statistical variation) between results of numerical simulation on a lattice and the combinatorial approach. I t T A B L E 3. R E S U L T S OF A S T R U C T U R A L A-WALYSIS OF G E L A N D SOL F R A C T I O N S OF COIII~OSITIONS B A S E D O1~ D E
[E]:[A] 2 2.5 2.96 3-4 4.5 6
~,%
~,%
(acetone/DMF)
(calc.)
0 2/1
0 3 10.5 18 47 100
9/1l 20 46 100
AND DS
~.~ind
e ,% (exp) 0 2/1
9/11 19 3O 41
Theoretical calculation J s~~d,% I G , %
so,% 0 3 10 17 42 84
0 3 8-9 12-14 22-32
0 33 46 56 60 84
Note. ,,.q. is the gravimetric proportion of the sol fraction; Sc gravimetric proportion of diepoxide not forming part o f the gel fraction; S. jnd, gravimetrie proportion of free diepoxide.
should be noted, however, t h a t the proportion of cyclic formations increases m a r k e d l y with relative concentrations of reagents close to the critical and disregard for reactions of ring formation m a y involve considerable error. The region of gel-like state of a three dimensional system is characterized b y higher conversions of reaction groups, the polymer being formed of an infinite network. Analysing three dimensional compositions with different degrees of hardening, or systems hardened to a m a x i m u m extent with different reagent ratios information m a y be obtained concerning the structure of a number of gel-like systems, starting from loose networks with a high proportion of soluble fraction
Structure of gel a n d sol fractions of epoxy compositions
1827
and ending with densely crosslinked compositions, in which sol forms fractions of 1%. A system with equimolecular reagent ratio was first analysed; different conditions of hardening (Table 2) were used to determine the maximum yield of the reaction (Table 2). Maximum conversion was less than 96% in every case and the soluble fraction was completely absent. With a diepoxide excess sol was formed (Table 3) and as shown b y chromatographic and I R analyses, up to 50% excess it consisted of free diepoxide. The molecular weight of the soluble fraction (Table:3) was close to Me of the individual diepoxide (Me~222, Ms=238).
70
50i
3O
I0
2
3
# [E] : [A]
Results of a comparative analysis of tim structure of gel and sol fractions: / - - c o n t e n t of free epoxy ends in gel, 2--wt.°/o of free diepoxide molecules in the system; notations of I and ~- correspond to theoretical calculation.
With a further increase in the [El : [A] ratio the proportion of free diepoxid~ ir~ sol decreased and reaction products not "crosslinked" in a network were extracted in the solution (Table 3). The gel fraction was analysed according to the content (%) of partially reacted diepoxide molecules in the network. In proportion to the increase in diepoxide excess, the proportion of these molecules (free ends) increased, which markedly loosened the network. When [El : [A] = 6, the combined state of the system was completely disrupted and the composition was a fully soluble polymer. A similar disruption in the combined state was also obserced in a diamine excess with a ratio of [El : [A]----0.67. As noted previously [1], a statistical model of crosslinked polymer structures enabled an analysis to be made of the effect of the relative concentration of components on network structure and maximum yield of the reaction for epoxide. Furthermore, the number of diepoxide molecules which had not entered the reaction and the number of free ends in the three dimensional system were calculated.
~828
V.A.
TOPOLKARAYEV 6~ al.
The gravimetric content of free diepoxide in the system and the percentage ~ f partially reacted diepoxide molecules in t~he network were calculated for compositions examined in Table 3. In every case the result was averaged for four-six similar methods. Statistical variation was under 3-4~/o of average values, k variation of the probability of monocyclization near the zero value did not improve the convergence of results, it was therefore assumed that mono-ring formation was absent. Results of a comparative analysis are shown in the Figure. Theoretical calculation and experimental results show satisfactory agreement. A somewhat :reduced content of free epoxy ends in gel could be caused by partial hydrolysis oof epoxy groups during extraction. The statistical model proposed therefore enabled a description to be given o f the structure of gel and sol fractions of epoxy compositions, whereby kinetics and the topology of network formation were only considered (ignoring the possible nonhomogeneity of the process). For a DE-DS system most satisfactory agreement between experiment and theory was observed assuming zero probability of monocyclization. Table 3 shows results of calculating the yield of the sol fraction for different ,~legrees of diepoxide excess, using the theory of cascade processes [9, 10]. The content of unreactcd epoxy groups in gel fraction G was calculated on the basis •of the existence of balance between reaction groups in the system using the formula G=Eun: (E~: 2)=(Es--A,) : ( E , : 2), where E g = 2 ( ~ °
SePo~, Mee J Ag___4(~o
(1)
SAP0.~, Mx / Eo and A o being the initial
concentrations of epoxy and amino-groups in the system and Po, weight of the :system. Comparing results shown in the Figure and in Table 3 it may be concluded that when describing the chemical structure of densely crosslinked networks the analytical calculation using the method of cascade processes correlates with results of numerical simulation, however, agreement is only observed with nonequimolar reagent ratios. With stoichiometric and near stoichiometric proportions there is a fundamental difference between these statistical methods. I n this range of relative concentrations the method of cascade processes, in which .the reactivity of groups in independent of the dimension and complexity of a "branching tree", predicts a 100% conversion of reaction groups. At the same time, it follows from the analysis described and the description given [1, 11, 12] that topological features of the structure of densely crosslinked networks with reagent ratios close to the stoichiometric, restrict the conversion of reaction g r o u p s (~res~96~/o) and lower the reaction rate constant at advanced stages. Summarizing the foregoing it may be concluded that the statistical model developed, in addition to giving a description of the topological structure of
Structure of gel and sol fractions of epoxy compositions
1829
~ r o s s l i n k e d p o l y m e r s a n d k i n e t i c s of f o r m a t i o n , enables a fairly a c c u r a t e p r e d i c t i o n to be m a d e of t h e p r o p o r t i o n of gel a n d sol fractions, M W D in sol a n d c o n v e r s i o n of r e a c t i o n g r o u p s in gel for real e p o x y compositions. T h e p r o b a b i l i t y o f m o n o c y c l i z a t i o u in t h e s y s t e m m a y be e v a l u a t e d . A n analysis of t h e c o m b i n e d s t a t e of t h e s y s t e m enables t h e r a n g e ~of gel-like s t a t e i.e. t h e b o u n d a r y o f t r a n s i t i o n f r o m 100% sol to p a r t i a l l y c o m b i n e d n e t w o r k to be d e t e r m i n e d . A c o m p a r ison o f m o d e l calculations of kinetics a n d limiting conversions of n e t w o r k - f o r m a t i o n [1] w i t h results of a p r e v i o u s s t u d y [12], w h e r e t h e existence of m a x i m u m yield a n d a r e d u c t i o u in r a t e c o n s t a n t in t h e r e a c t i o n of D E w i t h m - p h e n y l e n e d i a m i n e s w a s confirmed e x p e r i m e n t a l l y , is f u r t h e r evidence o f t h e suit a b i l i t y of t h e m o d e l e x a m i n e d . Translated by E. S]~M~m~ REFERENCES 1. V . A. TOPOLKAREV, V. G. OSHMYAN, V. P. NISICHENKO, A. N. ZELEi'~ETSgII,
A1. AI. BERLIN, E. V. PRUT and N. S. YENIKOLOPYAN, Vysokomol. soyod. A21: No. 7, 1979 (Translated in Polymer Sci. U.S.S.R. 21: 7, 1979) 2 . Kh. A. ARUTYUNYAN, A. O. TONOYAN, S. P. D A V r Y A ~ , B. A. ROZENBERQ and N. S. YENIKOLOPYAN, Dokl. AN SSSR 212: 1128, 1973 3. N. S. VEDENYAPINA, V. P. KUZNETSOVA, V. V. IVANOV and N. S. YENIKOLOPYAN, Izv. AN SSSR, ser. khim., 1970, 1956 4. Y. T. SMITH, Polymer 2: 95, 1961 5. J. DOBAS, G. EICHER and J. KLABAN, Collect. of Chem. Commun. 49: 10, 1975 6. R. B. PRIME and E. SACHER, Polymer 13: 9, 1972 7. M. A. ACITELLI, R. B. PRIME and E. SACHER, Polymer 12: 335, 1971 8. N. S. KOGARKO, V. A. TOPOLKARAYEV, G. M. TROFIMOVA, V. V. IVANOV, AI. AI. BERLIN, D. D. NOVIKOV and N. S. YENIKOLOPYAN, Vysokomol. soyod. A,20: 756, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 4, 852, 1978) 9. M. GORDON, Prec. Roy. See. A268: 1333, 1902 10. Ye. N. RASPOPOVA, V. N. IRZHAK, L. M. BOGDANOVA and N. S. YENIKOLOPYAN, Vysokomol. soyed. B16: 434, 1974 (Not translated in Polymer Sci. U.S.S.R.) 11. A1. A1. BERLIN and V. G. OSHMYAN, Vysokomol. soyed. AIS: 2282, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 10, 2612, 1976 12. L. K. PAKI~OMOVA, O. B. SALAMATINA, S. A. ARTEMENKO, AI. AI. BERLIN and N. S. YENIKOLOPYAN, Vysokomol. soyed. B20: 554, 1978 (Not translated ii~ Polymer Sci. U.S.S .1~.)
1823
3. P. G. BABAYEVSKII and Ye. B. TROSTYANSKAYA, Vysokomol. soyed. 17: 723, 1975 4. V. I. KLENIN, S. Yu. SHCHEGOLEV a n d V. I. LAVRUSHIN, Kharakteristicheskiye funktsii svetorasseyaniya dispersnykh sistem (Characteristic Functions of Light Scattering of Dispersed Systems). Izd. Saratovskogo un-ta, 1977 5. W. HELLER, H. L. BHATNAGAR a n d M. NAKAGAKI, J. Chem. Phys. 36: 1163, 1962 6. W. HELLER a n d W. PANGONIS, J. Chem. Phys. 26: 498, 1957 7. B. SEDLACEK, Collect. Czeehosl. Chem. Commtm. 32: 1374, 1967 8. G. VAN DE HOLST, Rasseyaniye sveta m a l y m y chastytsami (Light Scattering b y Small Particles). Izd. inostr, lit., 1961 9. V. I. KLENIN and S. Yu. SHCHEGOLEV, Vysokomol. soyed. A I 3 : 1919, 1971 (Translated in Polymer Sci. U.S.S.R. 13: 8, 2161, 1971) 10. D. A. KARDASHOV, Sinteticheskiye klei (Synthetic Resins). Izd. " K h i m i y a " , 1976 11. Ts. M. LEVITSKAYA, K a n d i d a t s k a y a dissertatsiya (Post-Graduate Thesis). L e n i n g r a d , IVS AN SSSR, 1970 f 12. T. E. LIPATOVA, K a t a l i t i c h e s k a y a polimerizatsiya oligomerov i formirovaniye polim e r n y k h setok (Catalytic Polymerization of Oligomers and Polymer Network F o r m a tion). Izd. " N a u k o v a d u m k a " , 1974 13. A.A. BERLIN, Sb. p r e p r i n t o v , D o k l a d y yubileinoi sessii po MMS, I K h F A N SSSR (Preprints) (Papers r e a d a t the J u b i l e e Session of ttMC, ICF, U S S R A c a d e m y o f Sciences), 1970 44. K. DUSEK, J. P o l y m e r Sci. C 16: 1289, 1967 15. S. F R E N K E L and V. BARANOY, Brit. P o l y m e r J., 228, 1977 16. T. L. HILL, Thermodynamics of Small Systems, W. A. Benjamin Inc. New Y o r k - A m sterdam, 1963 17. V. G. BARANOV and S. FRENKEL', 1976-th Prague Meeting on Macromolecules, p. 38 18. P. J. FLORY, J. Amer. Chem. Soc. 78: 5222, 1956
Polymer ScienceU.S.S.R. Vol. 21, pp. 1823-1829. Pergamon Press Ltd. 1980. Printed in Poland
0032-3950/79/0701-1823507.50/a
THE STRUCTURE OF GEL AND SOL FRACTIONS OF EPOXY COMPOSITIONS* V. A . TOPOLKARAYEV, L . A . ZHORIbTA, •. V. VLADIMIROV, AL. AL. BERIng, A. N. ZELENETSKII, E . V. ]:)RUT
and N. S. YESTIKOLOPYA:N I n s t i t u t e of Chemical Physics, U.S.S.R. A c a d e m y of Sciences
(Received 3 August 1978) A s t u d y was made of the clmmical structure of gel and sol fractions of solidified e p o x y compositions based on 4,4'-diaminodiphenylsulphone and resorcin diglycidyl ester. Decomposition of gel and sol fractions was carried out using a Soxhlet a p p a r a t u s and boiling acetone. The a m o u n t of unreacted e p o x y groups was determined in gel * Vysokomol. soyed. A21: N.o. 7, 1655-1659, 1979.
1824
V. A. TOPOT.~A~AYEV et al.
and the proportion of free dicpoxide, in sol. I t was shown that up to 50~/o diepoxide excess of the sol fraction consists mainly of free diepoxide. Results of experiments were compared with data concerning the statistic~al model of crosslinked polymer structure. A STUDY was made" o f t h e chemical s t r u c t u r e o f gel a n d sol f r a c t i o n s o f e p o x y c o m p o s i t i o n s b a s e d on 4 , 4 ' - d i a m i n o d i p h e n y l s u l p h o n e used as h a r d e n e r a n d resorcin diglyeidyl ester. This s y s t e m w a s selected for t h e q u a n t i t a t i v e a n d qualit a t i v e verification o f m o d e l theories concerning n e t w o r k f o r m a t i o n [11] for t h e following reasons: in spite o f t h e c o m p l e x i t y of t h e m e c h a n i s m of h a r d e n i n g o f e p o x i d e s b y a r o m a t i c a m i n e s [2-7] it was s h o w n t h a t p r a c t i c a l l y no s e c o n d a r y r e a c t i o n s t a k e place a t m o d e r a t e t e m p e r a t u r e s of h a r d e n i n g in t h e s y s t e m a n d n e t w o r k f o r m a t i o n is t h e result of t h e p o l y - a d d i t i o n of t h e N H g r o u p of d i a m i n e t o t h e e p o x i d e ring; initial r e a g e n t s b l e n d s a t i s f a c t o r i l y a n d during t h e r e a c t i o n t h e s y s t e m r e m a i n s fairly h o m o g e n e o u s ; t h e r i g i d i t y o f a d i a m i n e molecule arid t h e s h o r t c o n t o u r length of t h e e p o x i d e oligomer suggest t h a t t h e n e a r e s t a d j a c e n t links r e a c t d u r i n g n e t w o r k f o r m a t i o n , t h e r a p i d increase in t h e v i s c o s i t y o f t h e s y s t e m as a result of t h r e e d i m e n s i o n a l crosslinking c o n s i d e r a b l y r e d u c i n g molecular mobility. Chromatographically pure compounds were used: resorein diglycidyl ester (DE), (b.p. 170°/10 -z torr, M=222, epoxy number 37-8) and 4,4'-diaminodiphenylsulphone (DS), (m.p. 178 °, M=248). Initial substances were purified by standard methods. The degree of purity was determined from the melting point and by thin layer chromatography. Reaction components were mixed at 120°4~ntil the solution was fully homogeneous. Solidification was carried out in test tubes treated with an antiadhesive, dimethyldichlorosilane in a heal chamber at 150° for 5 hr. The samples obtained were ground to a finely dispersed powder. The powdered samples were extracted using boiling acetone in a Soxhlet apparatus and with dimethylformamide at room temperature. The solvent from the .extract (sol fraction) was distilled in vacuum using a rot.or type evaporator. Sol and gel fractions were dried at T = 20 ° under high vacuum to constant we.ight. To determine the molecular weight of the sol fraction a method was used which is based on the measurement of heat effects of condensation (MHEC). The composition of the gel fraction was analysed by thin layer chromatography. The amount of diepoxide in the mixture was determined by preliminary calibration ~/~' = k log c, where S is the area of the spot of the individual material on the chromatographic pattern (mm2), c, concentration of the solution applied in acetone (mole/1.), k, constant equal to 0.3 mole/1. The epoxy number in the gel fraction was determined by hydrochlorination in acetone or dioxane. Epoxy group content was determined from the relative band intensity at 910 cm -1, corresponding to bond stretching vibrations of the C--C bond in the epoxyring. The band at % / 770 cm -x corresponding to mixed vibrations of the C - - O - - C - - bond was used as inter/ \ nal standard. A UR-20 spe~tromv~er was used to obtain I R spectra. I n o r d e r to d e t e r m i n e t h e r a n g e of a p p l i c a b i l i t y o f t h o m o d e l p r o p o s e d for gel f o r m a t i o n [1], it wag of i n t e r e s t to c~rry o u t a s t r u c t u r a l a n a l y s i s b o t h bef o r e t h e gel p o i u t a n d in t h e region of th~ gel-like s t a t e w i t h h i g h d e g r e e s of con-
Structure of gel and sol fractions of epoxy compositions
1825
version of reaction groups. A s t u d y was made of compositions with different reagent ratios, which enabled the conversion of reaction groups to be varied within a wide range in the system. ridABLE 1.
EXPERIMENTAL
AND
THEORETICAL
TIOI~ O F D E
RATIOS
A1/A~
A1/A~
[E]:[A]
(exp)
( c o m b ) (sta$.mod)
0,2 0.15 0.125
4.9 5.95 7.5
Aj
• ~~-~x~
(A~/A2)
AND
(A,/A3) r ' o R
TEE REAC-
WITH m-P~ENYLENEDIANIINR
4.1 5.22 7.0
AI/A~ 5±0.5 5.7±0.5 6-3tl
A~/A8
AJA3
A,/Aa
(exp)
(comb)
(stat. mod)
3.6 5-3 --
4.1 4.5 6.0
3-3~0.5 5~1 --
A2 -'-
.A 3
In the range up to the gel point reaction products represent a soluble sol fraction which enables detailed chromatographic analysis to be made of the system and relative product concentrations to be calculated. This analysis was carried out previously [8] for epoxy compositions based on DE and m-phenylene diamine. The authors examined compositions with considerable diamine excess, [E] :[A]=0.125-0.2 and conversions of reaction groups much lower t h a n t h e critical, corresponding to the gel point (here and further [E], [A] are the molar concentrations of diepoxide and diamine). A numerical calculation was made o f relative concentrations of X-reefs formed during the reaction for the ratios examined in the study mentioned [8]. The calculation was based on an analysis of structural curves plotted using a computer. As a result the number of branched chains (i) of size x~ was calculated. Averaging was carried out in each case for four-five similar curves. Alternatives with different probabilities of monoeyclization were analysed. Most satisfactory agreement between numerical calculation a n d experimental results was observed with zero probability of monocyclization (Table 1). Analysis of structural curves indicates t h a t with such considerable
1826
V. fl-. TOPOLEARAYEVe~ al.
diamine excess branched chains are formed exclusively. The formation of closed cyclic mierostructures is unlikely. This rdsult confirms the assumption conrcening the absence of ring formation in combinatorial calculations [8]. Results of TABLE
2.
RESULTS
OF
ANALYSING
LIMITED
COI~VERSION
OF
]EPOXY GROUPS I N COMPOSITIOI~S W I T H ]~QUII~IOLECULAR RATIOS OF R E A G E N T S
Conditions of hardening time, hr 4 5 2
0/
13
Degree of conversion, % according to the epoxy according to number IR spectra
T, °C 150 150 139 150 130
]
95 96
. / I
96 96
90 92
calculation adopted from a previous study [8] are given in Table 1. Satisfactory agreement is observed (within the framework of statistical variation) between results of numerical simulation on a lattice and the combinatorial approach. I t T A B L E 3. R E S U L T S OF A S T R U C T U R A L A-WALYSIS OF G E L A N D SOL F R A C T I O N S OF COIII~OSITIONS B A S E D O1~ D E
[E]:[A] 2 2.5 2.96 3-4 4.5 6
~,%
~,%
(acetone/DMF)
(calc.)
0 2/1
0 3 10.5 18 47 100
9/1l 20 46 100
AND DS
~.~ind
e ,% (exp) 0 2/1
9/11 19 3O 41
Theoretical calculation J s~~d,% I G , %
so,% 0 3 10 17 42 84
0 3 8-9 12-14 22-32
0 33 46 56 60 84
Note. ,,.q. is the gravimetric proportion of the sol fraction; Sc gravimetric proportion of diepoxide not forming part o f the gel fraction; S. jnd, gravimetrie proportion of free diepoxide.
should be noted, however, t h a t the proportion of cyclic formations increases m a r k e d l y with relative concentrations of reagents close to the critical and disregard for reactions of ring formation m a y involve considerable error. The region of gel-like state of a three dimensional system is characterized b y higher conversions of reaction groups, the polymer being formed of an infinite network. Analysing three dimensional compositions with different degrees of hardening, or systems hardened to a m a x i m u m extent with different reagent ratios information m a y be obtained concerning the structure of a number of gel-like systems, starting from loose networks with a high proportion of soluble fraction
Structure of gel a n d sol fractions of epoxy compositions
1827
and ending with densely crosslinked compositions, in which sol forms fractions of 1%. A system with equimolecular reagent ratio was first analysed; different conditions of hardening (Table 2) were used to determine the maximum yield of the reaction (Table 2). Maximum conversion was less than 96% in every case and the soluble fraction was completely absent. With a diepoxide excess sol was formed (Table 3) and as shown b y chromatographic and I R analyses, up to 50% excess it consisted of free diepoxide. The molecular weight of the soluble fraction (Table:3) was close to Me of the individual diepoxide (Me~222, Ms=238).
70
50i
3O
I0
2
3
# [E] : [A]
Results of a comparative analysis of tim structure of gel and sol fractions: / - - c o n t e n t of free epoxy ends in gel, 2--wt.°/o of free diepoxide molecules in the system; notations of I and ~- correspond to theoretical calculation.
With a further increase in the [El : [A] ratio the proportion of free diepoxid~ ir~ sol decreased and reaction products not "crosslinked" in a network were extracted in the solution (Table 3). The gel fraction was analysed according to the content (%) of partially reacted diepoxide molecules in the network. In proportion to the increase in diepoxide excess, the proportion of these molecules (free ends) increased, which markedly loosened the network. When [El : [A] = 6, the combined state of the system was completely disrupted and the composition was a fully soluble polymer. A similar disruption in the combined state was also obserced in a diamine excess with a ratio of [El : [A]----0.67. As noted previously [1], a statistical model of crosslinked polymer structures enabled an analysis to be made of the effect of the relative concentration of components on network structure and maximum yield of the reaction for epoxide. Furthermore, the number of diepoxide molecules which had not entered the reaction and the number of free ends in the three dimensional system were calculated.
~828
V.A.
TOPOLKARAYEV 6~ al.
The gravimetric content of free diepoxide in the system and the percentage ~ f partially reacted diepoxide molecules in t~he network were calculated for compositions examined in Table 3. In every case the result was averaged for four-six similar methods. Statistical variation was under 3-4~/o of average values, k variation of the probability of monocyclization near the zero value did not improve the convergence of results, it was therefore assumed that mono-ring formation was absent. Results of a comparative analysis are shown in the Figure. Theoretical calculation and experimental results show satisfactory agreement. A somewhat :reduced content of free epoxy ends in gel could be caused by partial hydrolysis oof epoxy groups during extraction. The statistical model proposed therefore enabled a description to be given o f the structure of gel and sol fractions of epoxy compositions, whereby kinetics and the topology of network formation were only considered (ignoring the possible nonhomogeneity of the process). For a DE-DS system most satisfactory agreement between experiment and theory was observed assuming zero probability of monocyclization. Table 3 shows results of calculating the yield of the sol fraction for different ,~legrees of diepoxide excess, using the theory of cascade processes [9, 10]. The content of unreactcd epoxy groups in gel fraction G was calculated on the basis •of the existence of balance between reaction groups in the system using the formula G=Eun: (E~: 2)=(Es--A,) : ( E , : 2), where E g = 2 ( ~ °
SePo~, Mee J Ag___4(~o
(1)
SAP0.~, Mx / Eo and A o being the initial
concentrations of epoxy and amino-groups in the system and Po, weight of the :system. Comparing results shown in the Figure and in Table 3 it may be concluded that when describing the chemical structure of densely crosslinked networks the analytical calculation using the method of cascade processes correlates with results of numerical simulation, however, agreement is only observed with nonequimolar reagent ratios. With stoichiometric and near stoichiometric proportions there is a fundamental difference between these statistical methods. I n this range of relative concentrations the method of cascade processes, in which .the reactivity of groups in independent of the dimension and complexity of a "branching tree", predicts a 100% conversion of reaction groups. At the same time, it follows from the analysis described and the description given [1, 11, 12] that topological features of the structure of densely crosslinked networks with reagent ratios close to the stoichiometric, restrict the conversion of reaction g r o u p s (~res~96~/o) and lower the reaction rate constant at advanced stages. Summarizing the foregoing it may be concluded that the statistical model developed, in addition to giving a description of the topological structure of
Structure of gel and sol fractions of epoxy compositions
1829
~ r o s s l i n k e d p o l y m e r s a n d k i n e t i c s of f o r m a t i o n , enables a fairly a c c u r a t e p r e d i c t i o n to be m a d e of t h e p r o p o r t i o n of gel a n d sol fractions, M W D in sol a n d c o n v e r s i o n of r e a c t i o n g r o u p s in gel for real e p o x y compositions. T h e p r o b a b i l i t y o f m o n o c y c l i z a t i o u in t h e s y s t e m m a y be e v a l u a t e d . A n analysis of t h e c o m b i n e d s t a t e of t h e s y s t e m enables t h e r a n g e ~of gel-like s t a t e i.e. t h e b o u n d a r y o f t r a n s i t i o n f r o m 100% sol to p a r t i a l l y c o m b i n e d n e t w o r k to be d e t e r m i n e d . A c o m p a r ison o f m o d e l calculations of kinetics a n d limiting conversions of n e t w o r k - f o r m a t i o n [1] w i t h results of a p r e v i o u s s t u d y [12], w h e r e t h e existence of m a x i m u m yield a n d a r e d u c t i o u in r a t e c o n s t a n t in t h e r e a c t i o n of D E w i t h m - p h e n y l e n e d i a m i n e s w a s confirmed e x p e r i m e n t a l l y , is f u r t h e r evidence o f t h e suit a b i l i t y of t h e m o d e l e x a m i n e d . Translated by E. S]~M~m~ REFERENCES 1. V . A. TOPOLKAREV, V. G. OSHMYAN, V. P. NISICHENKO, A. N. ZELEi'~ETSgII,
A1. AI. BERLIN, E. V. PRUT and N. S. YENIKOLOPYAN, Vysokomol. soyod. A21: No. 7, 1979 (Translated in Polymer Sci. U.S.S.R. 21: 7, 1979) 2 . Kh. A. ARUTYUNYAN, A. O. TONOYAN, S. P. D A V r Y A ~ , B. A. ROZENBERQ and N. S. YENIKOLOPYAN, Dokl. AN SSSR 212: 1128, 1973 3. N. S. VEDENYAPINA, V. P. KUZNETSOVA, V. V. IVANOV and N. S. YENIKOLOPYAN, Izv. AN SSSR, ser. khim., 1970, 1956 4. Y. T. SMITH, Polymer 2: 95, 1961 5. J. DOBAS, G. EICHER and J. KLABAN, Collect. of Chem. Commun. 49: 10, 1975 6. R. B. PRIME and E. SACHER, Polymer 13: 9, 1972 7. M. A. ACITELLI, R. B. PRIME and E. SACHER, Polymer 12: 335, 1971 8. N. S. KOGARKO, V. A. TOPOLKARAYEV, G. M. TROFIMOVA, V. V. IVANOV, AI. AI. BERLIN, D. D. NOVIKOV and N. S. YENIKOLOPYAN, Vysokomol. soyod. A,20: 756, 1978 (Translated in Polymer Sci. U.S.S.R. 20: 4, 852, 1978) 9. M. GORDON, Prec. Roy. See. A268: 1333, 1902 10. Ye. N. RASPOPOVA, V. N. IRZHAK, L. M. BOGDANOVA and N. S. YENIKOLOPYAN, Vysokomol. soyed. B16: 434, 1974 (Not translated in Polymer Sci. U.S.S.R.) 11. A1. A1. BERLIN and V. G. OSHMYAN, Vysokomol. soyed. AIS: 2282, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 10, 2612, 1976 12. L. K. PAKI~OMOVA, O. B. SALAMATINA, S. A. ARTEMENKO, AI. AI. BERLIN and N. S. YENIKOLOPYAN, Vysokomol. soyed. B20: 554, 1978 (Not translated ii~ Polymer Sci. U.S.S .1~.)