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Polymer 54 (2013) 3079e3085

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Polymer

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Effect of isocyanate content on thermal and mechanical properties of polyurea

K. Holzworth a,*, Z. Jia a, A.V. Amirkhizi a, J. Qiao b, S. Nemat-Nasser a

aCenter of Excellence for Advanced Materials, Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0416, USAb School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China

a r t i c l e i n f o

Article history:Received 15 January 2013Received in revised form13 March 2013Accepted 22 March 2013Available online 12 April 2013

Keywords:PolyureaDynamic mechanical analysisStorage and loss moduli

* Corresponding author. Tel.: þ1 858 534 5918.E-mail addresses: kholzworth@ucsd.edu,

(K. Holzworth).

0032-3861/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.polymer.2013.03.067

a b s t r a c t

Novel polyureas with soft segments based on a difunctional amine, Versalink P-1000, and hard segmentsbased on Isonate 143L, which is a mixture of difunctional and trifunctional isocyanates, were synthe-sized. The stoichiometric ratio of Isonate 143L to Versalink P-1000 in the polyurea material systemwas incrementally varied. The properties of the resultant polyurea formulations were characterizedusing dynamic mechanical analysis (DMA) and modulated differential scanning calorimetry (MDSC). Thedynamic mechanical properties measured as storage and loss moduli were significantly altered throughthe variation of the stoichiometric ratio; however, the glass transition temperatures exhibited in allvariations were quite consistent. The experimental results indicate that judicious selection of hardsegment content can have a marked effect on the ultimate properties and performance of the polyureamaterial system.

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1. Introduction

Polyurea is a microphase-separated block copolymer formed bythe rapid reaction of an isocyanate component and an aminecomponent which yields a urea linkage [1e3]. Such copolymersexhibit unique properties as a result of their phase-separatedmorphology, which is due to the segregation of dissimilar blocksbeing restricted under 100 nm hard domain size. The soft segmentsform a continuous matrix reinforced by the hard segments that arerandomly dispersed as nanodomains [4,5]. Although the existenceof microphase separation in block copolymers was clearly estab-lished by Sadon et al., it remained little more than a curiosity untilHolden and Milkovich discovered the corresponding connectionbetween composition and architecture and the resulting propertiesand performance of materials [6].

The physical properties of the segregated phases influence theoverall properties of the polyurea. Typically, the long and softdiamine blocks form a flexible matrix. The multifunctional hardsegment domains serve as both physical crosslinks and as reinforc-ing fillers [1,6]. High mechanical toughness is a result of the exten-sive intermolecular hydrogen bonding in polyurea hard domains[3,7]. Depending on the chemistry, polyurea can exhibit a widerange ofmechanical properties, from soft rubber to hard plastic [2,8].

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Theoretically, the isocyanate component and amine componentmust be mixed in a stoichiometric ratio of 1:1, i.e., the total numberof isocyanate functional ends must equal the total number of aminefunctional sites. Most polyurea formulations are calculated to over-index the isocyanate component of the system on the order of 1.05,i.e. a five percent excess of the isocyanate component is usedbeyond the stoichiometric ratio required for a complete reaction, asspecified by the manufacturer [9]. This excess isocyanate helpsaccount for that which is lost upon reaction with residual moistureduring storage or application [10]. Furthermore, the slight excessaids in producing a lightly cross-linked polymer through thedevelopment of biuret structures [11,12].

Fragiadakis et al. [3] have studied the effect stoichiometry vari-ations have on local segmental relaxation dynamics of polyurea. Viadielectric spectroscopy, it was shown that increased hard segmentcontent was associated with a greater sensitivity to pressure andvolume changes.

While researching the high-strain rate mechanical behavior ofpolyurea, Roland et al. [7] demonstrated the influence of stoichi-ometry on the low strain rate response. It was shown that a 5e10%variation in chemistry could lead to dramatic changes in the me-chanical properties. Increased isocyanate content resulted inincreased yield stress and decreased failure strain. The resultsdemonstrated that increasing the amount of isocyanate componentis necessary to drive the crosslinking reaction towards completion.

Yi et al. [5] studied one polyurea formulation and variouspolyurethane chemistries in order to probe the influence of thehard segment content on the mechanical behavior of the materials.

Table 1Measured dimensions of dynamic mechanical analysis samples. Note that the valueis the arithmetic mean of three measurements.

Sample Width (mm) Thickness (mm)

PU_Iso_90_1 10.0 2.4PU_Iso_90_2 10.1 3.1PU_Iso_90_3 10.3 3.1PU_Iso_95_1 10.0 2.3PU_Iso_95_2 9.8 3.1PU_Iso_95_3 9.9 3.1PU_Iso_100_1 9.8 3.4PU_Iso_100_2 9.5 3.1PU_Iso_100_3 9.5 3.1PU_Iso_105_1 10.2 2.4PU_Iso_105_2 10.0 3.1PU_Iso_105_3 10.1 3.1PU_Iso_110_1 9.9 3.5PU_Iso_110_2 10.2 3.1PU_Iso_110_3 10.1 3.1PU_Iso_115_1 10.0 2.3PU_Iso_115_2 10.0 3.1PU_Iso_115_3 10.0 3.1PU_Iso_120_1 10.1 2.4PU_Iso_120_2 9.9 3.1PU_Iso_120_3 10.0 3.1

K. Holzworth et al. / Polymer 54 (2013) 3079e30853080

Softening under cyclic loading was observed for materials with acrystalline hard segment content, yet was absent for the materialwith an amorphous well-dispersed hard segment content.

A plethora of experimental studies have been conductedfocusing on polyurea, yet none have investigated stoichiometryeffects on the dynamic mechanical properties of polyurea. In thisstudy, a series of polyurea formulations are prepared to elucidatethe effect that stoichiometry variations have upon the thermalcharacteristic properties and dynamic mechanical properties,determined as the dynamic storage and loss moduli of the resultingpolyureas. Based on this data, the mastercurves and relaxationspectra are derived for each formulation and compared. The limitsof applicability of these methods are discussed in detail in thefollowing sections. However, based on the current primary interestin polyureas and their composites (i.e. their possible enhancementto structural response against blast), the use of such models espe-cially at high rate response in structural FEM codes appears to be areasonable approach. It is yet to be seenwhether thesemethods areusable at higher temperatures and/or annealing response of thesepolymers. Stoichiometry studies are essential for both under-standing and optimizing the performance of polyurea. By tailoringthe stoichiometry and thus the underlying morphology of themultiphase system through chemistry, one can further exploit thewide range of mechanical properties that polyurea has to offer.

2. Experimental procedures

2.1. Materials

Polyureas are synthesized from the reaction of an aromatic iso-cyanate component (hard segment) and an amine-terminated resinblend component (soft segment). The aromatic isocyanate compo-nent, Isonate 143L modified MDI (Dow Chemicals; 144.5 g/eq), is apolycarbodiimide-modified diphenylmethane diisocyanate. Isonate143L, which is in liquid form at room temperature, has a low vis-cosity and good storage stability down to 24 �C. In this diisocyanate,the carbodiimide linkage aids the stabilization of the polymer againsthydrolytic degradation [13]. The amine-terminated resin blendcomponent, Versalink P-1000 oligomeric diamine (Air Products;600 g/eq), is a polytetramethyleneoxide-di-p-aminobenzoate. Ver-salink P-1000 is a liquid at ambient temperature, which allows it tobe mixed, cast, and cured at room temperature. This oligomericdiamine is often used as a curative for both methylene diphenyldiisocyanates (MDI) and toluene diisocyanates (TDI) [9].

2.2. Polymer synthesis

The recommended stoichiometry for processing Versalink P-1000 oligomeric diamine is 105% theory (diisocyanate/diamine bymole) [9]. While 100% stoichiometry indicates the exact balance ofisocyanate to amine functional sites, a five percent excess of Isonate143L is typically recommended to produce a lightly cross-linkedpolymer [12]. The excess isocyanate also helps to account for thatwhich is lost upon reacting with residual moisture during storageor application, as mentioned earlier [10].

In this study, seven polyurea stoichiometric variations are pre-pared including those with 90%, 95%, 100%, 105%, 110%, 115%, and120% stoichiometry, which hereafter in the following are referred toas PU_Iso_90, PU_Iso_95, PU_Iso_100, PU_Iso_105, PU_Iso_110,PU_Iso_115, and PU_Iso_120, respectively.

The isocyanate and amine components are degassed separatelyfor 1 h. At ambient temperature, polymerizations are conducted ina 500 mL three-neck, round bottom reaction flask. The vacuumseals are broken. Using a scale, the precise mass of the isocyanatecomponent is added to the amine component. The mixture is

stirred via an egg-shaped magnetic stirrer and degassed for 5 minat a vacuum pressure level of approximately 1 Torr. Although theviscosity of Versalink P-1000 oligomeric diamine is relatively highat room temperature, the diluent effect of the isocyanate suffi-ciently lowers the viscosity to allow easy mixing and completedegassing prior to casting [9]. The polyurea working time, inclusiveof mixing time, is approximately 20min at ambient conditions [14].

2.3. Sample preparation

Teflon molds are used to create test specimens with specific,controlled geometries as well as a bulk material sample. Prior to use,themolds are stored inanenvironmental chamber thatmaintains therelative humidity level at 10% in order to minimize surface moisture.Themixture is transferred from the reaction flask to the Teflonmoldsvia syringe. Precautions are taken tominimize the introduction of airbubbles while transferring the material into the molds.

The polyurea specimens are cured at room temperature in amoisture controlled environmental chamber that maintains therelative humidity level at 10%. Two weeks are required to achievecomplete cure at ambient conditions, with 75% of the ultimatephysical properties being realized within 24 h [9]. All polyurea testspecimens are stored in the environmental chamber prior totesting. Table 1 shows the measured dimensions of the dynamicmechanical analysis samples.

2.4. Experimental characterization methods

2.4.1. Modulated differential scanning calorimetry (MDSC)A TA Instruments DSC 2920 in modulated differential scanning

calorimetry mode is used to determine the thermal properties ofthe polyurea stoichiometric variations. MDSC allows separation ofthe total heat flow signal into its reversible and irreversible heatflow components. The former allows calculation of the heat ca-pacity, while the latter represents possible chemical changes andtheir thermal signature [15]. Modulation calorimetry theory isstraightforward. When the power heating the sample is modulatedby a sine wave, the temperature begins to oscillate about a meanvalue. The amplitude of the temperature oscillations depends onthe heat capacity of the sample, while the difference between theupswing and downswing represent irreversible heat flow [16]. Anapproximately 15 mg sample is placed in a non-hermitically sealed

K. Holzworth et al. / Polymer 54 (2013) 3079e3085 3081

aluminum pan with lid. The accompanying reference pan mass ismaintained to within 0.05 mg of the mass of the sample pan tominimize measurement variations. Using a liquid nitrogen coolingaccessory in order to cool the system to sub-ambient levels, thespecimen is cooled to�100 �C and held isothermally for 5 min. Thespecimen is then heated to 220 �C at a rate of 3.0 �C/min, with atemperaturemodulation of 1 �C every 60 s. MDSC scans are taken atthe full curing duration of approximately 2 weeks.

2.4.2. Dynamic mechanical analysis (DMA)A TA Instruments DMA 2980 equipped with a single cantilever

clamp test fixture is used to characterize the dynamic mechanicalspectra of the polyurea stoichiometric variations. The cast spec-imen dimensions are approximately 2e3 mm in thickness with awidth of 10 mm. Sample measurements are provided in Table 1. Inthe single cantilever clamp, the specimen is clamped at a freelength of 17.5 mm. Clamping plates constrain both ends of thespecimen from rotation. In this configuration, one end of thespecimen is excited into a sinusoidal transverse displacement at amaximum amplitude of 15 mm. Using a nitrogen atmosphere inorder to cool the system to sub-ambient levels, the experiment isperformed over the temperature range from �80 �C to 50 �C,increasing by 3 �C steps. At each temperature step, the specimen issequentially tested at the five discrete frequencies of 20, 10, 5, 2,and 1 Hz; beginning with the highest frequency and progressing tothe lowest frequency in order to minimize sweep time [17]. Athermal soaking time of 3min at the beginning of each temperaturestep minimizes the effects of thermal gradients. For each polyureastoichiometric variation, a set of three specimens is tested, con-sisting of one sample from the initial batch, as well as two samplesfrom the second batch. All samples are tested at the full curingduration of approximately 2 weeks.

3. Results and discussion

3.1. Thermal analysis

The glass transition event results from a sharp significant increasein the mobility of the polymer chains as the polymer matrix goesfrom the glassy state to the rubbery state. Thus, the glass transition isa second order endothermic transition and as such, it appears as astep transition in the reversible heat capacity plots [18,19]. Thecalorimetric glass transition of the soft phase as well as the heatcapacity increment at Tg are quite comparable for the seven polyureastoichiometric variations, as detailed in Table 2. The glass transitionin the polyurea stoichiometric variations is extremely broad, with aDT ¼ Tend�Tonset of approximately 45e55 �C.

3.2. Dynamic mechanical analysis

The dynamic mechanical properties of the polyurea elastomervariations are determined as the dynamic storage and loss moduli.

Table 2Calorimetric soft segment glass transition temperature, heat capacity increment atTg, and width of the glass transition for polyurea stoichiometric variations.

Isonate 143Lstoichiometric index

Soft segment Tg (�C) DCp (J/g/�C) DT (�C)

0.90 �63 0.43 500.95 �65 0.46 551.00 �64 0.37 511.05 �61 0.38 501.10 �67 0.43 541.15 �64 0.34 441.20 �62 0.33 43

The dynamic storage and loss moduli are collectively referred to asthe complex modulus of a material, which is generally expressed as

E� ¼ E0 þ iE00 (1)

where E0 and E00 are Young’s storage and loss moduli, respectively.The complex modulus is a measure of the resistance of a ma-

terial to deformation, and it encompasses both the elastic andviscous responses. Through dynamic testing, which measures thephase difference between the sinusoidal force and displacementthat the sample is experiencing, the stress can be deconvoluted intoan elastic stress (in phase with the strain) and a viscous stress(p/2 out of phase with the strain). The elastic stress is used tocalculate the elastic modulus, or storage modulus. Storage modulusis a measure of the recoverable stored strain energy. The viscousstress is used to calculate the viscous modulus, or loss modulus.Loss modulus is a measure of the energy dissipated, generally lostas heat [20,21].

The storage and loss moduli of the polyurea stoichiometricvariations were obtained as functions of temperature at fivediscrete frequencies. The temperature dependence of the storageand loss moduli for the 105% theory polyurea stoichiometric vari-ation, PU_Iso_105, is plotted in logarithmic scale for 1 Hz and 20 Hzfrequencies in Fig. 1. Both storage and loss moduli clearly increasewith increasing frequency. Figs. 2 and 3 show the relative storagemodulus and relative loss modulus of the polyurea stoichiometricvariations as compared to the values measured for PU_Iso_105 at1 Hz and 20 Hz frequencies, respectively. The storage and lossmoduli of the polyurea stoichiometric variations are quite similar inthe glassy region (T < Tg), independent of the Isonate 143L stoi-chiometric index. However, above the glass transition temperaturein the rubbery region (T > Tg), as the Isonate 143L stoichiometricindex increases, there is an associated pronounced increase in boththe storage modulus and loss modulus. Above the glass transitiontemperature, the polyurea stoichiometric variations rich in Isonate143L content dramatically increase, while those lean in Isonate143L content decrease significantly. The trends become more pro-nounced as the Isonate 143L content becomes increasingly rich orlean, with significant jump from 110% to 115%.

Although there are several thermal techniques available tomeasure the glass transition temperature of polymeric materials,the most sensitive technique available is dynamic mechanicalanalysis. In Table 3, the soft segment glass transition temperaturedefined as the loss modulus peak is shown. In literature, both the

Fig. 1. Temperature dependence of E0 and E00 for the 105% theory standard polyureastoichiometry at 1 Hz and 20 Hz (the central points are the average values of threeresults and the error bars represent the standard deviation).

Fig. 2. Temperature dependence of relative storage modulus and relative loss modulusfor polyurea stoichiometric variations at 1 Hz.

Table 3C1 and C2 for WLF equation with T0 ¼ 0 �C for all polyurea stoichiometric variations.

Isonate 143L stoichiometric index C1 C2 [K]

0.90 16.8 156.60.95 17.1 155.91.00 20.0 165.91.05 18.0 156.61.10 21.3 169.71.15 22.4 170.11.20 24.9 185.1

K. Holzworth et al. / Polymer 54 (2013) 3079e30853082

loss modulus peak and tan d peak are defined as the glass transitiontemperature, with the tan d peak occurring at a higher temperaturethan the loss modulus peak. The tan d peak is a goodmeasure of theleather like midpoint between the glassy and rubbery states. Morerecently, the temperature corresponding to the loss modulus peakhas been preferred. The glass transition temperature determinedfrom the loss modulus peak value is similar to the intersection oftangents to the storage modulus curve from the glassy region andtransition region. Such a corresponding temperature better denotesthe end-use temperature where plastic materials begin to soften.The loss modulus peak is more closely related to the physicalproperty changes attributed to the glass transition. It reflectsmolecular processes and agrees with the idea of the glass transitiontemperature as the temperature at the onset of segmentalmotion [22].

The soft segment glass transition temperature of polyureastoichiometric variations as defined by the temperature corre-sponding to the peak of loss modulus curve at 1 Hz frequencyidentifies the temperature as ranging from �59 �C to �56 �C. It isimportant to note that the test temperature was increased by in-crements of 3 �C, which speaks to the accuracy of the values shown.However, as shown in the calorimetric glass transition measure-ments, the soft segment Tg is very similar amongst the polyureastoichiometric variations.

Fig. 3. Temperature dependence of relative storage modulus and relative loss modulusfor polyurea stoichiometric variations at 20 Hz.

3.3. Master curves

In order to approximate the storage and loss moduli for a widefrequency range, time-temperature superposition (TTS) is appliedto the experimental DMA data [20]. Master curves of E vs. au aredeveloped from the experimental DMA data, bEðT;uÞ:EðT0; auÞ ¼ T0

TbEðT ;uÞ: (2)

Here, E¼ E0or E00 is the modulus of interest and the shift factor a,

a function of temperature, represents the amount of shift in thelogarithmic scale that relates the response at temperature T0 to thatat temperature T. The factor T0/T (temperatures are in absoluteunits) represents the scaling of entropic rubber elasticity stiffness.We chose temperature only prefactor as it is the dominant term.Further components in this prefactor are ignored here, given theapproximate nature of this model and other ways of introducingtheir effect. For example, the mass (or chain) density of moleculesmay be combined based on free volume approach into the tem-perature effects; see for example [12,23]. For further discussion ofthe procedure to obtain the master curves, see the electronicSupplementary materials and other original references [20,24]. Theassembled curve, referred to as a master curve, represents thematerial property at the reference temperature and over a widefrequency range.

For each polyurea stoichiometric variation, the average log(a) ofthe storage and loss moduli is calculated from the measured value.The average shift factor can be fitted by William-Landel-Ferry(WLF) equation [24].

Fig. 4. log(a) averaged from the measured data of storage modulus and loss modulusand log(a) fitted by WLF equation with T0 ¼ 0 �C.

Fig. 5. Master curves at 0 �C. log(a) used in TTS are from WLF fit.Fig. 7. Relaxation spectra from the second approximation for PU_Iso_90.

K. Holzworth et al. / Polymer 54 (2013) 3079e3085 3083

logðaÞ ¼ �C1ðT � T0ÞC2 þ T � T0

(3)

C1 and C2 used in the WLF equation are shown in Table 3 for allthe polyurea stoichiometric variations. As the Isonate 143L contentincreases, C1 and C2 increase, which results in log(a) curves slightlyrotated clockwise with respect to the reference temperature,shown in Fig. 4.

The master curves for storage modulus and loss modulus areshown in Fig. 5. When u < 106.6 Hz, increased stoichiometric indexyields both increased storage and loss moduli. When u > 106.6 Hz,the storage moduli tend to approach a limiting value, and the lossmoduli decrease as the Isonate 143L content decreases.

3.4. Relaxation spectrum

The relaxation moduli relate to the relaxation spectrum via thefollowing expressions [20]:

E0 ¼ Ee þZN

�N

Fu2s2=�1þ u2s2

�dlns (4)

Fig. 6. Relaxation spectra from the first approximation for PU_Iso_90.

E00 ¼ZN

�N

Fus=�1þ u2s2

�dlns (5)

F(s)is the relaxation spectrum, which represents the contribu-tion of the relaxation mechanism of time constant s to the overallmodulus. Ee is the equilibrium storage modulus, which representsthe relaxation modulus at a time infinitely large or a frequencyinfinitely small. Eq. (4) and Eq. (5) share the same F(s). Thus whencalculated separately using storage modulus and loss modulus databy Eq. (4) and Eq. (5), the same F(s) should be realized if theexperimental data has good internal consistency [25]. In this study,master curves by TTS are used as the input data to calculateF(s). Toinvert Eq. (4) and Eq. (5), two approximation methods are applied[26,27].

The first approximation to calculate F(s) for storage and lossmoduli is

F1ðsÞ ¼ E0ðdlog E0=dlog uÞ���1=u¼s

(6)

F1ðsÞ ¼ E00ð1� dlog E00=dlog uÞ���1=u¼s

(7)

The second approximation (Eqs. (8)e(12)) [28] is applied basedon the result of the first approximation:

F2ðsÞ ¼ AE0ð1� jdlog E0=dlog u� 1jÞ���1=u¼s

(8)

F2ðsÞ ¼ BE00ð1� jdlog E00=dlog ujÞ���1=u¼s

(9)

A ¼ ð1þ jm� 1jÞ=h2G

�2�m

2

�G�1þm

2

�i(10)

Table 4Equilibrium storage modulus, Ee, based on fitting to Eq. (4). Note that thetests were not extended to equilibrium conditions.

Isonate 143L stoichiometric index Ee (MPa)

0.90 770.95 841.00 961.05 871.10 1051.15 1301.20 130

Fig. 8. F2 of storage modulus and loss modulus. Each curve is an average of relaxationspectra calculated from storage modulus and loss modulus.

K. Holzworth et al. / Polymer 54 (2013) 3079e30853084

B ¼ ð1þ jmjÞ=�2G

�32����m2

����G�32þ���m2

����� (11)

m ¼ �dF1ðsÞdlog s

(12)

The relaxation spectra calculated from the first approximationand the second approximation are shown in Figs. 6 and 7. Theagreement between the relaxation spectra calculated separatelyfrom storage modulus and loss modulus demonstrates that thestorage and loss moduli master curves obtained through imple-mentation of TTS have good internal consistency [25]. Equilibriumstorage moduli Ee are shown in Table 4. As expected, Ee increases asthe Isonate 143L increases.

Relaxation spectra of the polyurea stoichiometric variations areshown in Fig. 8.

4. Discussion and conclusions

The stoichiometric ratio of Isonate 143L (hard segment) toVersalink P-1000 (soft segment) in the material system wasincrementally varied. The properties of the resultant polyurea for-mulations were characterized. The glass transition temperaturesexhibited in all polyurea stoichiometric variations were quiteconsistent, as measured via both MDSC and DMA. The dynamicmechanical properties measured as storage and loss moduli weresignificantly altered through the variation of hard segment content.Above the glass transition, both the storage and loss moduli sharplyincreased with increasing Isonate 143L (hard segment) content.With the increase of Isonate 143L content, the actual effect onchemical structure is somewhat complicated. The polymerizationoccurs through a step-growth mechanism. The degree of poly-merization is controlled by the stoichiometric ratio. In theory, a 1:1ratio will yield the highest degree of polymerization, as summa-rized by the Carothers equation [29]. The increase in Isonate 143Lcontent would result in a decrease of polymer chain length forusual linear polymer extension. However, here Isonate 143L alsocontains a certain amount of three-arm crosslinking sites. The in-crease of total Isonate 143L content means an increase of cross-linking density as well, which explains the increased storagemodulus. It should be noted that in the stoichiometric variations

resulting in unreacted isocyanate functionalities, the material willabsorb moisture if left untreated under ambient conditions. Nomorphological changes may manifest if this happens slowly. Theeffect on themechanical properties is not investigated in this study.

Master curves were developed using DMA data to predict thematerial properties in a wide frequency range. The shifting factorlog(a) were compared among the different stoichiometric varia-tions. The slight difference in log(a) demonstrates that polyureatends to be more sensitive to temperature change as the Isonate143L content increases. In other words, a similar temperaturechange produces a more substantial equivalent change in the timescale of molecular motion for the more sensitive, high index poly-urea samples. Although a very small change, this trend agrees withthe observed increase in mechanically measured Tg at 1 Hz.

The applicability of time-temperature superposition shiftingprocedure in general has been addressed in great detail by Plazek[30]. It must be emphasized that the reduced moduli may be used,with care, when overall structural response is sought in the regimesthat the applicability of such approximation is verified. Forexample, high temperature or very low strain-rates are not withinthe range of use of polyureas. However, it would be quite inter-esting to explore whether the procedure and results are applicableunder such conditions. These issues have been even further scru-tinized for multi-phase materials; see, among others, Tschoegl et al.[23]. They discuss the shortcomings due to having multiple relax-ation mechanisms (in harder versus softer domains). It is suggestedby them that from a practical point of view, the method may beapplicable to lightly cross-linked and/or relatively rigid filler pha-ses. The difference between the relaxation time scales of hard andsoft domains in polyureas discussed here may be understood bylooking at the results of Rinaldi et al. [31,32], where it is shown thatthe glass transition of the hard domain is around 175 K higher thanthat of the soft domain. Given this difference and that these resultsare intended for use in higher rates, it is a reasonable approxima-tion to consider the hard domains as relatively rigid compared tothe soft domains. In other words, the hard domain relaxations areso slow in comparison with the soft domain that its effect isneglected in the present approximation. Knauss et al. [33] point outthat ultimately the quality of the shifting process determineswhether the superposition process is physically acceptable andperforming measurements at close enough temperature levels isthe best way of evaluating the shifting process. Knauss and co-workers have also successfully applied the superposition process topolyurea and developed mastercurves [34,35]. In our previouswork [27], we have compared the results of time-temperaturetransition with actual high-frequency measurements and notedthat the storage moduli are very will predicted. The loss moduli areunderestimated by the shifting of low-frequency data, which weassociate with extra loss mechanisms that may be produced due tothe dynamic of heterogeneous morphology.

Relaxation spectra of all the polyurea stoichiometric variationswere calculated. The spectrum flattens as the Isonate 143L contentlevel increases. This change in relaxation spectrum shows thecontribution from the relaxation mechanisms in the polyureaspreads out to a broader frequency range if hard domain contentincreases in polyurea as well as if the cross-linking density in-creases. Clearly, this explanation is compatible and essentially aconclusion of the observed flattening in log(a).

The inherent assumption in deriving a relaxation spectrum is thelinearity of response. The unique spectrum for the two mechanicallymeasured quantity allows us to verify the internal consistency of thederived mastercurves. Other authors have used different methods;see for example Han and Kim [36]. Furthermore, from continuousrelaxation spectrum F2 and Ee, discrete relaxation model for storageand loss modulus with limited number of elements can be easily

K. Holzworth et al. / Polymer 54 (2013) 3079e3085 3085

developed if necessary. Such a discrete model, though less accurate,is much more useful in FEM analysis [12].

The objective of this study was to elucidate how small changesin the isocyanate content of polyurea manifest themselves me-chanically. The experimental results have suggested that the in-crease in the hard domain content has an observable effect on thestiffness of the polyurea.We provide numerical data on such effectsto serve as a guide for the necessary tolerance of designs based onstoichiometric variations. The experimental results support thenotion that by tailoring the stoichiometry and thus the underlyingmorphology of the multiphase system through chemistry, one canexploit the wide range of mechanical properties that polyurea hasto offer.

Acknowledgements

This work has been supported by the Office of Naval Research(ONR) grant N00014-09-1-1126 to the University of California, SanDiego.

Appendix A. Supplementary data

Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.polymer.2013.03.067.

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