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Effects of Loading Conditions on the Nanoindentation Creep Behavior of Nation 117 Membranes.


Considerable attention has been paid to the chemical and mechanical properties of perfluorosulphonic acid (PFSA) membranes on the horizon of polymers, particularly Nafion, because of their excellent material properties including chemical stability, permselectivity, and high-proton conductivity, enabling them to be ideal candidates for technological application in Proton exchange membrane fuel cell (PEMFCs) [1, 2]. Cost and durability are critical in widespread commercialization of this technology, and generally, chemical and mechanical degradation are regarded as principal courses of unsatisfactory lifetime [3, 4]. Whereas a great deal of time and attention has been devoted to other viscoelastic materials, among which the efforts of Briscoe on PMMA, research of Beake and Leggett on PET stand out because these effects has made great significance [5, 6]. Meanwhile, Nafion has not been studied much under the influence of loading conditions. Hence, to meet more reliable durability, it is desirable to clearly understand basic mechanical properties of PFSA membranes and then effectively strengthen the ability to resist degradation and failure in the future. As a class of prototypical PFSA material, Nafion was developed and manufactured by E.I. DuPont Company in mid-1960s [7]. Similar to polymers, it was synthesized with a very complex chemical structure, thus possessing similar mechanical behavior as visco-elastic/plastic material [8]. A comprehensive study of the basic mechanical properties of Nafion membranes has been undertaken for decades and the mechanical response under controlled working environment, such as temperature and humidity conditions (hydration and thermal cycle), remains the key attention among experimental studies of PFSA membranes [9-14]. The synthesis and characterization of the Nafion-based composite also become important subjects to PEMFCs researchers [15-18]. In theoretical works, considerable attention has been paid to characterize the mechanical responses of PFSA by developed viscoelastic, viscoplastic and even vicoelasticplastic constitutive models [19-22]. For numerical simulations, the finite element analysis has been proved to be an effective tool to present the influence of the working condition on the performance of PEMFCs structure or PFSA material [23-25]. Moreover, micro/ nano scale simulations including, kinetic Monte Carlo and molecular dynamics simulations as well as ah Initio calculation were utilized to elaborate the evolution of Nafion's structure and properties upon chemical and mechanical degradation [26-28].

Nanoindentation method is the one of most valuable technique for evaluation of the surface and near-surface mechanical properties of thin films, including elastic modulus and hardness. Based on the method principle, which was first proposed by Doerner and Nix [29] and further developed by Oliver and Pharr [30], mechanical information is derived from recorded depth and measured applied load. Nevertheless, a significant creep effect at the peak load may influence the subsequent unloading behavior, causing the contact stiffness to be overestimated, especially for viscoelastic materials [5]. In such a scenario, Feng et al. [31] and Tang et al. [32] proposed a method to modify the contact stiffness data for creep and thermal drift based on the measurement of the displacement rate at the end of the holding period. Thus, the elastic modulus calculated by the Oliver and Pharr method can be reliable. Similar work has also been done by Flores et al. [33] who adopted an assumption of constant resultant modulus E and hardness H. E, H values as a function of indentation depth for PET and used an alternative approach to correct for the 'tip defect'. After these corrections, this technique is equally suitable for determining the mechanical properties of polymers. Much research has been done in nanoindentation analysis of the pristine Nafion and modified-Nafion membranes, for example, Mohamed et al. [34] characterized the structure in pristine Nafion and Lee et al. [35] investigated the mechanical behaviors of the annealed Nafion/sGO (N/ sG) composite membranes. Although nanoindentation is a promising strategy to better understand Nafion membranes, its application to polymeric materials is still facing a number of challenges [36]. Then, how to modify the currently available indent extracting criterion and loading/unloading condition in order to meet the time-dependent properties of material becomes the critical subject.

In this work, we investigated the indentation behavior of Nafion 117 membranes by using a Berkovich tip, whose effective radius is 100 nm with face angle of 142.3[degrees]. Because of the viscoelasticity of the polymer, its creep shows a strong loading effect, it is of great significance to study the effect of different loading conditions on its creep. The effects of loading rate, holding time and the peak load on the resultant modulus and hardness of membranes were examined. Based on the analysis of the results with consideration of the creep factor, optimized loading conditions for Nafion 117 were designed.



Commercially available Nafion 117 membranes developed and manufactured by DuPont with a thickness of 183 [micro]m were used for the experimental characterization. The picture of the sample was shown in Fig. la. Prior to nanoindentation, some preparations were to be done as follows: (a) Samples were tightly attached to the patches, ensuring no space under the membranes, (b) Samples were stored in a drying oven maintained at ambient condition (25[degrees]C and 58% RH out of the chamber) for a week to minimize the interference owing to aging and humidity effects, (c) Samples were weighed on an electronic balance to confirm no more weight loss. During experiment, each dried film is removed from the drying oven and undergoes a group of tests in the shortest time.


Nanoindentation experiments were conducted on membrane surfaces by using a Hysitron Triboscope TI950 (Hysitron Inc., USA) equipped with a replaceable diamond Berkovich tip (100 nm radius) whose face angle is 142.3[degrees] which has been shown in Fig. lb. In order to investigate the creep effect on nanoindentation of Nafion membranes, three sets of load scheme were designed for tests under load-control mode: (i) The peak load remains the unchanged value of 100 [mu]N and the holding time of 0 s, but the loading/unloading rate is variable with different constant values of 1, 5, 10, 20, 50, 100, and 250 [mu]N [s.sup.-1] respectively, (ii) The indenter loading/unloading rate is approximately 10 [mu]N [s.sup.-1] and peak load 100 [mu]N with different holding time of 0, 1, 5, 10, 30, 50, 100, 200, and 500 s. (iii) The holding time and loading/unloading are kept at 30 s and 10 [mu]N [s.sup.-1] but the peak load varies from 100 to 500 [mu]N with an increment of 100 [mu]N for each group of tests. A minimum of 9 indentation data are collected for each test condition, thus providing a total of 21 x 9 sets of data. In all the tests, the temperature of the test chamber remains at ambient temperature, within a fluctuation of [+ or -]0.5[degrees]C. In addition, all loading parameters are based on the thickness of the material itself. Considering the influence of the substrate effect, the depth is basically guaranteed to be <10% of the material's original thickness. The Oliver and Pharr method [30] was applied for analyzing the experimental data.


Theory of Polymer Creep

Creep is generally defined as long-term inelastic deformation which gradually increases with time under certain temperature and small constant stress (tension, torsion, pressure, etc.) [37]. The polymer creep reflects the stability of the material and the long-term load capacity. Usually, it can be divided into three stages [12, 38], (a) The first stage is called instantaneous elastic deformation. From the point of molecular motion, it explains the bond length and bond angle changes immediately, and the deformation is very small when the material is subjected to external forces, (b) The second stage is retarded elastic creep where the molecular chain moves, and the deformation can be gradually restored, (c) The third stage is called viscous flow creep where a linear polymer has no chemical crosslinking, and the relative slip between molecules occurs.

The four-parameter Burgers model [38, 40] is the most widely used physical model to describe the creep behavior of polymers. The viscoelastic behavior of Nafion can be described with a series of dashpots and linear springs. A simple four-parameter Burgers model consists of one spring and one dashpot connected in parallel. It has been proved to fit the experimental creep data well and give the exact changes of creep behavior of different polymers including Nafion during nanoindentation. Using this model, the total displacement h during the indentation creep can be expressed as [41]:

h = [h.sub.e] + [h.sub.1] (1 - [e.sup.-t/[tau]]) + t/n (1)

where [h.sub.e] is the indentation depth at the first spring, that is, the instantaneous elastic deformation, [h.sub.1] (1 - [e.sup.-t/[tau]]) represents the retarded elastic creep, [h.sub.1] is the indentation depth at the first Kelvin element, x is the retardation time for the first element, t is the experimental holding time and t/[mu] is the viscous flow creep in which [mu] is the constant related to the viscosity coefficient of the last dashpot. Figure 2 shows the schematic diagram of Burgers model and we have described a typical creep curve in the experiment with this model. Figure 3 exhibits a typical load-displacement nanoindentation curve of Nafion and the creep curve can be successfully fitted with Eq. 1 (correlation coefficient [R.sup.2] = 0.99887). The fitting parameters are also included in Fig. 3. It can be seen that the fitting is excellent and the different parameters clearly express the different stage of creep which provides a basis for our quantitative study.

Effect of Loading Rate

Typical indentation load-displacement curves (P-h curves) are illustrated in Fig. 4a for nine indentations at loading/ unloading rate of 50 [mu]N/s and peak load of 100 [mu]N (without peak holding). The curves for a given sample are approximately identical to one another, thus establishing homogeneity of each measurement. Figure 4b shows the typical P-h curves for Nafion 117 at different loading/unloading rates spanning 250-fold. Clearly, it demonstrates a rate dependence of the P-h relationship that the maximum penetration depths continually decrease with the increasing of loading/unloading rate from 663.8 nm at 1 [mu]N/s to 334.5 nm at 250 [mu]N/s, as shown in Fig. 4b One possible reason for this trend is that the lower loading rate (strain rate) corresponding to a longer time to the peak loading (about 100 [mu]N) provides more time for creep deformation [3, 7]. Moreover, when the loading/unloading rate is >10 [mu]N/s, the increment of maximum displacement caused by varying strain rate becomes smaller. We find that it's difficult to reach the peak load when the loading rate is fast. Owing to the instrument achieves peak load by controlling the loading rate and loading time, so it's hard to reach the peak load in specified time for the existence of sensor inertia. Furthermore, when the peak load falls to the minimum within the specified time, sensor inertia still plays an obstacle which causes the ultimate force recovery to be more than zero. So for indenting polymer, some researchers suggest that applying a rapid loading/unloading rate during tests is a feasible way to help mitigate the creep effect [42].

When the loading rate reaches 100 [mu]N/s and especially 250 [mu]N/s, there is not enough time to form a complete P-h curve. Then, the actual maximum load deviates significantly from the set peak value of 100 [mu]N. Moreover, Yang et al. [43] indicates that too fast loading rate may induce a large overshot on the preset indentation load which can further provoke the instability of peak load. So selecting appropriate load rate must be paid full attention to the nanoindentation test of polymers.

Effect of Holding Time

Representative P-h curves, which correspond to 9 indentations with loading/unloading rate of 10 [mu]N/s and peak load of 100 [mu]N for a specific holding time of 30 s, are shown in Fig. 5a, indicating the fair reproducibility of tests. For comparison, the P-h curves obtained under the same loading conditions (10 [mu]N/s and 100 [mu]N) but with varying holding time (0, 1, 5, 10, 30, 50, 100, 200, and 500 s) are presented in Fig. 5b. The loading segments appear approximately overlapping and obvious creep effects were observed in all tests during the holding time. It also can be seen that the creep displacement increases monotonously when the holding time is extended from 1 to 500 s. Figure 5c shows the creep curves with aligned starting points of holding period and creep displacement. All indentation creep displacements reveal a fast increase in the initial stage of holding period, and then the increase becomes moderate with extended holding time. For quantitative analysis, consideration of Fig. 5c indicates that the strain rate reaches a stage of slow blunting after a holding time greater than approximately 20 s (about 30 s after the start of loading). The main reason may be that the instantaneous elastic deformation and retarded elastic creep play the leading role before 30 s and viscous flow creep occurs after 30 s. It can also be seen that viscous flow creep is continuously strengthened with the lengthening of the holding time and the relative slip between molecules become more obvious [40]. So a minimum of 20 s is recommended for reducing the influence of viscoelastic creep on nanoindentation test of Nafion 117, and therefore 30 s is set for holding time in the following tests to optimize the experimental outcomes.

Effect of Peak Load

Figure 6a representatively presents the P-h curves for 9 nanoindentation tests at a peak load of 400 [mu]N with a 10 [mu]N/s loading/unloading rate and 30 s holding time. The typical P-h curves under conditions of peak loads of 100, 200, 300, 400, and 500 [mu]N with a 10 [mu]N/s loading/unloading rate and 30 s holding time are depicted in Fig. 6b. As the peak load increases from 100 [mu]N to 500[mu]N, the maximum indentation depth increases as expected. To better illustrate the creep effect, the indenter displacement at each holding-time segment is extracted into the Fig. 6c. Similar to the maximum indentation depth, the creep displacement during 30 s holding period increases from 57.4 to 126.1 nm, depending on the peak load. Moreover, by comparing with the slopes of the creep curves, it can be seen that the creep rates decrease gradually over holding time, and are easier to reach a steady state under the lower peak load within the same period. According to the creep curves, indentation creep rates e can be calculated by [??] = dh/(hdt), where h and t are the instantaneous indentation depth and time [44, 45]. The reason for this phenomenon may be due to the relaxation time [tau] decreasing with the increasing peak load which has been confirmed by Panayiotis Georgiopoulos et al. [38]. Figure 6d plots the fitting creep rate curves under different peak loads. All curves decrease rapidly at the beginning and then flatten, but it is noticeable that higher peak load corresponds to larger creep rate at the same timestamp and the difference becomes less apparent when the values are higher than 200 [mu]N. The creep rate under 100 [mu]N is observed to be nearly constant after 5 s and 500 [mu]N after 10 s, indicating that it undergoes more relaxation time for large peak load. So besides the optimized loading/ unloading rate and holding period, a lower peak load can also suppress the influence of creep effect on nanoindentation tests. However, the indentation depth must be obliged to be qualified to minimize the impact of surface roughness and rigid substrate.

Trend of Hardness and Reduced Elastic Modulus

Figure 7a represents the dependence of the reduced modulus [E.sub.r] and hardness H of Nafion 117 membranes on loading/unloading rate. The software brought by the equipment (Hysitron Tribo-scope TI950, USA) can directly fit the loading and unloading curves to get the data of reduced modulus [E.sub.r] and hardness H of Nafion 117 membranes based on Oliver and Pharr method. Clearly, the varying tendencies of [E.sub.r] and H with loading rate are nearly wholly consistent in the current architecture. Both values increase rapidly in the initial stage, and then tend to become flat at higher loading/unloading rate. It is possible that gradually steady increments may arise from a lack of time to creep due to the increasing loading rate. For the selected loading rates, the 10 [mu]N/s is almost a turning point of the slope change, which is used in the following tests. The average value of reduced modulus increases from 0.122 to 0.231 GPa and hardness from 0.013 to 0.036 GPa, corresponding to the loading rate from 1 to 250 [mu]N/s.

Figure 7b plots the variation of measured reduced modulus and hardness with different holding period. It can be seen (Table 1) that the longer holding at peak load corresponds to a lower [E.sub.r] and H. They reach to the maximum of 0.166 and 0.022 GPa without holding, and the minimum of 0.108 and 0.010 GPa when the peak period is 500 s. Moreover, there is an initial sharp reduction in the measurement values, followed by a region showing slowly changing amplitude. The reduced modulus and hardness remain relatively stable after a 200 s holding period. The reason may be that the creep effect is dominant during the initial stage, and then a longer holding time will exhaust the influence upon the unloading process, providing enough relaxation of membrane and therefore the system can reach a mechanical equilibrium before the subsequent unloading [5, 45]. Moreover, the reduction of modulus and hardness can be partially considered as the result of increased contact area due to the penetration depth growth. Actually, while creep displacement increases, the self-recovery of the membrane may occur in the zone around the indenter during load holding. Since evident recovery effect of the indents in the depth direction has been observed for Nafion 117 [46].

The result of reduced modulus and hardness at a constant loading rate and holding time but various peak loads are shown in Fig. 7c. Clearly, the parameter values decrease with the increasing peak load and have no slowdown region as shown under other two conditions (varying loading rates and holding times). Both the measured average values of [E.sub.r] and H for the highest peak load are only about one-third of the lowest one (see Table 1). To explain the reduction of [E.sub.r] and H, two reasons should be paid attention that larger peak load enhancing creep effect leads to the softening of membrane, and that deeper penetration depths will turn the total influence from membrane surface and rigid substrate. It is well known that larger load or greater maximum depth will enlarge the influence of substrate and weaken the effect of surface properties (surface roughness and surface material properties) on nanoindentation results [47]. By analyzing the trends in Figs. 6c and 7c, a peak load of 100 [mu]N may be the better option in the case of Nafion.

What must be emphasized is that the Nafion surface is not representative of the whole bulk, for example, membrane properties change below a thickness of a few tens of nanometers [48, 49]. Here, the maximum depth under 100 [mu]N and 500 [mu]N is 600 and 2,000 nm, respectively. But, as far as we know, concrete effect of the surface layer on mechanical properties of Nafion has not been analyzed, which will be an attractive topic in the future study. The key experimental data for different loading conditions are listed in Table 1.


Although nanoindentation is an effective technology for probing the mechanical response of solid materials, it is rarely applied into PFSA membranes analysis due to their high viscoelastic behavior. In this work, effects of loading rate, holding time and peak load are studied on dry Nafion 117 membranes respectively, which is a time-dependent viscoelastic material.

In the case of different load rate, the maximum penetration depths decrease gradually with increasing load rate. Consider varying holding period found that the creep displacement increases monotonously when holding time is extended, but the rate of increase will gradually ease. The higher peak load leads to increasing creep rate and displacement during holding period. The measured reduced elastic modulus and hardness appear consistent trend with changing load conditions, demonstrating decreasing value with increasing holding time and peak load, respectively. Though, an increase in loading rate tends to make the measured value grow.

Finally, we can conclude that faster loading/unloading rate, longer holding time and reasonably low peak load all contribute to mitigating the creep effect. For nanoindentation test of dry Nafion 117 membranes (at room temperature and 58% RH), a loading/unloading rate just above 10 [mu]N/s, a holding period longer than 20 s and a peak load lower than 100 [mu]N are recommended for future studies.


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Re Xia, (1) Hongjian Zhou, (1) Zhennan Zhang, (1) Runni Wu, (1) Wen-Ping Wu (iD) (2)

(1) Key Laboratory of Hydraulic Machinery Transients (Wuhan University), Ministry of Education Wuhan, Wuhan 430072, China

(2) Department of Engineering mechanics, School of Civil Engineering, Wuhan University, Wuhan 430072, China

Correspondence to: W.-P. Wu; e-mail:

Contract grant sponsor: National Natural Science Foundation of China; contract grant numbers: 11472195 and 51575404; contract grant sponsor: the State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics; contract grant number: MCMS-0414Y01.

DOI 10.1002/pen.24818

Published online in Wiley Online Library (

Caption: FIG. 1. (a) Commercially available Nafion 117 membrane; (b) Hysitron Triboscope TI950 experimental equipment. [Color figure can be viewed at]

Caption: FIG. 2. Schematic diagram of Burgers model.

Caption: FIG. 3. Typical experimental and fitted displacement-time curve for Nafion 117, loading rate of 10 [micro]N/s, holding time of 30 s and peak load of 200 [micro]N. [Color figure can be viewed at]

Caption: FIG. 4. (a) Nine load-displacement curves (P-h curve) obtained during nanoindentation of Nafion 117 membrane, which exhibit good reproducibility; (b) Typical P-h curves at different loading/unloading rates. All tests are under the peak load of 100 [micro]N and without peak holding. [Color figure can be viewed at]

Caption: FIG. 5. (a) Nine P-h curves obtained under the loading/unloading rate of 10 [micro]N/s, peak load of 100 [micro]N and holding time of 30 s; (b) typical P-h curves; and (c) displacement vs time curves with different holding time. The peak load is 100 [micro]N and loading rate is 10 [micro]N/s. [Color figure can be viewed at]

Caption: FIG. 6. (a) Nine P-h curves obtained under the peak load of 400 [micro]N; (b) typical P-h curves under different peak load; (c) creep response during 30 s holding period with aligned beginning (replot the holding segments from (b)); (d) Creep strain rate during the holding segments under different peak load. The loading rate is 10 [micro]N/s and holding time is 30 s. [Color figure can be viewed at]

Caption: FIG. 7. Reduce modulus and hardness data for Nafion 117 membrane at (a) various loading rate (with peak load of 100 [micro]N and 0 holding time), (b) various holding period (with peak load of 100 [micro]N and loading rate of 10 [micro]N/s), and (c) different peak load (with holding time of 30 s and loading rate of 10 [micro]N/s). [Color figure can be viewed at]
TABLE 1. Maximum displacement, creep displacement, reduced
modulus and hardness in different loading conditions.


Loading                                  Maximum         Creep
conditions                             displacement   displacement
                                           (nm)           (nm)

Peak load         Load rate       1       663.8
(100 [micro]N)    ([micro]N/s)    5       588.9
Holding time                     10       559.5
(0 s)                            20       537.9
                                 50       500.8
                                 100      454.9
                                 250      334.5
Peak load         Holding         0       551.7            0
(100 [micro]N)    time (s)        1       553.5           14.4
Load rate                         5       571.1           31.6
(10 [micro]N/s)                  10       585.1           49.2
                                 30       624.1           70.0
                                 50       637.6           88.7
                                 100      669.7          110.1
                                 200      696.2          133.2
                                 500      730.7          168.5
Holding time      Peak load      100      582.2           57.4
(30 s)            ([micro]N)     200      985.0           79.6
Load rate                        300      1394.0          96.0
(10 [micro]N/s)                  400      1846.3         110.3
                                 500      2341.0         126.1


Loading                                Reduced   Hardness
conditions                             modulus    (GPa)

Peak load         Load rate       1     0.122     0.013
(100 [micro]N)    ([micro]N/s)    5     0.143     0.018
Holding time                     10     0.158     0.021
(0 s)                            20     0.166     0.023
                                 50     0.184     0.026
                                 100    0.208     0.030
                                 250    0.231     0.036
Peak load         Holding         0     0.166     0.022
(100 [micro]N)    time (s)        1     0.165     0.021
Load rate                         5     0.155     0.020
(10 [micro]N/s)                  10     0.150     0.019
                                 30     0.134     0.016
                                 50     0.128     0.015
                                 100    0.118     0.013
                                 200    0.113     0.012
                                 500    0.108     0.010
Holding time      Peak load      100    0.140     0.018
(30 s)            ([micro]N)     200    0.095     0.015
Load rate                        300    0.072     0.013
(10 [micro]N/s)                  400    0.055     0.011
                                 500    0.044     0.009
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Author:Xia, Re; Zhou, Hongjian; Zhang, Zhennan; Wu, Runni; Wu, Wen-Ping
Publication:Polymer Engineering and Science
Date:Nov 1, 2018
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