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Frequency-tunable toughening in a polymer-metal-ceramic stack using an interfacial molecular nanolayer


Interfacial toughening in composite materials is reasonably well understood for static loading, but little is known for cyclic loading. Here, we demonstrate that introducing an interfacial molecular nanolayer at the metal-ceramic interface of a layered polymer-metal-ceramic stack triples the fracture energy for ~75–300 Hz loading, yielding 40% higher values than the static-loading fracture energy. We show that this unexpected frequency-dependent toughening is underpinned by nanolayer-induced interface strengthening, which facilitates load transfer to, and plasticity in, the polymer layer. Above a threshold interfacial bond strength, the toughening magnitude and frequency range are primarily controlled by the frequency- and temperature-dependent rheological properties of the polymer. These results indicate the tunability of the toughening behavior through suitable choice of interfacial molecular layers and polymers. Our findings open up possibilities for realizing novel composites with inorganic-organic interfaces, e.g., arresting crack growth or stimulating controlled fracture triggered by loads with specific frequency characteristics.


Tailoring the chemistry of heterointerfaces is crucial to controlling the fracture toughness of a variety of composite materials, such as, those used in load-bearing structures1, nanoelectronics devices2, energy systems3, and biomedicine4. Interfacial fracture can occur at significantly lower stresses than the static-loading fracture stresses5,6 of the materials comprising the interface, and can be exacerbated by chemical attack (stress corrosion) and cyclic loading (fatigue), thereby adversely impacting reliability and performance. Although fatigue has been widely investigated and well understood in bulk materials7,8, much less is known about fatigue-induced interfacial fracture, especially in coatings and thin films. Recent works have examined the effects of chemical treatment9,10, patterning11, micrometer-thick adhesion layers4,10, crack-tip blunting12, and cyclic loading amplitude13 on interfacial fatigue, and described the results in terms of Paris law-based bulk-fatigue models14,15. But, loading-frequency-dependence of interfacial fatigue, and related phenomena, remain largely unexplored. Our prior work has shown that introducing an interfacial molecular nanolayer (MNL) in model polymer-metal-ceramic structures can yield multifold increases in fracture energy under static loading16,17,18,19, enhance thermal20 and electronic21,22,23,24,25 transport, inhibit diffusion26,27,28, and alter phase formation29. However, the effects of cyclic loading on the fracture behavior of such molecularly modified model systems are not known. Understanding frequency-dependent effects in molecularly modified structures, such as, accelerated damage, crack growth mitigation, and interfacial healing, is not only of fundamental importance but also should enable the design of smart composites30,31,32 comprised of soft-hard and/or organic-inorganic interfaces for emerging applications in electronics, energy, and biomedicine.

Here we report loading-frequency-dependent multifold fracture toughening upon inserting a strongly binding MNL at the metal-ceramic interface of a layered polymer-metal-ceramic stack. The interfacial MNL results in up to threefold higher fracture energy in the ~75–300 Hz range than the invariant value at other frequencies. We demonstrate that this remarkable behavior is underpinned by MNL-induced interface strengthening that enables load transfer to, and plasticity in, the distal polymer layer. Furthermore, the magnitude and frequency range of fatigue toughening correlates with the rheological properties of the polymer, varied by altering the temperature relative to the polymer glass transition. Our findings suggest that fatigue fracture energy is tunable by appropriate choices of MNL(s) and polymer(s), opening up a completely new set of possibilities to tailor composite materials. For example, the interface can be tailored to shift from a crack growth mode to crack arrest mode, or controllably fracture in response to stimuli with specific loading-frequency characteristics.


Experimental work

We prepared polymer-metal-MNL-ceramic structures sandwiched between two silica-capped Si(001) wafers for four-point-bend mechanical tests19 (Fig. 1a). We self-assembled a mercapto-propyl-tri-methoxysilane (MPTMS) MNL on a silica-capped Si wafer surface. We then sputter-deposited a 40-nm-thick Cu layer with a 7 mTorr Ar plasma in a 5 × 10−7 Torr base pressure CVC tool. Without breaking vacuum, we also deposited a 100-nm-thick Ta layer to facilitate metal-polymer bonding 17. We glued the metal-MNL-silica structures to a dummy Si wafer with a System Three Resins® T88 epoxy polymer to obtain beams comprised of layered Si-polymer-Ta-Cu-MPTMS-SiO2-Si structures for four-point-bend mechanical tests19 (Fig. 1a). We also created and tested beams without the MNL (see Methods).

Fig. 1
figure 1

Fracture energy of epoxy-Cu-MPTMS-SiO2 structures under static and fatigue loading. a Schematic depicting the four-point bending test and b the strain energy release rate characteristics for load-shedding fatigue and static loading. c Fatigue fracture energy of polymer-metal-ceramic structures with Cu-MPTMS-SiO2 interfaces (red squares) and Cu-SiO2 interfaces (blue circles) determined at \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 0.6 kPa, shown together with d the corresponding static stress fracture energies. Each data point represents at least three tests. The width of the bands, drawn through the data points to guide the eye, connote the experimental uncertainty measured as standard deviation

Four-point bend tests were carried out under fatigue and static loading at temperatures ranging from 15 ≤ T ≤ 50 °C and at preset water partial pressures between 0.6 ≤  \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) ≤ 2.8 kPa. A Physik Instrumente P216-9S piezo actuator was used to produce load-cycling. Following crack initiation of the Cu-SiO2 interface33 at a critical strain energy release rate (ΓCritical), we conducted displacement-controlled subcritical (i.e., Γ < ΓCritical) load-shedding tests18,34. Example stress-time curves from a load-shedding fatigue test, and a static-loading test, are schematically depicted in Fig. 1b. For the fatigue tests, we chose a displacement-amplitude between 5 and 30 μm to obtain an initial stress slightly higher than that corresponding to the fatigue fracture energy ΓFatigue to be measured. We applied sinusoidal load oscillations in the 0.1 ≤ ν ≤ 1000 Hz range, with a maximum-to-minimum load ratio ~ 10. We extracted the ΓFatigue from strain energy release rate-crack velocity (Γ-ucrack) plots by recognizing that Γ = ΓFatigue at ucrack = 0. We also determined the stress corrosion fracture energy ΓStatic from static load tests19 to explicitly separate the effects of chemical attack and load-cycling. The fracture surfaces were examined by X-ray photoelectron spectroscopy (XPS) and polarized-light microscopy.

Loading-frequency-dependent toughening

Our results show that introducing a MPTMS nanolayer at the Cu-SiO2 interface of our polymer-metal-silica stacks significantly influences the fatigue fracture behavior. Stacks without the MPTMS nanolayer exhibit a ΓFatigue ~ ΓStatic = 1.6 Jm−2 at 25 °C and \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 0.6 kPa (Fig. 1c), irrespective of the loading frequency. Inserting an MPTMS nanolayer at the Cu-SiO2 interface produces a 30% higher ΓStatic = 2.1 Jm−2, as expected35 (Fig. 1d). But, MPTMS functionalization decreases the fatigue fracture energy to ΓFatigue ~ 1.1 Jm−2 (i.e., ΓFatigue < ΓStatic) at all frequencies, except ν ~ 75–125 Hz, where we observe ΓFatigue > ΓStatic and a maximum of ΓFatigue-peak ~ 2.6 Jm−2. In particular, ΓFatigue increases above a threshold frequency νLeading, which we refer to as the leading edge (Fig. 1c). For ν > νLeading, ΓFatigue goes through a maximum at νmax, and decreases at higher ν. Fatigue toughening is not detectable for ν > νTrailing, where νTrailing corresponds to the trailing edge of the ΓFatigue peak, i.e., where ΓFatigue < ΓStatic.

Our experiments revealing ΓFatigue < ΓStatic at very low and very high load-cycling frequencies is not unexpected because subcritical cyclic loading is known to hasten interfacial fracture11. However, the observed loading-frequency-dependent toughening at intermediate frequencies (i.e., νLeading ≤ ν ≤ νTrailing) indicated by the ΓFatigue peak in the MPTMS-modified structures, is unusual. This result indicates that molecular functionalization of the weakest interface can actually increase the fracture energy at certain loading frequencies, to values higher than the static-loading fracture energy.

In order to understand the MPTMS-induced fatigue toughening, we measured the fracture energy as a function of the water-sensitive siloxane bond strength36 at the Cu-MPTMS-SiO2 interface by adjusting the water partial pressure \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\). For low \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) < 2.2 kPa we obtain a ΓFatigue peak at ν ~ 75–300 Hz in structures with Cu-MPTMS-SiO2 interfaces (Fig. 2a). At higher \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) ≥ 2.2 kPa ΓFatigue is essentially invariant in the 0.1 ≤ ν ≤ 500 Hz range, with no observable fatigue toughening (Fig. 2b), reflecting a behavior similar to that in structures without MPTMS. Since moisture weakens siloxane bonds, our results indicate a minimum interface bonding strength, attainable below a threshold \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\), is a prerequisite for fatigue toughening. This is reminiscent of static toughening at Cu-MPTMS-SiO2 interfaces below a threshold \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) that provides adequate siloxane bonding strength to enable metal plasticity18,19.

Fig. 2
figure 2

Effect of moisture-dependent interfacial bond strength on fatigue toughening. Fatigue fracture energy ΓFatigue of polymer-metal-ceramic structures with Cu-MPTMS-SiO2 interfaces shown for water partial pressures a \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 1.9 kPa and b \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 2.8 kPa. c ΓFatigue peak value, i.e., ΓFatigue-peak (red squares) and average ΓStatic (blue circles) plotted versus \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) for stacks with Cu-MPTMS-SiO2 interfaces. Average ΓFatigue (green triangles) and ΓStatic (black stars) for stacks without MPTMS are also shown. There is no observable ΓFatigue peak for \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) > 2.2 kPa (open red squares). d Leading edge frequency νLeading of the ΓFatigue peak for Cu-MPTMS-SiO2 interfaces. No ΓFatigue peak is observed for \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) ≥ 2.2 kPa. Each data point represents at least three tests. The width of the bands, drawn through the data points to guide the eye, connote the experimental uncertainty measured as standard deviation

Unlike a monotonic increase in the magnitude of static toughening with desiccation, fatigue toughening increases with desiccation in the 1.9 kPa ≤ \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) ≤ 2.5 kPa range, but saturates at ΓFatigue = ΓFatigue-peak for \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) < 1.9 kPa and is insensitive to further desiccation (Fig. 2c). We note that ΓFatigue > ΓStatic at \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 2.2 kPa, despite the absence of a ΓFatigue peak. These observations suggest that the ΓFatigue-peak magnitude is limited by a mechanism other than desiccation-induced interfacial siloxane bond strengthening. Fatigue toughening occurs only below a threshold \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) and only for ν ≥ νLeading, indicating that νLeading corresponds to the threshold \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) at which the minimum required siloxane bond strength is attained at the crack tip. Toughening is precluded for ν < νLeading because of facile water-induced siloxane bond-breaking due to a higher \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) at the crack tip than the threshold \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\). Conversely, ν > νLeading corresponds to a lower \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) at the crack tip than the threshold \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\). Thus, increasing frequency for ν > νLeading (or equivalently, downshifting νLeading) is tantamount to crack-tip desiccation. This is indeed corroborated by our results showing desiccation-induced downshifting of νLeading below \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) ≤ 1.9 kPa (Fig. 2d).

The correlations between increasing ν and desiccation suggest that the water molecules are increasingly hindered from reaching the crack tip for ν > νLeading, similar to that reported for high loading rates37,38,39. The build-up of elastic energy in the unbroken interfacial bonds increases the interfacial work of adhesion γa and becomes available for activating plastic energy dissipation γp in the adjacent layers. Thus, siloxane bond strength is the limiting determinant of the toughening magnitude with increasing frequency in the νLeading ≤ ν ≤ νpeak range and desiccation in the 1.9 kPa ≤ \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) ≤ 2.8 kPa range. Decreasing ΓFatigue for ν > νpeak and the invariance of ΓFatigue-peak magnitude for \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) < 1.9 kPa are contrary to desiccation-induced bond strengthening, confirming that ΓFatigue at high ν and low \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) is not limited by the interfacial strength.

Interfacial fracture and plastic energy dissipation

Fracture surface analyses suggests that MPTMS-functionalization leads to fatigue toughening by facilitating plasticity in the metal-polymer bilayer. Core-level XPS spectra from fracture surfaces confirm that fatigue fracture occurs via siloxane bond-breaking at the MPTMS-silica interface (Supplementary Fig. 1), as reported for static loading17,18. Polarized-light micrographs of Cu fracture surfaces exhibit 5- to 20-μm-scale wrinkles (Fig. 3a). Etching off the metal film reveals microvoids in the polymer that are similar in shape and size of the metal wrinkles at the same location (Fig. 3b), suggesting that polymer voiding and metal wrinkling are correlated. In contrast, the silica fracture surfaces were featureless (Fig. 3c), consistent with our XPS analysis. Load-cycling results increases the average microvoid area ζMicrovoid multifold, e.g., from 175 to 980 μm2 (Supplementary Fig. 2). Radially oriented polarization fringes around the microvoids (Supplementary Fig. 3) indicate microvoid growth by shear banding involving the back-and-forth motion of polymer chains9. Fracture surfaces obtained by static loading show neither metal wrinkling nor polymer microvoid growth, confirming that these features arise from load-cycling-induced plasticity.

Fig. 3
figure 3

Fracture surface analyses of epoxy-Cu-MPTMS-SiO2 structures under fatigue loading. a Representative optical micrographs from an as-obtained Cu fracture surface (scale bar = 300 μm), b the same with the metal film etched off to expose the polymer (scale bar = 300 μm), and c the SiO2 fracture surface (scale bar = 100 μm). The sizes and shapes of the metal wrinkles and the polymer microvoids are correlated (circles regions). Average d metal wrinkle coverage χWrinkle (scale bar = 100 μm) and e microvoid coverage χMicrovoid (scale bar = 200 μm) from fracture surfaces of structures with (red squares), and without (blue circles) MPTMS. Representative optical micrographs inset in d and e capture metal wrinkling and polymer microvoiding at select frequencies. The data in this figure were from experiments at \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 1.3 kPa. The width of the bands drawn through the data points connote the experimental uncertainties measured as standard deviation

Both metal wrinkling and polymer microvoid coverages (χWrinkle and χMicrovoid) are dependent on the loading frequency. We observe χWrinkle peaks between ~75 and 125 Hz (Fig. 3d) with a 60% higher coverage than other frequencies, while χMicrovoid increases eightfold and peaks over a wider frequency range of ~75–200 Hz, and saturates at a slightly lower value above ~200 Hz (Fig. 3e). The frequency regimes of the coverage peaks correlate well with the 75–300 Hz regime of the ΓFatigue peak. In contrast, fatigue fracture surfaces of stacks without MPTMS exhibit ninefold lower χMicrovoid and fourfold lower χWrinkle, both of which are invariant with frequency. These results confirm that MPTMS-induced interfacial strengthening is key to activating loading-frequency-dependent plasticity in the polymer-metal bilayer.

The greater overlap in the frequency regime of the χMicrovoid peak and the ΓFatigue peak suggests a greater contribution of polymer plasticity to the observed fatigue toughening. Cu film strain, estimated from χWrinkle and wrinkle amplitude40 measurements (Supplementary Fig. 3), indicates a metal plastic energy Um ~ 0.02 ± 0.01 Jm−2, which accounts for <1% of the fracture energy at ΓFatigue-peak ~ 2.5 Jm−2 (Supplementary Methods). Such low metal plasticity is attributable to the high-yield stress Cu film that results in a highly confined plastic zone near the crack tip vicinity. This view is consistent with our estimates19 of <~2% plastic strain energy and a <1 nm plastic zone for a 40-nm-thick Cu film used in our experiments here. Thus, fatigue toughening observed in our experiments is underpinned primarily by polymer plasticity, while the metal film essentially serves as an elastic stress-transfer layer. We note that this mechanism is unlike MNL-induced metal-ceramic interface toughening due to metal plasticity under static loading19.

We propose that microvoid growth in the polymer leads to metal-polymer interface delamination at the voids. The consequent release of constraint leads to metal film wrinkling due to compressive stresses41. This hypothesis is supported by the disappearance of fatigue toughening and metal wrinkling when polymer plasticity is suppressed by replacing the T88 epoxy with the harder EPO-TEK 375 epoxy in our structures (Fig. 4 and Supplementary Fig. 3). The ΓFatigue peak frequency range is also consistent with the toughening of T88 epoxy composites42,43,44,45 at strain rates of ~0.02–0.1 s−1 (Supplementary Methods). If voiding were to initiate at the metal-polymer interface, we would expect significant metal wrinkling under static loading, and a fracture path change from the MNL-SiO2 interface, neither of which we observe. These results indicate that MPTMS-induced polymer plasticity is the primary fatigue toughening mechanism.

Fig. 4
figure 4

Effect of polymer hardness on fatigue toughening. a Fatigue fracture energy ΓFatigue and b ΓStatic of polymer-metal-MPTMS-SiO2 stacks with a soft System Three Resins® T88 polymer (red squares), and a harder EPO-TEK 375 polymer (blue circles) at \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 1.3 kPa. Each data point represents at least three tests. The width of the bands, drawn through the data points to guide the eye, connote the experimental uncertainties measured as standard deviation

Tuning the toughening magnitude and frequency range

In order to understand fatigue toughening magnitude and frequency characteristics in terms of polymer rheology, we examined the ΓFatigue peak at different temperatures below the polymer glass transition temperature Tg. Since Tg for our T88 epoxy is frequency-dependent (e.g., 52 ≤ Tg ≤ 75 °C between 0.01 ≤ ν ≤ 1000 Hz (Supplementary Fig. 4), we analyzed temperature-dependent toughening in terms of ΔT = Tg − T for data acquired at a fixed \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 1.3 kPa. Separate measurements of polymer film stress on SiO2 indicate that water-induced polymer swelling is insignificant, e.g., <~3% of the compliance change seen during crack growth (Supplementary Fig. 5).

We find that lower ΔT (i.e., higher T, closer to Tg) correlates with a higher ΓFatigue-peak, and a larger peak width (Δν = νTrailing − νLeading), indicating that both the fatigue toughening magnitude and frequency range are sensitive to polymer plasticity (Fig. 5a). For instance, a 20 °C increase in temperature from 16 to 36 °C (i.e., decreasing ΔT from 59 to 39 °C) doubles the ΓFatigue peak magnitude to ΓFatigue-peak = 2.9 Jm−2 (Fig. 5b), which is 40% higher than the highest static-loading fracture energy ΓStatic measured at \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 0.6 kPa (Fig. 2c). This ΓFatigue-peak doubling correlates with the doubling of the loss-to-storage moduli ratio tan δ of the epoxy for the same temperature increase (Supplementary Fig. 4), suggesting that polymer rheology determines the ΓFatigue-peak magnitude. Since tan δ increases with temperature for T < Tg, but decreases with frequency (Supplementary Fig. 4b-c), polymer plasticity is facilitated at higher temperatures but deterred at higher frequencies. Increasing ΓFatigue-peak magnitude with temperature and decreasing ΓFatigue for ν > νPeak mirror the tan δ behavior, confirming that polymer plasticity is the predominant contributor to the observed fatigue toughening. Thus, decreasing polymer plasticity at ν > νPeak counteracts increases in interfacial strength at ν > νLeading, leading to a fatigue toughening maximum.

Fig. 5
figure 5

Temperature-dependence of the fatigue toughening magnitude and frequency characteristics. a Fatigue fracture energy ΓFatigue of polymer-metal-MPTMS-silica interfaces for 24 °C ≤ ΔT ≤ 59 °C, at \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) = 1.3 kPa. b The ΓFatigue trailing edge frequency νTrailing (magenta squares), leading edge frequency νLeading (green triangles), and c ΓFatigue peak height ΓFatigue-peak (blue circles), plotted as a function of ΔT. The ΓFatigue-peak and νTrailing values shown for ΔT = 24 °C represent the lower bounds (open symbols) because the νTrailing edge at this temperature extends beyond our instrument frequency range. Each data point in b and c is extracted from the corresponding curve in a. The width of the bands, drawn through the data points to guide the eye, connote the experimental uncertainties measured as standard deviation

Decreasing ΔT (i.e., increasing T, closer to Tg) also extends fatigue toughening to higher frequencies. Both νLeading and νTrailing shift to higher frequencies, but the νTrailing shift is ~120% greater (Fig. 5c). The temperature-induced νTrailing shifts can be understood by recognizing that plasticity is arrested above νTrailing due to the diminished responsiveness of polymer chains to high-frequency load-cycling, which is consistent with decreasing tan δ with increasing frequency. Higher chain mobility at temperatures closer to Tg (i.e., high T and low ΔT) enables greater polymer plasticity, which is manifest as a higher ΓFatigue-peak magnitude and shifting of the plasticity arrest point νTrailing to higher frequencies as ΔT decreases. Since νLeading corresponds to a threshold strength of the water-sensitive siloxane bonds, and \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) is held constant here, the up-shifts in νLeading with decreasing ΔT indicates that increasing the temperature enhances the transport of water molecules to the crack tip.


Based upon our results, the salient mechanistic aspects of the frequency-dependent toughening observed in polymer-metal-ceramic structures with an MNL-functionalized metal-ceramic interface can be understood as follows. Interfacial fracture energy has two main contributors: the metal-ceramic interface work of adhesion γa, and plastic energy dissipation γp in the adjacent layers. Introducing the MPTMS MNL increases γa through siloxane bond formation at the MNL-SiO2 interface. Water attack of siloxane bonds lowers γa. However, increasing load-cycling frequency curtails water transport to the crack tip, leading to an effective increase in γa. Thus, increasing frequency is tantamount to desiccation, which strengthens siloxane bonds. The consequent build-up in interfacial elastic energy becomes available for activating plasticity (i.e., γp ≠ 0) in the adjacent layers. The minimum γa necessary for elastic energy build-up and plastic energy dissipation for detectable fatigue toughening is achieved at νLeading, and increases for ν > νLeading.

In our experiments, plasticity γp occurs mainly in the polymer by microvoid growth via shear banding. The high-yield stress metal film serves as an elastic load transfer layer, and wrinkles due to compressive stresses generated through release of constraint when microvoids reach the polymer-metal interface. Polymer plasticity itself, however, decreases with increasing frequency due to the increasing inability of polymer chain motion to keep up with load-cycling. Increasing γa and decreasing γp with frequency results in a fatigue toughening maximum, i.e., a ΓFatigue peak, at intermediate frequencies. The increase in ΓFatigue with frequency for νleading ≤ ν ≤ νPeak indicates that fatigue toughening is limited by γa. At ν ≥ νPeak, the decreasing contribution of γp due to inhibited chain motion begins to offset the frequency-induced increases in the elastic energy due to interfacial bond strengthening. Decreasing fatigue toughening for ν > νpeak and saturation for \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\) < 1.9 kPa are contrary to interfacial siloxane bond strengthening expected at high ν and low \(p_{{\mathrm{H}}_{2}{\mathrm{O}}}\), confirming that fatigue toughening is limited by polymer plasticity at high frequencies.

Although bond strengthening γa through the use of the MNL is a necessary condition for fatigue toughening, polymer plasticity γp is the predominant contributor. This is clearly seen from the suppression of fatigue toughening in MNL-modified structures with a hard epoxy. Furthermore, the maximum toughening magnitude ΓFatigue-peak and high-frequency limit of toughening νTrailing, are determined by the rheological properties of the polymer. For example, both ΓFatigue-peak and νTrailing increase with temperature (as T approaches Tg) due to facile chain motion, which is counteracted to some extent by the frequency-induced increase in Tg at higher frequencies. Therefore, choosing a polymer with the appropriate rheological properties is crucial for tailoring the toughening magnitude as well as the high-frequency limit.

Based upon the above, the overall mechanism of fatigue toughening of the epoxy-Cu-MPTMS-SiO2 polymer-metal-MNL-ceramic stack enabled by the MPTMS MNL can be understood in terms of Fig. 6. At low loading frequencies, water-induced siloxane bond-breaking at the MNL-ceramic interface limits the interface fracture energy. At intermediate loading frequencies, the increased interface strength caused by the diminishing effect of water attack at the MNL-SiO2 interface facilitates polymer plasticity resulting in fracture energies exceeding the static-loading fracture energy. Arrested polymer plasticity due to curtailed chain mobility at very high loading frequencies leads to the disappearance of polymer plasticity, and hence, fatigue toughening. Although the metal serves as an elastic layer in our experiments, using metals of different yield stresses, moduli, and/or thicknesses, may alter the contributions of metal and polymer plasticity, which could amplify, suppress, and/or modify the fatigue toughening frequency range.

Fig. 6
figure 6

Frequency-dependent toughening enabled by interfacial strengthening and polymer rheology. Schematic sketch of loading-frequency-dependent interfacial fracture energy increase in an epoxy-Cu-MPTMS-SiO2 stack caused by plasticity in the polymer layer through voiding activated by MNL-induced interfacial strengthening. At low frequencies, water-induced siloxane bond-breaking at the MPTMS MNL-silica interface limits the interface fracture energy, and no polymer voiding is observed. At intermediate frequencies, the increased interface strength due to diminishing water attack at the crack tip facilitates load transfer to, and plasticity in, the polymer, yielding fatigue fracture energies exceeding the static-loading fracture energy; polymer voiding is observed. Arrested polymer plasticity (no voiding observed) due to curtailed chain mobility at very high loading frequencies leads to a low interfacial fracture energy despite high interfacial strength

Our findings are relevant to the design, monitoring, and controlling the stability of smart composites with tunable frequency-dependent toughening and/or weakening behaviors. For example, low-frequency fatigue toughening commencement νLeading in polymer-metal-MNL-ceramic structures can be controlled by suitable choice of MNLs with termini that enable strong interfacial bonding that supports sufficient interfacial elastic energy build-up for activating plasticity in the adjacent layers. Choosing polymers with appropriate viscoelastic properties should allow the tuning of the maximum toughening magnitude ΓFatigue-peak and high-frequency toughening limit νTrailing. The use of multiple polymers with different rheological properties could result in novel ΓFatigue-ν characteristics with multiple peaks, plateaus, valleys, and combinations thereof. Such frequency-dependent phenomena could pave the way for realizing novel composites that respond to select loading magnitude/frequency stimuli by either controllably degrading46,47, or self-healing48 through polymer plasticity and crosslinking of healing agents released during microvoid growth in the polymers.

In summary, we have shown that functionalizing polymer-metal-ceramic structures with a MNL at the metal-ceramic interface can lead to multifold increases in fracture energy at certain loading frequencies, yielding values higher than that obtained during static loading. Nanolayer-induced interfacial strengthening allows load transfer to, and plasticity in, the polymer layer. While a threshold interfacial strength determines the minimum loading frequency for toughening, the magnitude and loading-frequency range of toughening are primarily dependent on polymer rheology. These facets of heterointerfacial mechanics could be harnessed to design, monitor, and control the stability of composite materials for diverse applications including energy and electronics devices46, biomedicine47, and smart-degrading and self-healing systems48.

Data availability

The data for the figures that support the findings of this study are available in figshare data repository with the identifier(s) 10.6084/m9.figshare.7154930 (fracture energy data), 10.6084/m9.figshare.7159529 (microscopy data), 10.6084/m9.figshare.7159541 (XPS data), and 10.6084/m9.figshare.7159553 (DMA data).


  1. Loehman, R. & Tomsia, A. Joining of ceramics. Am. Ceram. Soc. Bull. 67, 375–380 (1988).

    CAS  Google Scholar 

  2. Lane, M. W., Dauskardt, R. H., Krishna, N. & Hashim, I. Adhesion and reliability of copper interconnects with Ta and TaN barrier layers. J. Mater. Res. 15, 203–211 (2000).

    ADS  CAS  Article  Google Scholar 

  3. Yin, Z., Wei, J. & Zheng, Q. Interfacial materials for organic solar cells: recent advances and perspectives. Adv. Sci. 3, 1500362 (2016).

    Article  Google Scholar 

  4. Ohashi, K. L. & Dauskardt, R. H. Effects of fatigue loading and PMMA precoating on the adhesion and subcritical debonding of prosthetic-PMMA interfaces. J. Biomed. Mater. Res. 51, 172–183 (2000).

    CAS  Article  PubMed  Google Scholar 

  5. Kim, J.-K. & Mai, Y. High strength, high fracture toughness fibre composites with interface control—a review. Compos. Sci. Technol. 41, 333–378 (1991).

    CAS  Article  Google Scholar 

  6. Tang, L.-G. & Kardos, J. L. A review of methods for improving the interfacial adhesion between carbon fiber and polymer matrix. Polym. Compos. 18, 100–113 (1997).

    CAS  Article  Google Scholar 

  7. Suresh, S., Vasudévan, A. K. & Bretz, P. E. Mechanisms of slow fatigue crack growth in high strength aluminum alloys: role of microstructure and environment. Metall. Trans. A 15, 369–379 (1984).

    Article  Google Scholar 

  8. Yi, K. S., Cox, B. N. & Dauskardt, R. H. Fatigue crack-growth behavior of materials in viscous fluid environments. J. Mech. Phys. Solids 47, 1843–1871 (1999).

    ADS  CAS  Article  Google Scholar 

  9. Kawaguchi, T. & Pearson, R. A. The moisture effect on the fatigue crack growth of glass particle and fiber reinforced epoxies with strong and weak bonding conditions: part 1. Macroscopic fatigue crack propagation behavior. Compos. Sci. Technol. 64, 1981–1989 (2004).

    CAS  Article  Google Scholar 

  10. Snodgrass, J. M., Pantelidis, D., Jenkins, M. L., Bravman, J. C. & Dauskardt, R. H. Subcritical debonding of polymer/silica interfaces under monotonic and cyclic loading. Acta Mater. 50, 2395–2411 (2002).

    CAS  Article  Google Scholar 

  11. Cannon, R. M., Dalgleish, B. J., Dauskardt, R. H., Oh, T. S. & Ritchie, R. O. Cyclic fatigue-crack propagation along ceramic/metal interfaces. Acta Metall. Mater. 39, 2145–2156 (1991).

    CAS  Article  Google Scholar 

  12. McNaney, J. M., Cannon, R. M. & Ritchie, R. O. Fracture and fatigue-crack growth along aluminum-alumina interfaces. Acta Mater. 44, 4713–4728 (1996).

    CAS  Article  Google Scholar 

  13. Yan, Y., Sumigawa, T. & Kitamura, T. Effect of environment on fatigue strength of Cu/Si interface in nanoscale components. Mater. Sci. Eng. A 556, 147–154 (2012).

    CAS  Article  Google Scholar 

  14. Sharratt, B. M., Wang, L. C. & Dauskardt, R. H. Anomalous debonding behavior of a polymer/inorganic interface. Acta Mater. 55, 3601–3609 (2007).

    CAS  Article  Google Scholar 

  15. Paris, P. & Erdogan, F. A critical analysis of crack propagation laws. J. Basic Eng. 85, 528 (1963).

    CAS  Article  Google Scholar 

  16. Ramanath, G. et al. Self-assembled subnanolayers as interfacial adhesion enhancers and diffusion barriers for integrated circuits. Appl. Phys. Lett. 83, 383 (2003).

    ADS  CAS  Article  Google Scholar 

  17. Gandhi, D. D. et al. Annealing-induced interfacial toughening using a molecular nanolayer. Nature 447, 299–302 (2007).

    ADS  CAS  Article  PubMed  Google Scholar 

  18. Jain, A. et al. Atomistic fracture energy partitioning at a metal-ceramic interface using a nanomolecular monolayer. Phys. Rev. B 83, 35412 (2011).

    ADS  Article  Google Scholar 

  19. Kwan, M., Braccini, M., Jain, A., Lane, M. W. & Ramanath, G. Interplay between bond breaking and plasticity during fracture at a nanomolecularly-modified metal-ceramic interface. Scr. Mater. 121, 42–44 (2016).

    CAS  Article  Google Scholar 

  20. O’Brien, P. J. et al. Bonding-induced thermal conductance enhancement at inorganic heterointerfaces using nanomolecular monolayers. Nat. Mater. 12, 118–122 (2013).

    ADS  Article  PubMed  Google Scholar 

  21. Cardinal, T., Devender, F., Borca-Tasciuc, T. & Ramanath, G. Tailoring electrical transport across metal-thermoelectric interfaces using a nanomolecular monolayer. ACS Appl. Mater. Interfaces 8, 4275–4279 (2016).

    CAS  Article  PubMed  Google Scholar 

  22. Cardinal, T., Kwan, M., Borca-Tasciuc, T. & Ramanath, G. Effect of molecular length on the electrical conductance across metal-alkanedithiol-Bi2Te3 interfaces. Appl. Phys. Lett. 109, 173904 (2016).

    ADS  Article  Google Scholar 

  23. Cardinal, T., Kwan, M., Borca-Tasciuc, T. & Ramanath, G. Multifold electrical conductance enhancements at metal–bismuth telluride interfaces modified using an organosilane monolayer. ACS Appl. Mater. Interfaces 9, 2001–2005 (2017).

    CAS  Article  PubMed  Google Scholar 

  24. Ramanath, G. et al. Tuning of noble metal work function with organophosphonate nanolayers. Appl. Phys. Lett. 105, 81601 (2014).

    Article  Google Scholar 

  25. Kwan, M., Cardinal, T., Mutin, P. H. & Ramanath, G. Work function tuning at Au-HfO2 interfaces using organophosphonate monolayers. Appl. Phys. Lett. 108, 191607 (2016).

    ADS  Article  Google Scholar 

  26. Ganesan, P. G., Singh, A. P. & Ramanath, G. Diffusion barrier properties of carboxyl- and amine-terminated molecular nanolayers. Appl. Phys. Lett. 85, 579 (2004).

    ADS  CAS  Article  Google Scholar 

  27. Gandhi, D. D. et al. Molecular-nanolayer-induced suppression of in-plane Cu transport at Cu-silica interfaces. Appl. Phys. Lett. 90, 163507 (2007).

    ADS  Article  Google Scholar 

  28. Gandhi, D. D., Singh, A. P., Lane, M., Eizenberg, M. & Ramanath, G. Copper diffusion and mechanical toughness at Cu-silica interfaces glued with polyelectrolyte nanolayers. J. Appl. Phys. 101, 84505 (2007).

    Article  Google Scholar 

  29. Garg, S. et al. Metal–dielectric interface toughening by molecular nanolayer decomposition. J. Appl. Phys. 108, 34317 (2010).

    Article  Google Scholar 

  30. Yu, K. J., Yan, Z., Han, M. & Rogers, J. A. Inorganic semiconducting materials for flexible and stretchable electronics. npj Flex. Electron 1, 4 (2017).

    Google Scholar 

  31. Mir, S. H. et al. Review—organic-inorganic hybrid functional materials: an integrated platform for applied technologies. J. Electrochem. Soc. 165, B3137–B3156 (2018).

    CAS  Article  Google Scholar 

  32. D’Elia, E., Eslava, S., Miranda, M., Georgiou, T. K. & Saiz, E. Autonomous self-healing structural composites with bio-inspired design. Sci. Rep. 6, 25059 (2016).

    ADS  Article  PubMed  PubMed Central  Google Scholar 

  33. Charalambides, P. G., Lund, J., Evans, A. G. & McMeeking, R. M. A test specimen for determining the fracture resistance of bimaterial interfaces. J. Appl. Mech. 56, 77 (1989).

    ADS  Article  Google Scholar 

  34. Ma, Q. A four-point bending technique for studying subcritical crack growth in thin films and at interfaces. J. Mater. Res. 12, 840–845 (1997).

    ADS  CAS  Article  Google Scholar 

  35. Ramanath, G. et al. Self-assembled subnanolayers as interfacial adhesion enhancers and diffusion barriers for integrated circuits. Appl. Phys. Lett. 83, 383 (2003).

    ADS  CAS  Article  Google Scholar 

  36. Vlassak, J. J., Lin, Y. & Tsui, T. Y. Fracture of organosilicate glass thin films: environmental effects. Mater. Sci. Eng. A 391, 159–174 (2005).

    Article  Google Scholar 

  37. Zhang, X., Bogorin, D. F. & Moy, V. T. Molecular basis of the dynamic strength of the sialyl Lewis X—selectin interaction. Chemphyschem 5, 175–182 (2004).

    CAS  Article  PubMed  Google Scholar 

  38. Schmidt, S. W., Beyer, M. K. & Clausen-Schaumann, H. Dynamic strength of the silicon-carbon bond observed over three decades of force-loading rates. J. Am. Chem. Soc. 130, 3664–3668 (2008).

    CAS  Article  PubMed  Google Scholar 

  39. Schmidt, S. W., Pill, M. F., Kersch, A., Clausen-Schaumann, H. & Beyer, M. K. Mechanically induced silyl ester cleavage under acidic conditions investigated by AFM-based single-molecule force spectroscopy in the force-ramp mode. Faraday Discuss. 170, 357–367 (2014).

    ADS  CAS  Article  PubMed  Google Scholar 

  40. Chung, J. Y., Nolte, A. J. & Stafford, C. M. Surface wrinkling: a versatile platform for measuring thin-film properties. Adv. Mater. 23, 349–368 (2011).

    CAS  Article  PubMed  Google Scholar 

  41. Whitesides, G. M., Bowden, N., Brittain, S., Evans, A. G. & Hutchinson, J. W. Spontaneous formation of ordered structures in thin films of metals supported on an elastomeric polymer. Nature 393, 146–149 (1998).

    ADS  Article  Google Scholar 

  42. Jiang, W. et al. Loading rate dependence of mode II fracture behavior in interleaved carbon fibre/epoxy composite laminates. Appl. Compos. Mater. 8, 361–369 (2001).

    ADS  Article  Google Scholar 

  43. Todo, M., Takahashi, K., Béguelin, P. & Kausch, H. H. Strain-rate dependence of the tensile fracture behaviour of woven-cloth reinforced polyamide composites. Compos. Sci. Technol. 60, 763–771 (2000).

    CAS  Article  Google Scholar 

  44. Kusaka, T., Horikawa, N. & Masuda, M. Low-velocity impact fracture behaviour of impact-resistant polymer matrix composite laminates under mixed mode loading. Le. J. Phys. IV 10, Pr9-317–Pr9-322 (2000).

    Google Scholar 

  45. Vu-Khanh, T. & Fisa, B. Impact fracture of glass-flake reinforced polypropylene. Polym. Compos. 7, 375–382 (1986).

    CAS  Article  Google Scholar 

  46. Hernandez, H. L. et al. Triggered transience of metastable poly(phthalaldehyde) for transient electronics. Adv. Mater. 26, 7637–7642 (2014).

    CAS  Article  PubMed  Google Scholar 

  47. Kang, S.-K. et al. Bioresorbable silicon electronic sensors for the brain. Nature 530, 71–76 (2016).

    ADS  CAS  Article  PubMed  Google Scholar 

  48. Patrick, J. F., Robb, M. J., Sottos, N. R., Moore, J. S. & White, S. R. Polymers with autonomous life-cycle control. Nature 540, 363–370 (2016).

    ADS  CAS  Article  PubMed  Google Scholar 

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This work was partially supported by funding support from the National Science Foundation through CMMI 1100933/926 and ECCS 1002282/301 grants. We gratefully acknowledge Aditya Prasad and Steven Lee for help in characterizing the rheological properties of the polymer, Jackson Wong for carrying out some of the experiments, and Professor Linda Schadler for stimulating discussions.

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M.K. and M.B. carried out the experimental work and data analyses. G.R. and M.W.L. conceived the project, designed the experiments, and supervised and contributed to, the execution of the experiments, data analyses, and paper writing.

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Correspondence to Ganpati Ramanath.

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Kwan, M., Braccini, M., Lane, M.W. et al. Frequency-tunable toughening in a polymer-metal-ceramic stack using an interfacial molecular nanolayer. Nat Commun 9, 5249 (2018).

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