Network structure of bimodal epoxies—a small angle X-ray scattering study

Network structure of bimodal epoxies—a small angle X-rayscattering study

N.C. Beck Tana,1, B.J. Bauera, J. Plestilb, J.D. Barnesa, D. Liua, L. Matejkab, K. Dusekb,W.L. Wua,*

aPolymers Division, NIST, B 320, Building 224, Gaithersburg, MD 20899-8541, USAbInstitute of Macromolecular Chemistry, Acad. Sci. Czech Republic, Prague, Czech Republic

Dedicated to Professor Ronald K. Eby on the occasion of his 70th birthday

Received 20 November 1998; received in revised form 1 February 1999; accepted 1 February 1999

Abstract

Small angle X-ray scattering measurements were performed on epoxies to determine their network structure. To provide the necessaryscattering contrast the epoxy monomer used was a partially brominated diglycidyl ether of bisphenol A and the cross-linking agents werelinear, low polydispersity, amine terminated poly(propylene oxide)s. Samples with both single and bimodal molecular weight distributions ofcross-linking agent were prepared. A pronounced scattering maximum was observed in all networks and it can be interpreted in terms ofcorrelation holes. Networks cured with a mixture of two cross-linking agents with different molecular weights, i.e. bimodal networks,exhibited scattering maxima at significantly lower scattering vector (q) than was observed for any single amine networks. In model bimodalepoxy graft copolymers with nearly identical chemical structure as the networks the shift to lowq was barely perceptible. Experimentalresults from both epoxies and model graft copolymers are compared to a model calculation in order to establish a methodology to reducemolecular structure information from X-ray results.q 1999 Published by Elsevier Science Ltd. All rights reserved.

Keywords:X-ray scattering; Small angle neutron scattering; Epoxy

1. Introduction

The evaluation of structure in highly cross-linked poly-mer networks using small angle neutron scattering (SANS)methods has been the subject of a series of investigationsspanning the last decade [1–6]. In each of these studies thethermosetting epoxies were chosen as the model networksbecause of the simplicity of their crosslinking chemistry andthe availability of the monodispersed monomers. Diglycidylether of bisphenol A (DGEBA) cured with difunctionaldiamine terminated polypropylene oxide (PPO) cross-link-ing agents was used as the model system. DGEBA waspartially deuterated to provide scattering contrast forneutron measurements. Emphasis has been on identifyingheterogeneity in the network structure in general, and

specifically in evaluating the effects of the molecular weightdistribution between cross-links on the structure and physi-cal properties of epoxy networks.

In all of the previous SANS experiments a pronouncedmaximum was observed in the scattering from partiallydeuterated epoxy networks. The characteristic dimensionof the networks, which manifests itself as a scattering maxi-mum, has been correlated with the physical distancebetween epoxy linkages separated by a diamine chain innetworks formed from d-DGEBA with a nearly monodis-persed cross-linking agent [2]. However, a structural anom-aly was observed in a network formed from reaction ofepoxy with a mixture of diamines having two differentmolecular weights. The characteristic dimension of this‘bimodal’ network was found to be larger than the charac-teristic dimension of single diamine networks formed fromeither of the component diamines [3]. In addition, theresponse of the bimodal network to mechanical deformationwas found to differ from the response of single diaminenetworks [5]. Bimodal networks deformed almost affinelywith the macroscopic dimension while the single diamine

Polymer 40 (1999) 4603–4614

0032-3861/99/$ - see front matterq 1999 Published by Elsevier Science Ltd. All rights reserved.PII: S0032-3861(99)00096-8

* Corresponding author. Tel.:1 1-301-975-6839; fax:1 1-301-975-3928.

E-mail address:[email protected] (W.L. Wu)1 Present address: US Army Research Laboratory, AMSRL-WM-MA,

APG, MD 21005-5069, USA.

networks hardly underwent any changes. This sort of obser-vations has been interpreted by the existence of super-struc-tures in bimodal networks. For example, one modelproposes ordering of long and short molecular weightdiamine blocks along a linear path through the network[3] and a second, semi-quantitative treatments suggestscorrelation between sections of the network having a highdensity of a single diamine molecular weight [5]. Limitedsuccess has been achieved in qualitatively addressing thestructure of bimodal networks through these theoreticalmodels.

The purpose of this investigation was to confirm and tofurther examine structural changes occurring in epoxynetworks resulting from mixing the cross-linking agents ofdifferent molecular weights. To this end, small angle X-rayscattering (SAXS) has been employed to evaluate the struc-ture of brominated DGEBA/difunctional diamine termi-nated PPO networks. Formulations prepared include singlediamine networks having different PPO molecular weights,dual diamine or bimodal networks prepared using a givenmolecular weight pair mixed over a range of concentrationratios, and most significantly, model copolymers preparedfrom a single monoamine and monoamine pairs mixed invarious compositions. The anomalous scattering maximumobserved by SANS has been reproduced consistently in theX-ray scattering from bimodal brominated epoxy networks.This feature has been found to vary in position and intensitydepending on the molecular weight and composition of theblend of diamines used to form the network. Experimentalscattering results are compared with theoretical predictionsbased on a comb shape copolymer calculation [7].

2. Experimental section

2.1. Materials

Brominated DGEBA, (DER 542) epoxy resin obtainedfrom Dow Chemical Co. was chosen as the model epoxymonomer for use in this work2. Bromine atoms, substitutedfor the hydrogen in the ortho positions on the aromatic ringsof the epoxy monomer, provide X-ray contrast betweenDGEBA and the cross-linking agent. The cross-linkingagents employed were Jeffamines D-400, D-2000 and D-4000, supplied by Texaco Chemical Co.2. The D-seriesJeffamines are difunctional amines linked by poly(propy-lene oxide); the designation number refers to the approxi-mate molecular weight of each species. Model graftcopolymers were formulated using Br-DGEBA and mono-functional amine terminated PPOs, M-2000 and M-600(designation number represents again the approximate

molecular weight). Networks were prepared by mixingPPO diamines with stoichiometric amounts of Br-DGEBAfollowed by degassing at 708C in a vacuum oven. A fewdrops of the de-gassed mixtures were then sandwichedbetween two pieces of polyimide film separated by 1mmthick Teflon spacers, and then cured at 1208C for two days.Copolymer samples were prepared by mixing PPO mono-amines with stoichiometric amounts of Br-DGEBA at1308C, sandwiching the mixtures between polyimide sheets,and curing at 1108C for three days. At these temperaturesthe cure reaction is dominated by the amine/epoxide reac-tion. All samples were fully cured at under the conditionsemployed.

The specimens prepared for this study included threesingle amine networks, a series of twelve network formula-tions using a pair of diamines mixed over a range of molarratios, and model copolymers with both single and bimodaldistributions of PPO grafting molecular weights. The singlediamines used were D-400, D-2000, and D-4000. The bimo-dal networks were D-400/D-2000 mixtures in molar ratiosof 8/1, 5/1, 3.5/1, 2/1, 1.5/1, 1.22/1, 1/1, 1/1.22, 1/1.5, 1/2,1/3.5, 1/5, and 1/8. Model copolymers were preparedusing M-600/M-2000 mixtures in molar ratios of 0/1, 1/0,and 1/1.

2.2. Small angle X-ray scattering measurements

X-ray scattering measurements were carried out at the10 m SAXS facility at the National Institute of Standardsand Technology [8]. The X-ray source used was a rotatingcopper anode operated at 47 kV and 180 mA with a wave-length of 1.54 Aselected with a graphite monochromator.The instrument uses pinhole collimation. Two dimensionaldata were taken over the range of scattering vector,q, (q�4p /l sinu ) from 0.02 to 0.26 A˚ 2 1 and were subsequentlyreduced to one dimensional (1D) intensity via circular aver-aging. Data in theq � 0.25–0.5 A21 range were obtainedusing a 1D detector. All data were corrected for darkcurrents and empty cell scattering. Sample thickness andtransmission corrections were also implemented for eachscattering result. A polyethylene standard was used forconverting intensity data into absolute units. All Datapresented are scaled by a factorqEp(1 2 qEp), whereqEp

is the volume fraction of Br-DGEBA in the sample, in orderto normalize the dependence of scattering intensity on thecomposition of the network.

2.3. Thermal analysis

Differential scanning calorimetry was used to determinethe glass transition behavior of epoxy networks curing usingD-400/D-2000 diamine mixtures. The experiments wereperformed using a Perkin–Elmer instrument over aprogrammed temperature range of 213–423 K at a scanningrate of 30 K/min.

N.C. Beck Tan et al. / Polymer 40 (1999) 4603–46144604

2 Certain commercial equipment and materials are identified in this paperin order to specify adequately the experimental procedure. In no case doessuch identification imply recommendation by the National Institute of Stan-dards and Technology nor does it imply that the material or equipmentidentified is necessarily the best available for this purpose.

3. Results and discussion

The scattering intensity versus scattering vector curvesfor single amine networks are shown in Figs. 1 and 2.Pronounced scattering maxima are located at approximately0.32, 0.15 and 0.10 A˚ 21 for the D-400, D-2000, and D-4000

networks, respectively. These peaks are in essentially thesame position as those measured from deuterated DGEBA/D-series networks [3,5]. The scattering peak apparent in Fig.1 can be attributed to the intra-network correlation amongbrominated epoxy segments separated by amine linkages, inanalogy with the correlation between deuterated epoxy

N.C. Beck Tan et al. / Polymer 40 (1999) 4603–4614 4605

Fig. 1. X-ray scattering intensity versus scattering vector for an epoxy network made from Br-DGEBA and D-4000 diamine.

Fig. 2. X-ray scattering intensity versus scattering vector from epoxy networks: (W) Br-DGEBA//D-400/D-2000, 4//1/1; (X) Br-DGEBA//D-2000, 2//1; (P)Br-DGEBA//D-400, 2//1.

segments separated by amine linkages which was experi-mentally observed and theoretically verified previously[1–3].

Bimodal epoxy networks also show pronounced

scattering maxima (Figs. 2–5). The scattering from the D-400/D-2000 1/1 bimodal network is compared to the scat-tering from D-400 and D-2000 single amine networks inFig. 2. The main peak from the bimodal network occurs at


Fig. 3. X-ray scattering intensity versus scattering vector from epoxy networks. Br-DGEBA//D-400/D-2000 diamine cross-linking agent mixtures. D-400 richmixtures. D-400/D-2000 ratios as indicated.

Fig. 4. X-ray scattering intensity versus scattering vector from epoxy networks. Br-DGEBA//D-400/D-2000 diamine cross-linking agent mixtures. D-2000 richmixtures. D-400/D-2000 ratios as indicated.

much lowerq than the main scattering peak from either ofthe single amine networks formulated using the componentdiamines. This result confirms the earlier indications of peakshifting in bimodal networks observed in a deuteratedDGEBA/D-series epoxy network [3]. In addition to a shiftin position, the contrast normalized intensityIabs/2(qEp(1 2qEp)) of the main scattering peak from the D-400/D-2000network exceeds the intensity of the scattering peak fromboth the D-400 and the D-2000 networks.

The shift of the main scattering peak in the bimodalnetworks to lowerq relative to the single amine specimensraises questions about the arrangement of the differentamines in the network. (Previous studies suggested orderingof long and short chain diamines [3]). For this reason,additional information about the development of bimodalepoxy network structure was sought by investigating ofthe structure of a specific bimodal network system, D-400/D-2000, as a function of the compositions of the diamine


Fig. 5. X-ray scattering intensity versus scattering vector from epoxy networks. Br-DGEBA//D-400/D-2000 diamine cross-linking agent mixtures. D-400/D-2000 ratios as indicated.

Table 1Scattering characteristics of Br-DGEBA//D-400/D-2000 bimodal networks

Mole ratio: D-400/D-2000 Peak position, qpeak(A21) Peak intensity,Ipeak (cm21) Normalized peak

intensity,Ipeak/(qEp(1 2 qEp)) (cm21)

1/0 0.32 0.29 1.20/1 0.15 0.78 3.81/1 0.10 1.4 5.81.22/1 0.085 1.6 6.71.5/1 0.082 1.7 7.02/1 0.075 2.0 8.03.5/1 0.065 1.5 6.1 (diffuse)5/1 0.060 1.2 4.8 (diffuse)8/1 0.055 0.83 3.3 (diffuse)1/1.22 0.11 1.4 5.91/1.5 0.11 1.3 5.51/2 0.12 1.2 5.31/3.5 0.14 0.98 4.71/5 0.14 0.95 4.51/8 0.15 0.89 4.5

cross-linking agent mixtures. It is important to note that thestoichiometric molar ratio of epoxy to amine, 2:1, is main-tained throughout this series of formulations, and only theratio of the number of amine groups contributed by D-400chains relative to the number of amine groups contributedby the D-2000 chains is changed. The results of the compo-sition study, shown in Figs. 3–5, clearly demonstrate thatthe main scattering peak from bimodal networks prepared inany D-400/D-2000 mole ratio is positioned below the mainscattering peak from either D-400 single diamine network orthe D-2000 single diamine network. The position and inten-sity of the scattering peak in the bimodal networks is clearlya function of composition of the diamine mixture (Table 1and Figs. 3–5). Peak intensity reaches a maximum near themiddle of the concentration range on the D-400 rich side,where the molar ratio of amine groups contributed by D-400to amine groups contributed by D-2000 equals 2/1. The peakposition appears to shift continuously towards lowerq as theconcentration of D-400 in the network increases (Fig. 3)although it becomes difficult to identify a peak positiononce the ratio of D-400 to D-2000 exceeds 3.5/1 as thezero angle scattering intensities also increase.

The D-series diamines are expected to mix homoge-neously regardless of molecular weight due to the nearlyidentical chemical compositions of the molecules. There-fore, it is also expected that the two diamines used to formu-late any given bimodal network will incorporate themselvesrandomly into the epoxy network. However, the appearanceof a highly reproducible, anomalous scattering peak at lowqin all bimodal networks suggests the formation of a structurehaving a larger correlation length than that corresponding tothe spacing between amine linkages, as observed in singleamine networks. This suggestion of longer range

correlations raises questions about the arrangement ofdiamines within bimodal networks; what sort of structuremay lead to an increase in the correlation length of bimodalnetworks relative to single diamine networks?

One possibility is a macroscopic segregation within thenetwork of Br-DGEBA//D-400 linkages and Br-DGEBA//D-2000 linkages. This possibility was investigated usingdifferential scanning calorimetry, which would be expectedto show evidence of a single glass transition temperature fora chemically homogeneous network, and two glass transi-tion temperatures for a segregated network. The results forD-400/D-2000 bimodal networks, illustrated in Fig. 6, showevidence of a single, broad glass transition occurring overthe region spanning the glass transition temperatures of D-400 and D-2000. This behavior indicates that segregationhas not occurred over a macroscopic length scale in thebimodal network. The SAXS results may also be examinedin terms of the structural heterogeneity in the bimodalnetworks. Power law behavior in the highq region with alimiting power law exponent ofn � 2 4 is a signature ofscattering from phase separated systems with sharp inter-faces [9]. For those networks in which the maximum occursat low enoughq such that power law behavior may beobserved, the characteristic exponent is fromn � 2 1.3to n � 2 1.5 which is considerably lower than would beexpected for a phase separated system.

In the absence of phase segregation, one may look tointra-network structure to account for the observed beha-vior. This approach was taken in previous work by Wuand Bauer [3], and an ordered, linear, alternating copolymerof the type (A1–B–A2–B)N was chosen as a model systemwhere A1 represents diamine 1, A2 represents diamine 2, andB represents the epoxy linkage. The scattering from such a


Fig. 6. DSC traces from Br-DGEBA/ diamine networks: (W) Br-DGEBA//D-400/D-2000, 4//1/1; (X) Br-DGEBA//D-2000, 2//1; (P) Br-DGEBA//D-400, 2//1.

model system was calculated for comparison with that fromsingle amine chains (A1–B)N or (A2–B)N. The comparisonbetween such a model system and a network structure isbased on the observation that as one maps out the monomersin the network along the (A–B–A–B–…) paths, many (A1–B–A2–B–…) paths will be encountered. Thus, the theore-tical prediction for the scattering from an (A1–B–A2–B)Nmodel structure was derived, and the following points havebeen demonstrated; 1) the primary scattering feature of sucha structure is a single peak occurring at lowerq than thatresulting from either an (A1–B)N structure or an (A2–B)N

structure; 2) the scattering maxima corresponding to theindividual A1–B and A2–B structures are absent. Theseresults agree qualitatively with the scattering behavior ofbimodal epoxy networks, as observed currently andpreviously [3], and are the motivating factor for examiningthe scattering from bimodal networks over a range ofcomposition.

While the previous calculations based on A1–B–A2–B–…, a regularly alternating structures, provided encouragingresults, they are difficult to compare to the scattering frombimodal networks in which the ratio of A1 to A2 monomersis greatly different from unity. This difficulty can be circum-vented by modeling the networks in an alternative manner.In addition to mapping along the Ai–B paths, the monomerpositions in an Ai/B network can also be fully mapped along(B 0–B0–B0–…) paths, in which B0 represents a B monomerhaving an Ai graft (Fig. 7). Such a comb-shaped, B0 mole-cule is taken as the basic building block or the structural unitfor the networks. Exact replicas of the idealized comb-shaped or graft molecules were synthesized from epoxymixed with mono-functional amines. This allows a directcomparison of the scattering from these copolymers to ourcalculation, and to the scattering from nearly chemicallyidentical networks. Though the theoretical calculationswill be compared to network scattering, they are strictlyderived for bulk systems in which comb-shaped or graftcopolymers are packed randomly. The connectivity amongthe graft copolymer chains to form a network has not beenincluded in the model calculation. In principal, the connec-tivity inherent in real networks could significantly affect thescattering.


Fig. 7. Schematic representation of a bimodal network, illustrating therepeat unit chosen as the building block of the network for modeling.

Fig. 8. Comparison between experimental scattering (X) from the Br-DGEBA//D-2000 network and the best numerical fit to the data (z ).

The theoretical framework for the calculation of scatter-ing from bimodal comb-shaped molecules is outlinedbelow. Random phase approximation scheme was usedand the form factors for the comb-shaped copolymerswere calculated using the expressions given by Benoit andHadziioannou [7]. For the bimodal networks a randomplacement of the long diamine chains and the shortdiamine chains is assumed and the resultant scatteredintensity, I(q), from an (A–B)N multiblock copolymer

is given by:

I �q� � Db2 PA�q�PB�q�2 PAB�q�2PA�q�1 PB�q�1 2PAB�q� ; �1�

whereDb2 is the difference in scattering length densitybetweena and b monomer units, andPA, PB, and PAB

are intra-chain structure factors corresponding to all A–A, B–B, and A–B correlations along a given comb or


Fig. 9. Simulated scattering from epoxy networks based on the copolymer scattering model withl � 6.44 A: (a) D-400 and D-2000 single amine networks andthe 1/1 D-400/D-2000 bimodal network; (b) D-400/D-2000 bimodal networks (mixtures as indicated).

graft molecule, respectively. Throughout this work themolecular weight of a PPO repeat or monomer unit wastaken as unity. The thermodynamic interaction para-meter between A and B units (xAB) is assumed to bezero. The structure factorsPi, for a block copolymerhaving a comb shaped or graft architecture are:

PA�q� � uPa�q�

na1

2A2a�q�Xb

Nna

N1 2 xb

21 2 xN

b

1 2 xb

ÿ �2 !" #

;

�2a�

PB�q� � vPb�q�

nb1

2A2b�q�

Nnb

N1 2 xb

21 2 xN

b

1 2 xb

ÿ �2 !" #

;

�2b�

PAB�q� � uNna

Aa�q�Ab�q�

� 1 2 xNb

1 2 xb

ÿ � 12

1 2 xbN 2

1 2 xNb

1 2 xb

!" #; �2c�

whereN is the total number of (A–B) repeat units,nb isthe number of monomers per B block,na is the averagenumber of monomers per A block defined as (fa1na1 1fa2na2) where fai is the number fraction ofai blocks, uthe volume fraction ofa monomers,v the total volumefraction of b monomers identical toqEp (used tonormalize the scattering intensities in Figs. 1–5, 10,11), and xi, Ai and Pa,b are defined in the followingequations for polymer chains approximated as Gaussian

coils:

Pa�q� � n2a1fa1Pa1�q�1 n2

a2fa2Pa2�q�; �3a�

Pai�q� � 2q2r2

ai

�1 2 Aai�q��;

Pb�q� � n2b

2q2r2

b

1 2Ab�q�

nb

� �" #; �3b�

Aa�q� � na1fa1Aa1�q�1 na1fa2Aa2�q�;

Aai�q� � 1q2r2

ai

�1 2 xai�; �4a�

Ab�q� � nb1

q2r2b

�1 2 xb�" #

; �4b�

xai�q� � �1 1 eq2r2ai�21=e

; �5a�

xb�q� � �1 1 hq2r2b�21=h

; �5b�

Mw

Mn

� �A� 1 1 e; �6a�

Mw

Mn

� �B� 1 1 h; �6b�

where ri � ((1/6) ni)0.5 l i is the radius of gyration of

block i with ni monomer units of step lengthl i. Eqs.(1)–(3b) may be used to calculate the scattering for a


Fig. 10. X-ray scattering intensity versus scattering vector from the Br-DGEBA//D-4000 network (B) and the Br-DGEBA//M-2000 copolymer (V).

comb copolymer if the parametersN, n, l i, e and h areknown, or to fit one or more of these parameters bymatching the calculation with experimental scatteringdata.

The expressions (1)–(6b) have been employed to fit theexperimental data from both single diamine and bimodalnetworks using a non-linear least squares numerical routine.The fitted parameters include an arbitrary intensity scalingfactor and a single monomer step lengthl. While it is recog-nized that the epoxy segments should be stiffer than the PPOsegments and thereforelEpoxy should be larger thanlPPO, it isnot possible to fit these variables separately using thecurrent analysis due to close coupling of these two variables.Consequently a single fitted parameterl was used for both Aand B units and this provides a simplistic average of char-acteristic lengths of all the chains in the network.

A comparison between the theoretical fit and the experi-mental data from the Br-DGEBA//D-2000 network is shownin Fig. 8. The peak position is fit reasonably well, though theshape of the peak and the lowq intensity do not match wellbetween experiment and the best fit to the comb copolymerscattering prediction. The fitted values ofl (D-400: 6.3A, D-2000: 6.6 A, D-4000: 8.5A) are similar to what may beexpected for the Kuhn length of PPO [10]. Fitted curvesfor the bimodal networks have been generated in the samemanner, the agreement between experiment and the modelis only marginal. In addition, an acceptable fit of the peakpositions in bimodal networks can be achieved only whenthe characteristic length,l, of the bimodal network isallowed to substantially exceed that of the single amine

networks. The maximuml value occurs in the networkwhere the weight fraction of D-400 and D-2000 chains areroughly equal (Table 2). If this result were valid it wouldimply that the PPO chains assume a stretched configurationin bimodal networks relative to single amine networks.However, previous evidence gathered from swelling studieshas shown that the swelling ratios of bimodal networks liebetween those of the corresponding single diamine networks[4], indicating that there is not significant perturbation ofchain conformations in bimodal networks relative to singleamine networks. The scaling factor,Is, for normalizing thescattering intensities between the calculated and the experi-mental results, varies widely from case to case, but is signif-icantly greater than the expected value ofDb2� 0.22 cm21

Eq. (1). This suggests that the interaction parameter,xAB,between the brominated epoxy and the diamines is greaterthan zero. Alternatively, this observation can be interpretedin terms of an inter-chain segregation between (A1–B) unitsand (A2–B) units. All calculations conducted so far havebeen based on a simplified model withxAB � 0.

Without resorting to the unrealistic notion that the valueof characteristic lengthl depends on bimodal or unimodalcompositions, (1)–(6b) with a fixedl � 6.44 A(the averagefrom the D-400 and D-2000 fits) are used in the followingcalculations to evaluate the effect of a bimodal cross-linkermolecular weight distribution on the scattering from Br-DGEBA//D-400/D-2000. The calculated results (Figs. 9aand 9b) show very little similarities with experimentaltrends; such as a shifting of the scattering peak in bimodalnetworks to lowerq than for single amine networks across


Fig. 11. The experimental results and their best fits of Br-DGEBA//M-600/M-2000 copolymer series. M-600/M-2000 ratios as indicated.

the entire composition spectrum and broadening of themaxima corresponding to highly D-400 rich formulations.The only exception is the enhancement in zero angle scat-tering intensity, this enhancement is easily predictable oncethe building block of networks or linear chains is changedfrom a monodisperse structure unit to a mixture of two unitsof different molecular weight. Thus, it is concluded that the‘‘bimodal comb or graft copolymer model’’ formulatedabove does not adequately describe the scattering frombimodal networks.

Owing to the failure of applying the aforementionedmodel to bimodal networks, it becomes interesting to exam-ine whether it ever works for bimodal comb copolymersystems. To investigate this point, measurements on copo-lymers made from Br-DGEBA and monoamine terminatedPPO were conducted. Before one makes a comparisonbetween the model calculation and the experimental data,the scattering curves from a Br-DGEBA//M-2000 copoly-mer and a Br-DGEBA//D-4000 network are compared inFig. 10. If the scheme outlined in Fig. 7 holds true, i.e. ifthe scattering of a network can be simulated by a randomlypacking of comb-like chains, one expects the scatteringintensities from the D-4000 and the M-2000 samples to beidentical. Clearly, there is a difference between the scatter-ing from the two systems— the network peak is sharper andoccurs at lowerq than the peak in the model copolymerscattering. The enhanced peak intensity indicates the exis-tence of inter-chain correlations in the networks and thesecorrelations have not been included in the current calcula-tion based on randomly packing. One possible remedy tothis deficiency is to introduce a positive interaction para-meter between the amine chains and the epoxy chains asdiscussed before.

Bimodal comb copolymers were synthesized in additionto single monoamine chains, and the scattering results fromthese molecules (Fig. 11) can be fitted reasonably well usingthe theoretical model described before. The differencesbetween the single amine copolymer scattering and thebimodal copolymer scattering are clearly less dramaticthan the parallel comparison in scattering between

networks; there is virtually no shift in the peak positionobserved in the bimodal copolymer scattering relative tothe scattering from the corresponding single monoaminecopolymers. Fitting of the data with the equations outlinedabove results in predictions of nearly identical characteristiclength for bimodal copolymers and single monoamine copo-lymers, in contrast to the widely varying characteristiclengths predicted for bimodal versus single amine networks(Table 2). These results indicate that the model developedherein works well for graft copolymers even it failed badlyfor networks.

4. Conclusions

The small angle X-ray scattering behaviors from singleamine epoxy networks, bimodal epoxy networks, and modelepoxy graft copolymers have been examined. Prominentscattering peaks have been observed in all the materials.The scattering from a model graft copolymer with uniformgraft molecular weight was found to be significantly differ-ent from that of a network comprised of identical chains.The network scattering exhibits a sharper maximum atlower q than that from the model graft copolymer. Thisobservation indicates that the molecular structure ofnetworks can not be adequately described by a randomlypacking of equivalent graft chains. Inter-network correla-tions, which have not been included in our model calcula-tion, are likely the cause of these differences. A theoreticalframework based on randomly packing comb-shaped orgraft copolymers work well for all the model graft copoly-mers including the bimodal graft copolymer. The scatteringfrom bimodal graft copolymer did not exhibit the anomalousshift of peak to lowerq, such a shift was conspicuous in thescattering from bimodal networks as compared to the corre-sponding single amine networks. This shift of the scatteringmaxima to lowerq in bimodal networks has been highlyreproducible, occurring in networks over a wide range ofcompositions. This observed shift in peak position indicatesthe existences of longer correlation distances in bimodal


Table 2Fitting Parameters. Characteristic length,lfit, and scaling factor,Is

Amine pair (I/II) Mole fraction I Weight fraction I Peak positionqpeak (A21) lfit (A) Is

D-400/D-2000 (1/0) 1.00 1.00 0.32 6.27 0.67D-400/D-2000 (0/1) 0.00 0.00 0.15 6.61 3.88D-400/D-2000 (8/1) 0.89 0.62 0.085 11.2 6.32D-400/D-2000 (3.5/1) 0.78 0.41 0.075 12.9 8.38D-400/D-2000 (2/1) 0.67 0.29 0.065 13.1 1.97D-400/D-2000 (1/1) 0.50 0.17 0.10 10.1 6.26D-400/D-2000 (1/2) 0.33 0.09 0.12 8.62 1.09D-400/D-2000 (1/3.5) 0.22 0.05 0.14 7.30 4.25D-400/D-2000 (1/8) 0.11 0.02 0.15 6.82 4.18M-600/M-2000 (1/0) 1.00 1.00 0.17 6.83 0.87M-600/M-2000 (0/1) 0.00 0.00 0.12 7.65 0.74M-600/M-2000 (1/1) 0.50 0.23 0.12 7.91 0.85

networks. Both thermal analysis and limiting power lawbehavior of the X-ray scattering data preclude phase segre-gation in the bimodal epoxy networks studied so far. Themolecular structure responsible for this long correlationlength remains elusive.

Acknowledgements

NCBT wishes to acknowledge the financial support of theNRC Post-doctoral Research Associateship program at NIST.This study was also financially supported by the US Depart-ment of State and the Czech Republic Ministry of ForeignAffairs under a US/Czech Republic Joint Projects program.

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Network structure of bimodal epoxies—a small angle X-ray scattering study