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Polymer 52 (2011) 4528e4535

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Polymer

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Effect of free volume hole-size on fluid ingress of glassy epoxy networks

Matthew Jackson a, Mukul Kaushik a, Sergei Nazarenko a, Steve Ward b, Rob Maskell b, Jeffrey Wiggins a,*

a School of Polymer and High Performance Materials, University of Southern Mississippi, 118 College Dr. #5050, Hattiesburg, MS 39406, USAbCytec Engineered Materials, 2085 E Technology Cir # 300, Tempe, AZ 85284, USA

a r t i c l e i n f o

Article history:Received 21 June 2011Received in revised form26 July 2011Accepted 27 July 2011Available online 2 August 2011

Keywords:Solvent-transportGlassy networkFree volume

* Corresponding author. Tel.: þ1 601 266 4869; faxE-mail address: Jeffrey.wiggins@usm.edu (J. Wiggi

0032-3861/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.polymer.2011.07.042

a b s t r a c t

This manuscript demonstrates the synthesis of glassy polymer network isomers to control morphologicalvariations and study solvent ingress behavior independent of chemical affinity. Well-controlled networkarchitectures with varying free volume average hole-sizes have been shown to substantially influencesolvent ingress within glassy polymer networks. Bisphenol-A diglycidyl ether (DGEBA), bisphenol-Fdiglycidyl ether (DGEBF) and tetraglydicyl-4,40-diamino-diphenyl methane (TGDDM) were cured with3,30- and 4,40-diaminodiphenyl sulfone (DDS) at a stoichiometric ratio of 1:1 oxirane to amine activehydrogen to generate a series of network architectures with an average free volume hole-size (Vh)ranging between 59 and 82 Å3. Polymer networks were exposed to water and a broad range of organicsolvents ranging in van der Waals (vdW) volumes from 18 to 88 Å3 for up to 10,000 h time. A clearrelationship between glassy polymer network Vh and fluid penetration has been established. As pene-trant vdW volume approached Vh uptake kinetics significantly decreased, and as penetrant vdW volumeexceeded Vh a blocking mechanism dominated ingress and prevented penetrant transport. These resultssuggest that reducing the free volume hole-size is a reasonable approach to control solvent properties forglassy polymer networks.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Transport phenomena are a major research thrust for polymericmaterials. Time and temperature dependant transportation ofgasses, water, organic solvents, oligomers and polymers movingthrough high molecular weight linear and crosslinked polymershave led to several models and theories being reported. Despite thisbroad scientific literature base, one important area that lackssufficient reporting is the transport of small organic moleculesthrough highly crosslinked polymer glasses. This gap is significantsince we are witnessing a rapid proliferation of polymer matrixcomposites as structural materials in transportation, energy andinfrastructure sectors. Glassy polymer networks used as matrixmaterials in composites control critical properties such as thermal,chemical, interfacial and environmental performance. For example,during its operating life a composite aircraft will be exposed toa number of aggressive chemical fluids, including water, MEK, jetfuel, hydraulic fluids, cleaners and etc. which have the potential toalter matrix performance. Exposure to these fluids can causea reduction of key mechanical properties such as modulus andstrength [1,2], but transport mechanisms are not well-understood.

: þ1 601 266 5504.ns).

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As a result, matrix chemistries used in composite materials areformulated to minimize the mechanical impact of fluid exposurebut it is logical to assume that fluid resistance and performanceconfidence could be improved if the mechanisms of solvent ingresswithin glassy polymer networks were better understood.

Due to natural abundance, diffusion of water through polymericglasses has been sufficiently studied and shown to follow classicFickian behavior with the rate of ingress being proportional to theconcentration gradient of water [3e5]. Recently, free volumearguments have been used to explain the ingress of water intoglassy polymer networks. Free volume is one of the most importantcharacteristics of glassy amorphous polymers controlling physical[6], thermal [7] and transport behaviors [8]. Soles et al. studied theeffects of fractional and hole-size free volume on moisture uptakeand concluded free volume played a significant role, but a directrelationship was not determined. Network polarity was suggestedas the primary effect, and free volume hole fraction as a secondaryeffect with larger holes providing greater access to polar bindingsites [9]. Zhang and Mijovic, through spectroscopic techniques,reported more than 95% of water content resides near polar groupsin epoxies and equilibrium water content would be determined bythe number of polar groups [10,11]. Yee and coworkers suggest thatwhile a correlation between free volume and ultimate moistureuptake is clear, hole volume fraction alone is not sufficient topredict the ultimate moisture uptake [12,13].

Table 1Sample nomenclature.

Epoxy Amine Abbreviation

DGEBA 4,4’DDS 44ADGEBA 3,3’DDS 33ADGEBF 4,4’DDS 44FDGEBF 3,3’DDS 33FTGDDM 4,4’DDS 44TG

M. Jackson et al. / Polymer 52 (2011) 4528e4535 4529

Reports defining the transport mechanisms of organic solventsthrough glassy polymer substrates are less studied than water andgenerally believed to be dependent upon the composition of thepenetrant, and unlike water follow non-Fickian kinetics [14e16].Transport of organic solvents through these materials has beenshown to follow Case II diffusion defined by linear mass uptakeover time with a constant moving well-defined flow front leavingan unperturbed region of material in the center of the sample untilequilibrium [17,18]. Attempts to predict this behavior have relied ona model first introduced by Thomas and Windle [19] but modifiedto describe a dual sorption theory where a steady moving Case IIdiffusion was predicated by a Fickian flow front [20]. These modelswhich have typically been reported for linear polymer glasses alsoapply to the diffusion behavior of small molecule transport withinglassy polymer networks. Limitations in linear polymer modelsoccur when predicting glassy network behavior since the rheo-logical environment changes with crosslinks which alter uptakekinetics. Crosslinks are reported to restrict plasticized Brownianmotions that assist in fluid uptake behavior [21], therefore freevolume is even more important in glassy crosslinked networkssince it replaces viscosity as the dominant factor which controls therate of solvent ingress [19].

Positron annihilation lifetime spectroscopy (PALS) free volumeanalysis has been coupled with real-time near infrared spectros-copy (NIR) spectra to gain a better understanding of how networkarchitectures develop and control glassy state free volume. NIR wasused to track the concentration of primary and secondary aminesduring cure to determine morphological differences in networksresulting from amine isomer positions. For example, para- vs. meta-substituted aromatic amines displayed different reaction rates dueto electronic resonance effects leading to variances in final networkstructures. The utilization of curative isomers resulted in measur-able differences in glassy state free volumes without altering thechemical interactions between the network and solvent. As a result,we were able to eliminate matrix chemical effects and sufficientlyalter morphology to study glassy state free volume effects onsolvent transport.

2. Materials and methods

2.1. Materials

Bisphenol-A diglycidyl ether (DGEBA, EPON 825, 175 g perequivalent, Hexion Specialty Chemicals Co.), bisphenol-F diglycidylether (DGEBF, EPON 862, 165 g per equivalent, Hexion SpecialtyChemicals Co.), tetraglydicyl-4,40-diamino-diphenyl methane(TGDDM, Araldite MY 721, 109 g per equivalent, HuntsmanAdvanced Materials), and 3,30- and 4,40-diaminodiphenyl sulfone(DDS, 97%, Aldrich Chemical Co.) were used as received. Water,methyl ethyl ketone (MEK), acetone, acetonitrile, methanol, tetra-hydrofuran, and 1-butanol (all 99þ% HPLC grade), Fisher, were usedas received.

2.2. Glassy polymer network preparation

In a typical reaction, 200.0 g (571.4 mmol) DGEBA was chargedto a 500 ml Erlenmeyer flask equipped with a vacuum fitting andmagnetic stirring device. The epoxy prepolymer was heated to100 �C when 70.9 g (285.7 mmol) 4,4’-DDS was slowly added overa 10e15min period to avoid agglomeration. Upon addition, vacuumwas slowly applied to a level of w10�3 Torr when the temperaturewas increased to 120 �C and the mixture was stirred until disso-lution of amine was observed. Vacuum was removed and the clearsolution was poured into preheated (100 �C) silicone molds ofvarious dimensions. Samples were cured for 5 h at 125 �C and

subsequently post-cured for 2 h at 225 �C. Slight variations of thecuring prescriptions were applied to alternate curative chemistriesin an effort to achieve the fully vitrified glassy state withoutthermal degradation. All networks were cured using a 1:1 stoi-chiometric equivalent of oxirane to amine active hydrogen. Table 1describes the nomenclature employed within this manuscript forglassy polymer network chemistries.

2.3. Dynamic mechanical analysis measurements

Dynamic mechanical analysis (DMA) experiments to probechanges in thermomechanical properties with fluid exposureswere conducted on a Rheometric Scientific DMTA V, or a TAInstruments Q-800 DMA using a tensile fixture. Strain amplitudesof 0.05% and frequencies of 1 Hz were applied over a range oftemperatures from �125 �C to 300 �C at a ramp rate of 5.0 �C/min.Specimens were formed by casting b-stage resins into siliconemolds with rectangular cavities of 60.0 mm length � 5.0 mmwidth � 1.5 mm deep.

2.4. Fluid uptake measurements

Rectangular epoxy samples having mass of approximately300 mg and thickness of 1.5 mm were conditioned in a vacuumoven for 12 h at 100 �C prior to measuring starting weights. Thedried polymer samples were placed in 20 mL scintillation vialscontaining w15e18 mL of fluid. The jars were sealed and stored at25 �C in a Fisher Scientific Model 146E incubator. When calculating% change in mass (fluid uptake), two samples were removed fromsolution, carefully patted dry, weighed to the nearest 0.1 mg andaveraged. The % change in mass for each sample was calculated asfollows:

% Change in Mass ¼ mh �mi

mi� 100 (1)

where mh is the hydrated mass and mi is the initial mass.

2.5. Differential scanning calorimetry (DSC) conversion

Isothermal DSC experiments to measure cumulative heat (Q)were performed under various curing conditions on a TA Instru-ments Q200 DSC with samples ranging from 5 to 10 mg in sealedaluminum pans. Nitrogen was used as purge gas and Indium andSapphire were used as temperature and enthalpy calibrates,respectively.

2.6. Near infrared spectroscopy (NIR)

NIR spectra in transmission mode were recorded usinga Thermo Scientific Nicolet 6700 FT-IR in the range of4000e8000 cm�1. A white light source was used in conjunctionwith a KBr beam splitter and a DTGS KBr detector. Samples wereprepared by sandwiching B-stage resins between glass slides witha 0.8 mm Teflon washer used as a spacer. The reaction progressed

Fig. 1. DSC measured exotherm from epoxy amine reaction.

M. Jackson et al. / Polymer 52 (2011) 4528e45354530

according to varying curing prescriptions in a Simplex ScientificHeating Cell where 16 scans at 4 cm�1 resolution were acquiredevery 10 min during cure. Molar absorptivities ( 3) were determinedby taking scans of pure monomers and applying Beer’s law [22].

3¼ Abc

(2)

where A is the area under the curve for the specific absorbingspecies, b is the path length and c is the concentration of functionalgroup. Concentrations of pure substances were calculated by usingdensity, molecular weight, and functionality values provided bymaterial suppliers. Concentration of glycidyl groups in DGEBA resinwas 6.55 mol/L while concentration of primary amine in 3,30 and4,40 DDS was 10.95 mol/L.

For the crystalline DDS, micronized powder was pressed intoapproximately 0.03mm thick films with a KBr press. Primary amine3 at 4525 cm�1 and 5030 cm�1 was measured to be 18.48 L/(mol� cm) 86.82 L/(mol� cm) respectively. Secondary amine 3wasdetermined from the B-staged resin under the assumption thatonly primary amine was consumed during mixing and was calcu-lated to be is 51.91 L/(mol� cm) at 6500 cm�1. Epoxy 3, determinedfrom pure resin, was measured to be 36.64 cm�1 at 4525 cm�1.

2.7. Positron annihilation lifetime spectroscopy (PALS)

Positron annihilation lifetime spectroscopy (PALS) measure-ments were conducted using a custom built instrument employing22Na as a positron source. The spectrometer holds two samples of1 mm thickness and 1 cm diameter with the positron sourcesandwiched in it. For this purpose, a custom built setup was usedwith Hamamatsu H3378-50 Photo Multiplier Tubes with BaF2scintillation crystals attached on them, to detect birth and deathsignals of positron. A fastefast coincidence system based oncommercial EC&G Ortec NIM modules (model 583 constant-fraction discriminators), and a model 566 time-to-amplitudeconverter. Temperature scans were carried out from �30 �C to200 �C in a stepwise fashionwith 5 �C intervals with 1 h periods for106 number of counts at each data point.

Because only the longest lifetime was used for further analysis,no source corrections were carried out. The time resolution wasdetermined with the program Resolution of the PATFIT-88 package.The spectra were decomposed into three discrete lifetime compo-nents using the PARFIT-88 package. The longest lifetime wasattributed to o-Ps pick-off annihilation.

For the calculation of hole-sizes, a simple quantum mechanicalmodel proposed by Tao-Eldrup was used, which assumes the Ps tobe confined to a spherical potential well with infinitely high walls.The assumption of spherical holes has been justified for flexible-chain polymers (poly-propylene) as well as relatively stiff-chainpolymers (bisphenol A-polycarbonate) [7]. In the Tao-Eldrupmodel, the electron density of the surrounding molecules isapproximated by an electron layer of constant thickness. In poly-mers, Ps is trapped by local free volumes (holes) of the disorderedstructure and their size controls the o-Ps lifetime s3 in the nano-second (ns) range. From s3 the mean radius R of the local freevolume, Vh, may be calculated using a semiempirical equationproposed by Tao-Eldrup.

s3 ¼ 0:5�1� R

R0þ 12p

sin�2pRR0

���1

(3)

where ΔR ¼ R0�R ¼ 0.1656 nm.The prefactor 0.5 ns in Eq. (2), is equal to the Ps annihilation rate.

The quantities R and ΔR are the radius of the hole and an empiricalparameter that describes the thickness of the electron layer,

respectively. The value of ΔR has been determined before to be1.656 Å by fitting Eq. (2) to positron lifetime values measured insystems of known hole-sizes. Because the o-Ps lifetime is expectedto show a distribution in polymers, the discrete o-Ps lifetimeobtained using the PATFIT88 package actually represents a meanvalue. Thus, we use the terms “average o-Ps lifetime” for o-Ps and“average hole radius” for R.

3. Results and discussion

3.1. Network formation

To probe the effects of network structure and free volume onfluid transport, chemical affinity variations were minimized bycuring epoxies with amine isomers. This approach altered networkarchitectures and packing densities while maintaining similaratomic compositions and network polarities. The meta-substitutedisomer benefits from resonance stabilization promoting a lowertransition state activation energy effectively increasing reactivity.Fig. 1 compares exotherms of the DGEBA oxirane ring openingreactions for 3,30- and 4,4’-DDS cured at 125 �C for 5 h. The 3,3’-DDSsample (33A) displayed a substantially higher exotherm comparedto the 4,4’-DDS sample (44A) suggesting higher conversion andarchitectural variances during pre-gel network formation.

Variances in network structures were further investigated bytracking the reactions in real-time and monitoring the changes inconcentration of functional groups. Fig. 2 shows the NIR spectrawhere each line represents 1 h intervals throughout the reaction.Absorbances associated with functional groups tracked during thecuring reactions include primary amine overtones(4962e5129 cm�1), primary amine e secondary amine combina-tions (6504e6805 cm�1), and primary amine e epoxy overlaps(4493e4568 cm�1). To determine functional group concentrationsover time, Beer’s law was applied according to the equation:

c ¼ A3b

(4)

where A is themeasured NIR absorbance, 3is the molar absorptivityof the absorbing species, and b is the path length.

Fig. 3 shows the NIR real-time kinetic plots derived for 33A and44A. Each plot shows the concentration of epoxide groups, primaryamine, and secondary amine at 1 h intervals throughout the reac-tion. The data points at �1 h represent the initial reactionconcentrations which were calculated from molecular weights anddensities of the components. A typical 1:1 stoichiometric mixtureof epoxy to reactive amine hydrogen gave starting concentration

Fig. 2. NIR spectra of 33A system showing the progression of reaction and peaks ofinterest.

M. Jackson et al. / Polymer 52 (2011) 4528e4535 4531

ratios of 2:1 epoxy to primary aromatic amine. Since the amine wasa crystalline solid which would not solubilize in the liquid epoxyresin at room temperature, heat was applied to the system forsolubilization, which resulted in consumption of a certain amount

Fig. 3. Real-time NIR plots tracking conversion of epoxy B, primary amine -, andsecondary amine: for 33A (A) and 44A (B).

of primary amine during this solubilization period. Time zero inFig. 3 refers to the solubilization point of the amine and was used asthe starting point for NIR acquisition.

33A showed rapid consumption of primary amine which was99% consumed after 2 h at 125 �C. Secondary amine concentrationreached a maximum after w1 h as the primary amine concentra-tion approached 0 indicating all primary amine reacted prior tosignificant secondary amine conversion. After 2 h the epoxide andsecondary amine concentrations became equal and trackedconcurrently for the remainder of the reaction. After 5 h at 125 �Cthe epoxide conversion approached 88% suggesting somesecondary amine conversion. In 33A, primary amines react initiallyto form more linear chain segments. Subsequently, secondaryamines reacted to crosslink the system until a vitrified state wasreached. After 5 h the temperature was raised to 200 �C for 2 h tofurther drive the vitrified state during which time the remainingsecondary amines reacted to near 100% conversion.

44A showed lower amine reactivity compared to 33A as only 1/2of the primary amines reacted after 2 h. The primary aminecontinued to react slowly and secondary amine concentrationincreased until 5 h at which point epoxide conversion remainedbelow 50%. At this point primary amine was still present andthrough our analysis the gel point had not been reached. As thetemperature was increased, in this case to 225 �C for 2 h, theresidual primary and secondary amines reacted simultaneously,resulting in a rapid vitrification of the system. As this systemvitrified the reaction slowed and eventually locked into a highlyrandom configuration leaving 6% of the epoxide groups unreacted.We have observed higher post-cure temperatures for 44A lead tochemical degradations of the networks and elected to maintain the225 �C post-cure for this report. Epoxide concentrations andconversion data are displayed in Table 2 (33A) and Table 3 (44A). Asmentioned, the data points at �1 h represent calculated initialconcentrations before amine solubilization. The reactivity differ-ences between the isomers are apparent after the amine solubili-zation step where 28% of epoxide was converted duringsolubilization for 33A and 15% was converted for 44A.

The reactivity differences of the isomers manifested into glassystate morphological differences as is observed in the average hole-size free volume (Vh) measurements shown in Fig. 4. 33A exhibiteda smaller hole-size free volume at all temperatures in the glassystate. Average hole-size (Vh) measured by PALS elucidated networkstructure by probing unoccupied space with a 1 Å radius positron.Unoccupied space or free volume is inherent to all polymericmaterials and arises from non-uniform packing of molecules.Typically, samples with higher glass transition temperaturespossess higher free volumes [23]. As the epoxy samples cooled fromthe rubbery-to-glassy states after post-cure, longer rangesegmental chain motions became restricted and free volume wasessentially frozen into network architectures. PALS has a distinctadvantage since sample modifications which perturb network

Table 2NIR epoxide concentration (33A).

Temperature (�C) Time (hrs) [Epoxy] (mol/L) Conversion (%)

25 �1 5.07 0.00125 0 3.67 27.66125 1 2.93 42.26125 2 1.82 64.20125 3 1.16 77.10125 4 0.79 84.51125 5 0.58 88.48225 6 0.12 97.73225 7 0.02 99.59225 7.5 0.02 99.59

Fig. 5. Comparison of water absorption curves for 33AB and 44A-.

Table 3NIR epoxide concentration (44A).

Temperature (�C) Time (hrs) [Epoxide] (mol/L) Conversion (%)

25 �1 5.07 0.00125 0 4.30 15.16125 1 4.29 15.42125 2 4.06 19.86125 3 3.83 24.38125 4 3.53 30.43125 5 3.10 38.88225 6 0.86 82.97225 7 0.36 92.97225 7.5 0.32 93.73

M. Jackson et al. / Polymer 52 (2011) 4528e45354532

structures are not necessary and themethod provides direct insightinto true glassy state network morphology. The 25 �C average hole-size free volumes for 33A and 44A were calculated to be 76 Å3 and82 Å3, respectively. The lower free volume of 33A is related to theincreased conformational freedom of the meta-substituted isomerproviding a higher order of packing. The free volume data illus-trated in Figure validated isomer variances in network topologiesand provided the basis for studying fluid transport dependence onhole-size free volume.

3.2. Moisture absorption

Fig. 5 shows moisture uptake curves for 33A and 44A depictingcurve shapes with rapid initial transport followed by a continualdecline in rate until equilibrium was reached (w1600 h). Expo-nential decay curves were fit to the data and the asymptote valuewas determined as the equilibrium water content (Minf). Waterabsorption behavior for the 33A and 44A networks followed trendsreported for other glassy network polymers [24].

It is generally agreed upon that water sorption into epoxy resinsfollows Fickain diffusion, where at short times the diffusion coef-ficient can be approximated as follows [25]:

Mt

Minf¼ 4

L

ffiffiffiffiffiffiDtp

r(5)

where Mt is the water absorption at time t, Minf is the equilibriumwater absorption found in Fig. 5, L is half the sample thickness toaccount for diffusion from both sides, and D is the diffusion coef-ficient. Fig. 6 plots Mt/Minf vs.

ffiffit

pwhere the slope is proportional to

Fig. 4. Average hole-size free volume as a function of temperature of 33AB and 44A-.

the diffusivity of water through the individual network. Fickiankinetics were observed since the initial rates of uptake were linearto

ffiffit

p.

Diffusivities provided in Table 4 were calculated from the slopesof theMt/Minf vs

ffiffit

plines. This method normalized the data to each

network’s equilibrium value providing a direct comparison ofdiffusivities.

Due to the relative sizes of water to free volume hole-size, waterwas able to traverse the network and occupy space throughout thesample prior to saturation. The rate of diffusion has been reportedto be controlled by the ability of the water to navigate the freevolume pathways through the network [26] and is similar to thebehavior of gas diffusion in thin films where a tortuosity factorgoverns diffusion rate [31]. A larger average hole-size free volumeincreases the probability that the free volume will be inter-connected providing a less tortuous path and a higher diffusionrate. Comparison of the PALS data with the diffusivities in Table 4confirms the larger 44A average hole-size led to a higher diffu-sion rate and equilibrium of water uptake.

Fig. 7 shows the E0 and Tan-d curves generated for 44A at 0 h,528 h and 1632 h. The main difference we observed is shown in theFig. 7A Tan-d plots where the presence of water created two broadpeaks. High amounts of intermolecular hydrogen bonding is known

Fig. 6. Mt/Minf vs.ffiffit

pplots to determine diffusivities of 33A and 44A.

Table 4Water equilibrium and diffusivity values.

Sample Thickness(mm)

Equilibrium(Minf)

Slope Diffusivity(10�9 cm2 s�1)

33A 1.64 2.88 0.0395 0.57244A 1.63 3.85 0.0442 0.708

M. Jackson et al. / Polymer 52 (2011) 4528e4535 4533

to occur in epoxy amine systems [27] which gives the appearance ofa homogeneous network [28]. As water was introduced into thenetwork it disrupted the intermolecular hydrogen bonding andbegan to form secondary bonds with hydroxyl and tertiary aminemoieties [29,30]. Disruption of this intermolecular bonding causedthe heterogeneities of the networks to become apparent in theform of two broad Tan-d peaks. The peak at 175 �C shows the waterplasticized material and is consistent with the Fox equation Eq. (6)which predicts the glass transition temperature of a plasticizedmaterial based on the weight fraction and Tg of the low molecularweight diluent [31].

1Tg

¼ w1

Tg;1þ w2

Tg;2(6)

wherew1 is the weight fraction of polymer andw2 is the weightfraction of water. As the temperature increases during the experi-ment, water was driven from the sample and the Tg of the materialincreased, however never reaching the magnitude of the virginsample. Heating rate will influence this behavior and it may bepossible to recover full properties at a very slow heating rate.Storage modulus curves depicted in Fig. 7B suggest the room

Fig. 7. DMA plots of Tan-d (A) and E0 (B) for 44A upon water ingress.

temperature modulus is not significantly affected by the presenceof water, and the elevated temperature moduli shifted in a mannerconsistent with the Tan-d data.

3.3. Organic solvent uptake

Similar to water, absorption behaviors of organic penetrantswere governed by network hole-size free volumes in the glassystate, but displayed linear absorptions compared to the exponentialdecay Fickian behavior of water. We have studied the transportbehavior for a broad range of organic solvents into glassy polymernetworks and consistently observed hole-size free volume as thedominant factor controlling uptake. Although more quantitativearguments will be provided later in this discussion, it is instructiveat this point to provide a universal comparison of data whichdescribes our general observations between penetrant volume andglassy network average hole-size. Fig. 8 compares solvent uptakedata for a range of solvents ingressing within a series of well-controlled network architectures based upon DGEBA, DGEBF andTGDDM epoxy chemistries cured with 3,30- or 4,4’-DDS. Thiscombination of chemistries provided a range of measured averagehole-sizes in the glassy polymer networks while maintainingrelatively similar chemical architectures (Table 5). In every case, asthe penetrant size approached, or was larger than the average hole-size, uptake kinetics dramatically decreased. In contrast, if thepenetrant size was smaller than the average hole-size, a more rapiduptake behavior was observed.

Fig. 9 shows the 3 week absorption data for 44TG, 44A and 33Fin seven polar solvents of various penetrant molecule sizes. Thesethree networks were chosen in this example for their measuredvariations in Vh. Mass uptake was plotted against penetrant van derWaals volume and each polymer was soaked in the various solventsfor 22 days. Solvent kinetic diameters would perhaps be moreappropriate, however these values are not known for these solventsystems and such a comparison could not be made. Van der Waalsvolumes provided for the best chance of comparison betweensolvent size and hole-size. The vertical dashed lines represent theaverage hole-size free volume for each network as measured byPALS. The 44TG network exhibited the lowest Vh of 59 Ǻ3 and onlyallowed absorption of water, methanol and acetonitrile which allhave smaller vdW than 59 Ǻ3. Solvents above this size did notabsorb into the resin after 22 days. As the Vh of the networkincreased, larger solvent molecules were able to ingress into thepolymer as evidenced by the absorption behaviors of 33F and 44A.

Fig. 8. Correlation of free volume hole-size and penetrant vdW volume.

Fig. 10. MEK uptake curves.

Table 5Solvent van der Waals Volume and Network Vh.

Penetrant Free-Volume

Solvent vdW Volume (Ǻ3) Network Vh (Ǻ3)

Methanol 37 44A 82Acetonitrile 46 33A 77Acetone 65 44F 76THF 77 33F 67MEK 81 44TG 591-butanol 88

M. Jackson et al. / Polymer 52 (2011) 4528e45354534

As a general trend, as penetrant size deviated progressively smallerfrom Vh, total mass uptake continued to increase supporting thata larger average hole-size increased the probability that the freevolume is interconnected resulting in a less tortuous path anda higher diffusivity.

MEK was chosen to further study the relationship of tortuosityand diffusivity with average Vh since its van der Waals volume of81.5 Å3 falls within the range of average free volume hole-sizes for44A and 33A, or 82 Å3 and 77 Å3, respectively. Fig. 9 exhibits MEKabsorption and depicts linear uptake in 33A and 44A until equi-librium is reached around 30 wt%. The differences in average hole-size become apparent through changes in uptake kinetics as 44Aequilibrates around 2000 h compared to 6000 h for 33A. Smalleraverage hole-sizes appear to restrict transport through a blockingmechanism that prevents penetrant ingress. The average hole-sizefactor we have observed to govern transport in glassy polymernetworks is analogous to geometrical impedance diffusivities andcrystallite blocking factors reported for semi-crystalline polymers[32,33]. As a result, 44A shows increased penetration due to a largeraverage hole-size which created a statistically higher probabilityMEK would transport. To further clarify the relationship betweenpenetrant size and glassy network average hole-size, we includedMEK transport for 44TG in Fig. 10 which has an average hole-size of59 Å3. In this case, even after >7000 h of MEK immersion, nomeasurable uptake of MEK was observed. This epoxy networkclearly shows the restriction blocking behavior for MEK attributedto the smaller average hole-size for this glassy network polymer. Inaddition, the 44TG-MEK result suggests the distribution in hole-sizes for the network is narrow since an appreciative

Fig. 9. 22 day uptake data for 33F, 44A and 44TG.

concentration of holes greater than the vdW size of MEK wouldlead to swelling and measurable weight gain.

Although 33A and 44A have different average hole-sizes andMEK uptake kinetics, both network isomers appear to equilibrate atthe same level, around 30 wt%, which confirms the chemicalenvironments for the isomer networks are the same. This resultsuggests that regardless of average hole-size, both plasticizednetworks have similar morphologies expected for isomers in therubbery state. As MEK ingressed through free volume of appro-priate hole-sizes, the glassy polymer networks began to swell

Fig. 11. DMA plots of 44A-MEK Tan-d (A) and E0 (B).

Fig. 12. Sub-Tg motions of MEK and water soaked 33A samples.

M. Jackson et al. / Polymer 52 (2011) 4528e4535 4535

through increased local chain mobilities leading to plasticizationand expansion. Network connectivity lead to an increase in localcooperative motions and created a boundary between rubbery andglassy domains resulting in a migration of free volume at theinterphase which propagated transport. This diffusion behaviorcaused a moving flow front similar to that described for Case IIdiffusion [20]. The overall results were steady flow fronts whichmigrated through the samples from exposed surfaces leading todistinct regions of rubbery and glassy domains until reaching thefully saturated rubbery states.

Fig. 11 shows DMA curves of 44A exposed to MEK for 0 h, 960 hand 2376 h. The 0 h network shows a single sharp Tan-d peak witha Tg of 223 �C. After 960 h of MEK exposure, a second broad Tan-d peak centered around 110 �C is evident and associated with theplasticized portion of the network. The original Tan-d peak isdiminished at 223 �C but still evident and attributed to theunperturbed fraction. After 2376 h of exposure the sample was fullysaturated and the Tan-d shifted to a single broad peak centered at70 �C which remained unchanged after additional exposure. Incontrast to the exposure behavior observed for water ingress, themechanical storage modulus data displayed a substantial reductionin room-temperature moduli and much lower values upon equili-bration demonstrating MEK plasticization of the networks.

Fig. 12 depicts sub-Tg transitions for 33A fully equilibrated withwater and MEK (over 10,000 h exposure). MEK clearly displayeda higher plasticization of the network through increased localnetwork chain motions during room temperature transport leadingto an ultimate solvent uptake at around 30 wt%. It is these motionswhich control the dilational expansion of the network creatingadditional free volume and increased uptake. The unexposed glassynetwork polymer displayed two broad sub-Tg transitions centeredaround �50 �C and 50 �C. The plasticization effects of MEK ingressresulted in the Tg shifting to 62 �C and sub-Tg transitionsbelow �100 �C. In contrast to MEK, the equilibrated absorption ofwater (w3 wt%) had a minor effect on the sub-Tg motions anda substantially lower plasticization effect as discussed above.

4. Conclusion

Glassy polymer network isomers with well-controlled morpho-logical variations were used to study the relationship between hole-

size free volume and fluid transport. The free volume average hole-size was varied in epoxy networks by curing with the aromaticamine isomers, 3,30 and 4,40 DDS. The amine isomer substitutionwasuseful to alter reaction kinetics and produce inherently differentnetwork architectures and packing densities while keeping thechemical compositions and polarities of the network identical. Thisapproach allowed us to study morphological contributions withuptake behavior. Fluid uptake kinetics were shown to have a strongdependence upon hole-size free volume for glassy polymernetworks. In caseswhere the ingressing solventwas small comparedto the average hole-size, transport was facilitated by providinga direct interconnected pathway and rapid ingress. As the ingressingsolvent approached the average hole-size, the glassy polymernetworks showed significantly lower uptake kinetics. When theingressing solvent was significantly larger than the average hole-sizewe did not detect appreciable solvent uptake suggesting a blockingmechanism dominated ingress behavior and prevented penetrantingress. These results suggest that reducing the free volumehole-sizeis a reasonable approach to control solvent properties for glassypolymer networks.

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