1854 [CONTRIBUTION
ALLANIt. SHULTZ hTo. 119 lcROM T H E C E N ~ R ARESEARCH L DEPARTMENT, MII~NESOTA M I N I N G AND
VOl. so MANUPACTURINC
COMPANY]
Crosslinking Efficiencies in the Methyl Methacrylate-Ethylene Dimethacrylate and Ethyl Methacrylate-Ethylene Dimethacrylate Systems. Degradative Analysis by Electron Irradiation BY ALLANR. SHULTZ RECEIVED NOVEMBER 27, 1957 The intermolecular crosslinking efficiencies, e, of ethylene dimethacrylate have been determined in four methyl methacrylate (hfMA)-ethylene dimethacrylate (EDMA) co-polymers and four ethyl methacrylate (EMA)-EDMA copolymers. Random scission of the copolymer networks by 1000 kvp. electrons was employed t o determine the number of crosslinked units per gram. MMA-EDMA copolqmers having EDMA mole fractions, N2, of 0.00578, 0.00291, 0.00147 and 0.000868 exhibited e-values of 0.39, 0.395,0.44 and 0.48, respectivcly. EMA-EDMA copolymers with f i of ~ 0.00675,0.00333,0.00172 0) are 0.46 and and 0.00102 had e-values of 0.32, 0.36, 0.38 and 0.39, respectively. The extrapolated efficiencies lim e ( f i z 0.40. These limiting efficiencies are consistent with the postulate of slightly gr_eater than 50% loss of doubly reacted EDMA units t o small intra-chain ring formation. The decrease in e with increase in N Zin this low EDMA concentration range is in for pendant double bond isolation on a polyqualitative agreement with the limited accessibility coiicept of Loshaek and FOY mer network.
Introduction Attempts have been made to dctcrii~inc the crosslinking efficiency of ethylene diniethacrylate (EDMA) in MMA-EDMA copolymerization by dilatometric' and by kinetic-incipient gelation' techniques. The former method was based on total volume contraction measurements and was a measure of residual unreacted double bonds in the high conversion copolymers. The latter study combined kinetic, viscometric and dilatoinctric data to examine the classical theory3p4of network formation. Correlation of the critical conversion for incipient gelation with polymerization rate and with dimethacrylate concentration permitted estimation of the productive (inter-chain) crosslink formation. The present paper describes the application of another technique for studying tetrafunctional crosslinking efficiency which is complementary, and in some respects preferable, to the above metliods. I n recent years the theory of polymer networks3f4has been amplified and specialized to treat random crosslinking and degradation of polymers by ionizing radiations.5 Certain types of polyniers, includirig polyiiiethyliiiethacrylate6-8 and polycthyl undergo randoiii iiiaiii-chain scission without concurrent crosslinking when irradiated. Simple relatioilships betmccn gel content aiitl radiation dose therefore are available for calculatiiig tlic iiuiiiber of crosslinkcd units per gram of hfMi\--EDMA arid EMAEDMA copoly~iicrs. This degradative analysis
gives information concerning thc final productive crosslinking efficiency of EDMA in the high conversion copolymers and is less sensitive to experimental and theoretical difficulties encountered in handling pregelation and incipient gelation of a polymerizing system. Experimental
Materials and Polymerization.-The methyl methacrylate (Rohm and Haas) and ethyl methacrylate (MotioiiierPolymer) monomers were washed successively with 5% ,"uTaN02,5y0 NaHS03, 5y0 NaOH arid water. The monomers were then dried over MgS04. Two per cent. by weight of phenyl-0-naphthylamine (PBNA) was added t o each and the monomers were distilled through a short Vigreux column. The central cuts used for polymerization were: methyl methacrylate, b.p. 46" at 100 mm.; ethyl methacrylate, b.p. 59' at 100 mm., saponification equiv. 114, C 63.1, H 8.9. Three per cent. by weight of PBNA was added t o ethylene dimethacrylate (Monomer-Polymer) and a 73% central cut was obtained by distillation through a Vigreux column at about 1 mm. pressure. K O accurate boiling point was obtained due to considerable pressure fluctuation during distillation. The benzoyl peroxide ("Lucidol," Novadel-Agene Corp.) used as a polymerization initiator was not subjected to purificatiou. A mold-release agent Triton X-100 (Rohm and Haas) an aryl alkyl ether alcohol was incorporated in the polymerizing mixtures to facilitate removal of the copolymers from the plate-glass molds, cf. seg. Polymerization data indicatetl no excessive chaintransfer ability for this chemical. Its coiicentration TV:IS held nearly constant in tlie eight copolymer feetls and 110 influelice upou the measured crosslinking cflicieucy of El)hSIA is tu be expected. Tlic feed cornpositiolis for the eiglit c~op~~lyinerizalioiis :ire given in Table I. These solutions wcrc syringed irito the space bctweeii 30 rm. X 30 c m . gla5s plates scp;irated at the outer edge by a Tcfloii gasket of 0.68 tnm. tliickiiess. The glass plates were taped togetlicr with a Scotch brand polyester film ta vent-resistant adhesive. Polymeriza ( I ) S. 1,osliack and T. C. l:ox, 1'111s JOURNAI.,'75, 3514 (1053). ill an air oven at GO" for 72 hr. T h ( 2 ) M. Gordon a n d R.-J. Roe, J . Polymer Sri.. 21, 27 (10513); (b) 21, 39 (1956); (c) 21, 57 (19.56); (d) 21, 75 (1056). then removed from the glass molds and were lieatcd in a ( 3 ) P. J. Flory, THISJOUKNAL, 63, 3083, 3001, 3090 (1941); J . 125' oven for 24 hr. Some retardation of tlie initial polyPhys. Chcm., 46, 132 (1942); THISJOURNAL, 69, 30, 2893 (1947); merization (at 60") was observed in a zone approximately 1 "Principles of Polymer Chemistry," Cornel1 Univ. Press, Ithaca, N. Y., cm. deep at the upper edge of the polynlerizing mixture 1953, pp. 347-398. which was accessible to air through the injection holes. (4) W. H. Stockmayer, J . Chent. Phys., 11, 45 (1043); 12, 125 This region was avoided in sampling the polymer sheets for (1944). crosslink concentration study. The co-polymer sheets had somewhat uneven surfaces due to differential contrac( 5 ) (a) A. Charlesby, Proc. Roy. SOC.(Londorr), 2158, 187 (1052); (b) 222A, 60, 542 (1954); ( c ) J . Polymer Sci., 11, 513 (1953); (d) tion a t higher conversions from the rigidly spaced glass plates. Pvoc. R o y . SOL.(London), 224A, 120 (1954). The thickness of the samples used varied in the range 0.650.69 mm. (6) P. Alexander, A. Charlrsby and 11. Ross, ibid., 223A, 393 (1954). Electron Irradiation and Gel Measurement.-Strips, (7) L. A. Wall and M. Magat, J . chim. p h y s . , 60, 308 (1953). each weighing approximately 0.15 to 0.20 g., were cut from ( 8 ) A. R. Shultz, P. I. Roth and G. B. Rathmann, J . Poiyiner Sci.. eets. These were irradiated in air t o suc22, 405 (1056). s with 1000 kvp. electrons from a General ( 0 ) A. R. Shultz and I. R. M a w , unpublished data.
April 20, 1958
INTERMOLECULAR CRO55LINKING
EFFICIENCIES
1855
TABLE I FEEDCOMPOSITIONS
FOR COPOLYMERIZATIONS (WEIGHT I N
GRAMS)
co-
polymer MMAEDMA
MMA
EDMA
x-100
BzzO:
I I1 I11 IV
92.48 93.14 93.47 93.56
1.0645 .5377 .2722 .1609
0.501 .497 .500 .500
0.1009 .lo02 .lo06 .lo12
EMAEDMA
EMA
I I1 I11 IV
89.50 90.86 90.29 90.42
0.8
0.6 1.0556 .5272 .2701 .1603
0.478 .528 .500 .499
0.0994 ,0987 .lo03 ,1008
Electric Company resonant transformer electron beam generator.10 All portions of each thin sample received essentially equal ( +570) radiation doses. The electron beam was calibrated against an air ionization chamber furnished by the General Electric Company for absolute intensity determination. The maximum dose rate received by the samples a t the beam center was 5.84 megarep min.-'. Extensive relative intensity distribution studies were performed to give accurate integral dose calculation for samples transported through the beam on a water-cooled aluminum tray. A value of 1 megarep = 5.24 X lo1@electron volts g.-1 (in standard air) was used in subsequent calculations. I t is possible that a higher value (5.8 X lo'@ e.v. g.-l megarep-') is preferable for energy dissipation in a polymer. However, the important consideration is that the same conversion factor is used here as in the linear polymethyl methacrylate degradation study8 upon which the degradation energy absorption, 59 e.v. per main-chain scission, is based. Addition of 0.5 weight % of Triton X-100 to linear polymethylmethacrylate had no measurable effect on this energy per scission value. The energy absorption per main-chain scission is found to be 75 e.v. for linear polyethyl methacrylate.@ The irradiated films were weighed into lOO-mesh monel screen cages and immersed in benzene. The extraction of solubles was accomplished by constant gentle stirring of the surrounding benzene for 72 hr. a t 25". The benzene-todissolved polymer ratio was never less than 4000: 1 by weight. The extracted, coherent gels in their respective cages were dried in air followed by vacuum drying a t 100" for 72 hr. As will be mentioned later, even this method failed to free the gels completely of benzene, but the small amount of residual solvent did not critically influence the data interpretation. The dried gels were weighed in their cages and the weight fractions of gel in the irradiated films were calculated. Weights on the swollen gels before drying were also obtained to reveal the nature of the gel-swell relationship. These data are incidental to the more conclusive gel content study and will not be iucluded here.
6
Q 1
0.4
0.2
0 8
16
24
R (megareps). Fig. 1.-Reciprocal of the number of crosslinked units per weight-average primary molecule, 1/AR, plotted against radiation dose, R, for four MMA-EDMA copolymers. Exterior scale on right indicates per cent. by weight of gel.
10 20 30 40 50
60
70
Results and Discussion Treatment of Data.--Subject to certain as-
80
sumptions, which are discussed below, the weight fraction, g, of non-extractable material in a tetrafunctionally crosslinked polymer is given by$-5
90
1 - g = [l
+ (6g/2)]
--2
(10) E. E. Charlton and W. F. Westendorp, Gen. Elec. Rev., 44, 652 (1941); E. J. Lawton, W. D. Bellamy, R. E. Hungate, M . P. Bryant and E. Hall, Toppi, 94, No. 12, 113A (1951).
d
95
(1)
where 6 is the number of crosslinked units (two crosslinked units equal one crosslink) per weightaverage molecule of the primary (linear polymer) distribution. If main-chain scissions are introduced a t random into the original crosslinked polymer in numbers proportional to R, the radiation energy absorbed per gram of material, the following relation is valid
?3 .
99 10
20
30
R (megareps). Fig. 2.-1/6, plotted against R for four EMA-EDMA copolymers. Exterior scale on the right indicates per cent. by weight of gel.
to a good approximation 1/88 = 1/60
4-( 2 A E d ) - ' R
1856
ALL.4N
R SHULTZ
0.8
Vol.
so
0.8
-3.
0.6 c._ T5
0.6
v
v
c
v
? ri
,.
? i
0.4
0.4
0.2
u.2
0
0 0
8
16
0
24
R (megareps). Fig. 3.-l/SR (adjusted) vs. R for four MMA-EDMA copolymers; 6, (adjusted) is calculated by equation 1 assuming g (adjusted) = 0.96g (observed).
S R is the number of crosslinked units per instantaneous primary weight-average molecule a t dose R (e.v. g.-'), A is the number of crosslinked units per gram, and Ed (e.v. scission-') is the total energy dissipation within the polymer per main-chain scission. The three terms in equation 2 obviously represent, respectively, the instantaneous, original and scission-produced number of weight-average primary molecules per crosslinked unit in the polymer. From the observed g value of each MMA-EDMA and EMA-EDMiZ copolymer irradiated to dose R, the value of S R was calculated by equation 1. The calculated 8~ values are plotted in Figs. 1 and 2 as 1 / 6 ~against R for the eight copolymers as suggested by equation 2. The corresponding values of g are indicated to the right of the plots. The predicted linear form of the plots is satisfactorily reproduced. However, negative (physically unreal) values for 1 ' 6 , are found by this direct treatment of the raw gel content data. Some extracted copolymer samples a t zero and low radiation dose levels were found to have experiiiiental g values of nearly I .04 by the described extraction and drying procedure. Preliminary experiments on the effect of extraction time variation indicated no further loss of extractable material over much longer extraction periods. On the other hand, increase of drying temperature or time did slightly reduce the weights of the extracted samples. Rather than employ an extremely elaborate drying procedure, i t was decided to apply a reasonable, though arbitrary, correction for incomplete drying. All experimentally observed g values were multiplied by 0.96, i.e., g (adjusted) = 0.96g (observed), for the MMA-EDMA series
20
10
30
R (megareps). Fig. 4.-1/6, (adjusted) vs. R for four EMA-EDMX copolymers; ,6 (adjusted) is calculated by equation 1 assuming g (adjusted) = 0.98g (observed).
and 0.98 for the EMA-EDMA series. This adjustment made all calculated 1/6 > 0. A more exact correction for incomplete drying would introduce a factor nearer unity for the lower g, higher l / 6 , samples. A glance a t the l/S and g scales in Figs. 1 and 2 shows such a refinement to be inconsequential. Figs. 3 and 4 present 1 / 6 ~(adjusted) plotted against R. Table I1 gives the intercepts, 1/80, and slopes (2AEd)-I (cf. equation 2) for the lines shown in Figs. 1 through 4. It is seen that the slight arbitrary adjustment of the measured gel fractions does not greatly lower the slopes, the quantities of greatest interest. The adjusted intercepts are obviously of no value in estimating the primary chain lengths of the COpolymers. Both the relative and absolute magnitudes of the adjusted 1/S0 for EMA-EDMA 11, 111 and IV are reasonable, however. SLOPES @A&)
TABLE I1 INTERCEPTS, I/&, OF OBSERVED ASD ADJLWED 1 1 6 us. ~ R PLOTS
-l,
AND
Slope (megarep. -1)
l l h l A-.EIl.\I A
I I1 111 IV
Ohsd.
.\dJ.
0.OliO ,0356 ,0598
0.01fi.4
,0940
,0322 ,0569 ,0885
EhT.4-EDM A
I I1 111
,0168 .0283 ,0537
IV
,0887
,0154 .02i5 ,0512 ,0838
intercept (dimensionlrss) Obsd. Ad j
-0.035 ,070
-
-
0.012
,000
,060 ,060
,012
.Os0 ,015
,004 ,022 ,040 ,050
,000 ,003
,065
Ed, the energy dissipation per main-chain fracture, in poly-MMA undergoing electron irradiation
April 20, 1958
INTERhf OLECULAR CROSSLINKING
EFFICIENCIES
is 59 electron voltss and for poly-EMA it is 75 electron volts.g Using these Ed and the factor 1 megarep = 5.24 X 1019e.v. g.-l employed in their calculation the values of A (crosslinked units per gram) for the eight copolymers were obtained from the slopes of Figs. 3 and 4 and are listed in Table 111. The maximum theoretical values of A , assuming 100% efficiency of EDMA in useful crosslink formation, were calculated from the feed compositions (Table I ) . The actual crosslinking efficiencies were then obtained as E = A(expt.)/A (max.).
1S57
ization period” for primary chain length distribution will have a negligible influence on the slope of the observed 1 / 8 ~8s. R plots constructed from data according to equations 1 and 2 when 1/60 for the copolymer is small. Equation 2 is formulated to treat pure random chain scission of a randomly crosslinked network. Crosslink severance is not included in this expression. Assuming equal a priori scission probabilities for crosslinks and main-chain bonds, it is easily seen that for random fracture of a net having crosslinks representing only a small fraction of the total TABLE I11 units, the crosslink severance contribution to the CROSSLINKED UNITSPER GRAM,A , A N D CROSSLINK I N G EFgel dissolution is minor. Scission of networks FICIENCY, e, FOR EDMA COPOLYMERS having high crosslink concentration or having cross(T2= mole fraction EDMA) links which are extremely labile to the degrading Copolymer A X 10-19 agent must be treated by a more general theoMMA-EDMA Nz Max. Expt. e retical formulation. Appendix I presents equations I 0.00578 6.92 2.70 0.39 I1 .00291 3.49 1.38 ,395 for evaluating such situations. There is no evidence to suggest a markedly greater a priori scis111 .00147 1.77 0.78 .44 sion probability for the EDMA crosslinks than for IV ,000868 1.04 0.50 .48 the MMA main-chain units under ionizing radiaEhlA-EDI\IA tions. The use of equation 2 in treating the data I ,00675 7.08 2.26 .32 of the present study is consequently readily justiI1 ,00333 3 51 1.27 .36 fied. Appendix I1 extends the treatment of differI11 ,00172 1.81 0.68 .38 ing a priori scission probabilities to evaluate gelIV ,00102 1.08 0.42 .39 swell data of randomly scissioned networks. The Theoretical Considerations.-Before discussing relations developed give a more quantitative measthese observed crosslinking efficiencies for EDMA ure of the effects predicted by Horikx.12 Ala brief examination of the assumptions which are though these relations are not used in the experiimplicit in the data evaluation method employed mental study a t hand their natural derivation is in order. from the approach of Appendix I dictates inclusion Both equations 1 and 2 rest on the assumption of a t this point. a ‘most probable” molecular weight distribution of The formulation of equation 2 does not consider = the primary chains in the copolymer (iVW~/M,,o intra-chain ring formation occasioned by a radical 2). Such a distribution would be produced in a on a given growing primary chain threading back narrow conversion range by radical disproportion- through one of its own pendant EDMA double ation or by chain transfer termination steps in the bonds. EDMA units engaged in small rings will polymerization. Radical combination prod_uces-a not contribute to the network as analyzed by elecslightly “sharper” primary distribution (Mw/Mn tron degradation and will be counted as “wasted” = 1.5). A broader than most probable primary or non-crosslinking units. Concentration considmolecular weight distribution is actually obtained erations will make the occasional fracture of such for the high conversion copolymer due to variation rings (giving no noticeable network change) unin monomer concentration and in initiation rate important in the present study. EDMA units actthroughout the polymerization. Of possibly ing as couplers in large intra-chain rings, on the greater importance is the lengthening of both kinetic other hand, will contribute as bona fide crosslinks and physical primary chains due to decreased radi- when studied by the random degradation techcal termination in the crosslinked media a t high nique. Crosslinking of pendant double bonds on the conversions. The influence of breadth of con- ring with other primary chains will incorporate the tinuous primary molecular weight distributions ring into the gel network in such a manner that the upon the g us. 6 relation is considerable and must network defect created by the ring closure is minor. be recognized in handling polymer crosslinking.5~ (In statistically treating the network formation, In the present random degradation study, however, however, every intra-chain ring closure is unique.) ‘deviation of the primary chain-length distribution As in the case of deviation of the original primary froni the most probable form is eliminated rapidly chain length distribution from most probable, ranin the early stages of irradiation. The original dis- dom scission will destroy the identity of large rings tribution loses its identity and the action of further in the initial introduction of new chain ends a t low random scission of most probable primary distri- radiation doses. A theoretical treatment. of the butions having progressively shorter average chain effects of rings of all sizes and in appreciable conlengths is the phenomenon measured throughout centrations on the relation of observed 1 / 6 ~to R the major portion of the copolymer degradation. would involve an analysis requiring several assumpA slight deviation of the lines in Figs. 3 and 4 tions. There is, however, considerable assurance from linearity would theoretically exist in the re- that small rings greatly preponderateI3,l4and their ~ but measurement difficulties gion of low 1 / 6 values, (12) M . M. Horikx, J . Polynzcv Sci., 19, 445 (1950). completely obscure this deviation. The “random(13) H. Jacobson a n d W. €1. S t o c k m a y e r , J . Ciiem. P h y r . , 18, 1600 (11) A. R. Shultz, P r e p r i n t 241, Nuclear Engineering a n d Science Congress, Cleveland, Ohio, Dec. 1955.
(1950). (14) R. h-.H a w a r d , J . Polymev Sci., 14, 535 (1954).
AILAN K.SHULTZ
1S38
Vol. 80
effect is that of rendering the involved doubly reacted EDMA4units non-contributory to the copolymer network stability.
theoretical rclationship of Loshaek and Fox' into this concentration range. Positivz curvature must be found in the region 0.006 < N z < 0.15 since a linear extrapolation of the M3JA-EDMA4 line Discussion drawn in Fig. 5 would give a t N Z = 0.02s an E The e (intermolecular crosslinking efficiency) value about one-half the lowest e' value found values listed in Table I11 exhibit a systematic in- dilatometrically. The near equivalence of ethylcrease with decreasing EDMA concentration in the ene dimethacrylate's intermolecular crosslinking monomer feed. This is in qualitative agreement efficiency in copolymerization with the two similar with the behavior predicted by Loshaek and Fox1 methacrylates is not surprising. Although there who derived explicit expressions relating the ulti- appears to be a systematic separation of the E mate (high conversion) crosslinking efficiencies of values obtained for the two systems, the broken dimethacrylates to the dimethacrylate concentra- line in Fig. 5 passes through the & l o % uncertion and structure. The principal postulate of tainty limits in E for all but one copolymer. their treatment was the existence of a finite accesThe comparison of EDMX crosslinking ellisible domain for each unreacted pendant double ciency as determined by electron degradation of bond attached to an existing polymer network. the high-conversion co-polymer with the efficiency When the concentration of pendant double bonds as determined by critical conversion for gelation of is reduced by reaction to the extent that domain the copolymerizing systeni2d has several points of overlap becomes highly improbable 110 appreciable interest. The latter method is not concerned with further crosslinking occurs. Thus, a certain frac- the ultimate crosslinking efficiency. The problem tion of pendant double bonds becomes isolated a t of accessibility for further reaction of pendant high conversion ; the conditions determining this double bonds on an established network is nonfraction are the number-average n, of chain atoms existent in the pre-gelation analysis. The critical between crosslinked units and the number n, of conversion is dependent on the weight-average prichain atoms in the pendant reactive side chain. mary chain length of the co-polymer (and thereby Assumptions required to couch the theory in a use- on the polyiiierizatioti ratc), the tetra-functional ful mathematical form invalidated its uncritical nionoiner concentration, tlie extent of intra-chain application to very low initial dimethacrylate feed ring formation and the extent of pre-gelation tnulticompositions. In particular the diffusional free- ple crosslinking of primary chains. Using a few dom of crosslinked units about their relative equilib- basic assumptions Gordon and Roe exainincd the rium positions would enhance crosslinking prob- classical theory of gelation with rrgdrd to the perabilities in this composition region in a complex turbing influence of the latter two factors. Thcy manner. The logical extrapolation of the limiting first determined dilatometrically that no accelcraaccessibility concept, however, was that as the tioii of polymerization attributable to diffusioninitial tetrafunctiona1:difunctionalmonomer ratio controlled radical termination occurred in NII.1approaches zero E approaches unity. EDMA mixtures prior to gelation.2d (At least It was recognized15 that dilatometric measure- good evidence was presented for the mixtures which ment of double bond disappearance does not dis- reached gelation a t low conversion.) The inciptinguish between the doubly reacted EDMA units ient gel point (critical conversion) was measured which participate in network crosslinks and those by obscrving a fairly abrupt iniinobilizatioli of a which exist in intrachain rings. Gordon and iiiacroscopic probe.2d The displacement of gel RocZatddiscuss this problem a t some length citing incipience to higher conversions by increasing the theoretical prediction^'^^^^ and experimental evi- polymerization rate was studied. The iiiodified dence16p17 that an appreciable fraction of cross- theory allowed estimation of the iiitra-chain cylinkable iiionoiiiers may be involved in sniall intra- clization froiii the deviatioii of thc critical coiiverchain rings. This fraction was cstiniatcd oii ap- sion Z J ~ . ratc slope froiii that predicted by igiioring proxiiiiate steric mtl ratc coiisitleratinns to he ititr,~cliain cyclization or iiiultiple crcisslinkiiig. .ibout one-half for ET>lI,\ iii MKI T3DM.I co- 'I'Iic cupcriniciital data indicatcd a1)out 67% of the polyineri7ation (S. _(:ratch). Tllc prcscnt tl,it,i tloubly rcactcd I'DAf.2 chain uiiits participated ‘ire plotted ;IS E 'LIT. n - 2 (inole fr'iction of RDII.\) iii in tlicsc latter reactions during tlic prc-gclatioii Fig. 3 , ' r h ~einprical straight line tlirougli the 1)erioc-l. Most of these were believed to be ac1lAIAI13lI3Ll data c~trapolatcsto E -- 0 413 a n d counted for by iiitr'i-chain ring foriiiatioll although the line drawn through the Ebl.1-EDM.4 data cxpcrinientally this was indistinguishable from thc extrapolates to E = 0.40. The c&se agreenic~ntof multiple crosslinking effect. The 6776 figure was the cstitnated value16 for liiri E (IV~ + 0) with this based upon assumed radical teriiiiuation by coniexperimentally measured value must be mainly bination. If the terminating step were assumed to fortuitous. I t is important to emphasize herc, be disproportionation, the data would indicate 73% however, that lim E ( N 2 0) as measured by the consumption of the EDMA chain units in these side present random degradative analysis is an accurate reactions.'* An attempted theoretical descripindication of the depression of cro_sslinking due to tion2b of the relative viscosities of the polyineri7itig small ring formation. The E us. N2 curves of Fig. mixture suggested the formation of an appreciable 5 do not exhibit the positive curvature predicted number of large intra-chain rings. This viscosity by unwarranted extrapolation of the approximate analysis should be largely discoutited, however, since it was based upon the crrorieous assumption (15) 5 Loshaek J Polymev S c t , 1 5 , 391 (1055) --f
(111) W Simpqon, T. Halt and R 1 Zeitie, gbtd (17) hI Gordon. J Lhefn. P h y s , 22, CllO (1954)
10, I S 9 (105J)
(18) T h e author IS indebted to Dr J C 11. IIwn for detecting error i n t h e original corrertlon for this cflcct
LU
April 20, 1958
INTERMOLECULAR CROSSLIXKING EPFICIEXCIES
1,959
that pre-gelation crosslinking has negligible effect upon the hydrodynamic volume of the polymer molecules. Both t h e o r e t i ~ a l * -and ~ ~ ~recent ~~~~~ experimentals,11*21 work show the importance of crosslinking in depressing the molecular volume-tomass ratio of a polymer system approaching gelation. The agreement between the kinetic-gel incipience and electron degradation measured intermolecular crosslinking efficiencies for EDMA in the MMA-EDMA system is only fair. The 0.33 or 0.25 value of E observed by the former method might possibly be adjusted to the value lim E (SP 0) = 0.46 if multiple crosslinking were quantitatively accountable. It is not necessary 4 6 2 to postulate large intra-chain ring formation to explain the experimental evidence. Small intrai?iz x 103. chain rings are shown to exert the limiting inFig. 5.-Intermolecular crosslinking-elticiency, B , v s . mole fluence on E as the initial EDMA concentrations fraction of ethylene dimethacrylate, Xz, in MMd-EDMA are decreased to very low values. In addition, (solid circles) and EMA--EDhXh (open circles) copolymers. the electron degradation analysis of the high conversion copolymers reveals the effect of double finite” progenitor chain before impressment of R. bond isolation by the existent infinite network. CY, PI and Pz are the proportionality constants for The analysis of the MMA-EDMA copolymer crosslinked unit formation, crosslink scission and system by electron irradiation illustrates the po- main-chain scission, respectively, of the polymeric tential usefulness of this technique. The greatest material. As set forth here the crosslinks introlimitation is obviously its applicability only to duced by R are assumed equivalent to the original networks which randomly fracture under ionizing crosslinks with regard t o subsequent scission. radiations. Cured butyl rubber is another sys- Equation 4 reduces to simplified forms5 for various tem which is amenable to this analysis. Slight limiting values of the parameters. concurrent crosslinking during irradiation could be Assumed production of the primary linear molehandled theoretically, but accurate knowledge of cules by random scission of a “semi-infinite” chain both scission and crosslinking energies would then makes the primary chain length distribution a be necessary for satisfactory determination of the most probable one. The number of crosslinked original crosslink concentration. The crosslinking units per weight-average molecule of the initial density range covered in the present study is per- primary distribution is therefore haps optimum for the degradative analysis method. (5) 60 = 2% = 2qo/po Considerably higher and lower tetrafunctional : difunctional ratio networks could be investigated The number of crosslinked units per weight-average if desired. molecule of the instantaneous primary distribution is Acknowledgment.-The author wishes to thank 6R = 2 ? R (6) X r . Ivan R. &law for performing a large portion of the experimental work. since continuance of random scission perpetuates the most probable primary chain length distribuAppendix I tion. Consider R to be the total energy dissipation per Crosslinking and Scission of a Polymeric Material.-The number of crosslinked units per num- gram of polymer undergoing irradiation and assume the absorption to be independent of the exber-average primary molecule of a polymer is tent of reaction. If no crosslinking is induced by Y = a/p (3) the radiation (i.e., a = 0) SR may be expressed as g is the probability that a chosen unit is a cross6~ = 2 q o p - * P l R / [ 1 - (1 - p o ) e - ” R ] (Aa) linked unit and p is the probability per unit that a chain severance exists. If crosslinks (tetrafuncNoting t h a t 40 = G o P ~ where ~ ~ - ~P,o is the numtional), main-chain scissions and crosslink scissions ber of units per primary weight-average molecule are independently, introduced a t random into a ma- before irradiation terial in numbers proportional to an agency R, the 1 / 6 = ~ (1/Go)efiP2R[e-P2R 1 / 2 F B o ( l - e-@zR)] (6b) cross1inki:ig index may be formulated as I n this equation h = & / p 2 = Edz/Edl is the ratio Y R = ~ R / P R= [ 1 - ( 1 - q o ) e - a R ] e - 2 P 1 R / [ 1 - (1 of a priori susceptibilities of crosslinks anld mainp ~ ) e - a 2 ~ 1( 4 ) chain bonds t o cleavage by the radiation. qI and po are the initial random crosslinking and Expanding the gxponentials in eq. 6b and subscission probabilities for an assumed “semi-in- stituting & = (So/P,o) @Ed*) yields
-
+
(19) B. H. Zimm a n d W. H. Stockmayer, J . Chem. P h y s . , 17, 1301 ( 1 ‘349). (20) W . H. Stockmayer and M. Fixman, A n n . N . Y. Acad. Sci., 67, 334 (1953). (21) A. Charlesby, J . Polymer Sci., 17, 379 (1955)
;/6R =
B=2h
+
(I/&) f [ 1 ( 2 A / P w 0 ) ] ( 2 1 1 E d 2 ) - ~fR [2B 1 (2Bz/~,~,o)1(2.4E~~)( 62 ~ 8) ~ / ~ ~ ~ ) R 2
+ +
-
1
ALLANR.SHULTZ
18GO
Equation 6c reveals more clearly the effect of relative and absolute crosslink and main-chain scission on the 1 / 6 ~vs. R relation. The important factor determining the deviation of initial slope from (2AEd4-l and determining the degree of curvature is the ratio (2h - l)/pWo.Figure G illus-
Vol. 80
The number of elastic elements per gram in the gel network is given byI2 ve
All
- (1
- g)i/zI2
(8)
A as previously defined is the number of crosslinked units per gram in the total polymer (gel plus sol). Therefore in the present formulation V ~ = R
[ I - (1 -
qo)e-aR]e-2PlR[1
- (1
- g ~ ) ' / 2 ] ~ 'm (9)
where m is the mass of the polymer unit upoll which the probability parameters are based. Considering only degradation t o occur ( z k , (II = 0) the ratio of the number of elastic elements a t irradiation dose R to the number before irradiation is
1.0 0.8
3 0.6 1 3
/
V e R UeO
0.4
0.2
0.2
0.4
0.6
0.8
= e--281R[l - (1 - g n ) ' / z ] 2 / [ 1- (1 -
gO)'/2]2
(10)
Equations 10, 1 and Ga permit the coinparison of weight-fraction sol (1 - g R ) , with the swelling variable, 1- ( v e ~ / v , O ) ,as suggested by Horikx. For a crosslinked polymer having given qo and $0 values there is a series of curves relating (1 - g K ) to I ( Y , R / v ~ o ) . Each curve corresponds to an h = p,/p, ratio. Figure 7 illustrates the relationship
1.0
Fig. 6.-Reciprocal of the number of crosslinked units per weight-average primary molecule, CY^, plotted as a function of the original network composition and the absolute and relative crosslink arid main-chain scission = 2000 and probabilities. C j , equations Oh and 6c. I,'o 60 = 10.
trates the effect of h variation on the l j 6 ~ns. R relation as calculated by eq. 6b for PWo= 2000 and 60 = 10. [I (2B/PWo)] (2AEdz)-lR is chosen for the abcissa scale to give initial coincidence of the curves. For reasonably high PwO and moderate 60 values there is negligible deviation of the curves from the form of eq. 2 unless h is considerably greater than unity. Discounting a peculiarly high value for h, it is seen readily that eq. 2 is a satisfactory approximation for the copolymers in the present study.
0.32
+
0.08
20
40
(
102 1 -
Appendix I1 Determination of Relative Stabilities of Crosslinks and Polymer Chains Toward Degradative Agents.--A combination of gel content and swelling data to determine the relative scission rates of crosslinks and main chains of a polymer network was proposed recently by Horikx. This analysis is readily made in theory for the particular type of network and mode of degradation treated above. The theory of polymer network swelling relates v?, the volume fraction of polymer in a swollen gel, to the thennodynaniic interaction parameter, x12, and to the number of elastic elements per gram, Y,, in the gel throughz2 111
(1
-2'2)
+ + 'J2
x>2022
+ u,dzV,(v,l'J - z d 2 ) = 0
(7)
d2 = density of the relaxed polymer network and
I?,
molar volume of the imbibed solvent. When is known, ve may be calculated from swelling data on the gel. =
x12
(22) P J Flory, J Ciicin. P h v ? , 18, 108 (1950)
00
80
3 -
Fig. 7.-Il'eight fraction extractahles, (1 - g R ) , plotted against the fractional decrease in elastic elenients per grain , various a p r i o r i (crosslink scission)/ of gel, (1 - u C R / u e O )for (rnaiii-chain scission) probahility ratios, h.
for a polymer having $0 = 3.4 X lop4 and qo = 1.36 X l o p 2 (thus 6o = SO) when h = 0, 1, 10, 100 and a . The ratio of crosslinks to main-chain units governs the sensitivity of h estirnation. Low crosslinking densities render the estimation extremely difficult unless h is large. Possibly the greatest problem is the proper assignment of XIZ to the solvent-polymer pair. &41so, the assumption of x12constancy over a large range in v2 is necessary. This method of estimating relative stabilities of crosslinks and polymer chains deserves further investigation. Careful consideration of the assumed network model and mode of degradation applicability should be made before subjecting a given system to such an analysis. SAINT PAUL 0, ~ ~ I N X E S O T A
