Active layer thickness across the crack plane and fracture energy consumption in polymer nanocomposites: adhesion against tear strength

Abstract

The tear strength of a model methyl methacrylate–butyl acrylate copolymer containing 30 wt% methyl methacrylate (MBC30) and its adhesion strength to poly(ethylene terephthalate) were determined to be 10.2 and 0.26 kN m⁻¹, respectively. The addition of 5 wt% mono-size, 180 nm in diameter, soft nanoparticles of poly(styrene-co-acrylonitrile) with 30 wt% acrylonitrile (SAN70) through latex blending, followed by drying, amplified the adhesion strength while reducing the tear strength. Mild and harsh annealing of the nanocomposite led to partial and full deterioration of work of failure per unit volume (WoF), resulting in augmented adhesion and tear strengths followed by their severe decline, respectively. The G₀(1 + ϕ) model-based partitioning of interfacial and bulk fracture energies of the annealed nanocomposites into intrinsic energy × viscoelastic dissipation led to minimum active layer thicknesses of 0.46 and 33.5 nm across the crack plane, respectively. They implied extension of three consecutive C–C bonds or 70% of the matrix entanglement-to-entanglement strand contour length, respectively, corresponding to maximum WoF.

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Introduction

Resistance to crack growth through the bulk of soft adhesives or their interfaces with various solid substrates is of great technological importance and has therefore been the subject of many studies in the last 40 years.^1–3 Its magnitude depends on bulk toughness, primary bond strength-governed intrinsic fracture energy and/or joint interfacial bonding strengths.^4,5 A pressure-sensitive adhesive (PSA) is a two-layer laminate, which functions desirably provided that it wets the solid surface and bonds under finger-tight stress.⁶ It is made through coating a stiff backing with a soft viscoelastic adhesive to meet the requirements of different applications, such as packaging, labelling, transdermal drug delivery, etc. Water-based colloidal adhesives containing a rubber-forming matrix, tackifier, and other auxiliaries have attracted the interest of researchers from both industry and academia due to their environmental friendly character.⁷ They experience a drying-induced complex film formation process, and may end up with two-dimensional undulating free surfaces.^3,8 The system viscosity rise during film formation may kinetically stabilize the resultant equilibrated or non-equilibrated microstructure.⁹ In addition, colloidal polymer blends may also evolve into different morphologies, due to the components’ size and/or stiffness disparity, through searching for structures with minimum free energies.^10–13 Interfacial healing among soft polymer nanoparticles starts with capillary forces and continues up to molecular-scale homogeneity.^10,14–16 Meanwhile, chain interdiffusion through the interfaces functions as the main mechanism of cohesion build-up.^2,3,17 The adhesive film surface wettability and interfacial bond formation through nonlinear viscoelastic deformation are other key parameters determining joint formation and target performance.^2,4,18 Finally, competition between the adhesion strength of a PSA and its adhesive film tear strength determines adhesive and/or bulk failure, which depends on the adhesive components’ state of mixing, intrinsic properties, and interfacial strength.^19,20

The addition of rigid particles, specifically at the nano-scale, to a polymer matrix presenting strong interfacial strength usually enhances the system’s bulk properties, either mechanical or rheological.^21,22 It improves the system’s deformability through effectively bonded and confined inter-ligament chains, leading to augmented toughness. Nanoparticle segregation, however, may reduce the maximum achievable properties.²³ The stabilization of dispersed particles by tethered polymer chains may activate long-range chain deformation in the system through their sliding over each other, i.e. a bridging regime.^21,24,25 Advantageously, rigid organic particles may present soft rubber elasticity in the melt state, resisting segregation through elastic collisions, while reinforcing the system in the solid state.¹⁵ Consequently, the size and size distribution of dispersed rigid particles, their state of mixing and interfacial strength are the key parameters governing the system’s toughness and resultant adhesion and tear strengths.^26–28

In this research work, the bulk work of failure per unit volume (WoF) and resultant adhesion and tear strengths of model nanocomposites exhibiting different dispersion morphologies were investigated and correlated. In other words, the prime goal of the research was to elucidate the effects of segregation state from particulate to bi-molecular on the bulk WoF and the resultant interfacial and bulk strengths. Moreover, the intrinsic fracture energy was modified using the concept of active layer thickness across the crack plane to predict and rationalize more precisely the consumed interfacial or bulk fracture energy.

Experimental

Materials

Methyl methacrylate (MMA), butyl acrylate (BA), styrene (St) and acrylonitrile (AN) monomers, sodium lauryl sulfate (SLS, ionic surfactant), Triton X-100 (nonionic surfactant), potassium persulfate (KPS, initiator), tertiary dodecyl mercaptan (TDM, chain transfer agent) and potassium hydroxide (KOH, pH regulator) were purchased from Merck and used without further purification. Distilled water with conductivity of 3 μS cm⁻¹ at 30 °C was utilized as the emulsion copolymerization medium.

Synthesis

Poly(styrene-co-acrylonitrile) with 30 wt% acrylonitrile (SAN70) and poly(methyl methacrylate-co-butyl acrylate) containing 30 wt% methyl methacrylate (MBC30) were synthesized through batch emulsion copolymerization based on the prescribed recipes³ (Table 1). They were designed to produce mono-size particles, 180 nm in diameter (determined by dynamic light scattering in our group’s previous work³), containing MBC30 or SAN70 copolymers with molecular weights above and below their entanglement thresholds, respectively.³

Table 1 The recipes of emulsion copolymerization

Ingredients (g)	SAN70	MBC30
a Data was extracted from ref. 29.b Data was reproduced using ref. 29 and 30.
Styrene	70	—
Acrylonitrile	30	—
Methyl methacrylate	—	30
Butyl acrylate	—	70
Water	800	800
Potassium persulfate	0.5	0.5
Sodium lauryl sulphate	0.15	0.38
Triton X-100	3	—
Potassium hydroxide	0.15	0.15
Tertiary dodecyl mercaptan	1	1
Critical entanglement molecular weight (kg mol^−1)	18^a	45^b

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All the reagents were mixed thoroughly before their addition into the reactor. The emulsion copolymerization was conducted within a 2.5 litter stainless steel reactor with a filling factor of 40%, at 80 °C and 250 rpm for 4 h using an anchor impeller.

Preparation of nanocomposite free films and three-layer laminates

160 cm³ of MBC30 latex was gently mixed with 5 wt% SAN70 latex and cast in a Teflon-coated aluminium Petri dish (19 × 25 × 4 cm³). Similar casting was practiced for making neat free film out of MBC30 latex. Drying was performed using a piece of paper as a cover, 75 g m⁻² in areal density, at room temperature for a week (slow drying, SD). A blend of MBC30 latex and three-month room-temperature aged SAN70 latex, containing aggregated nanoparticles, was also dried into a nanocomposite film in three days under the air convection of a laboratory hood (fast drying, FD). Model PSAs, however, were prepared by casting MBC30 latex or its blend with SAN70 latex on a thin film (20 μm in thickness) of poly(ethylene terephthalate), PET, then drying and subsequently annealing. Three-layer laminates (ESI, Fig. S1†) were then built through adhesive bonding of the PSAs to the same-thickness PET film or aluminium foil followed by being rolled over with a two kg cylinder. The thickness of the free film or adhesive layer was about 400–700 μm.

Atomic force microscopy (AFM)

The microstructure of MBC30-SD and the nanocomposites was investigated by an AMBIOS TECHNOLOGY AFM instrument in intermittent contact mode at room temperature. Imaging was performed using a silicone cantilever with a nominal spring constant of 45 N m⁻¹ and a resonance frequency of 190 kHz, equipped with an ultrasharp silicone tip, 16 nm in diameter. Images of 5 μm × 5 μm of the free surfaces of the adhesives were collected using a scan speed of 1.5 Hz, after their prewashing with distilled water and accelerated drying at room temperature.

Scanning electron microscopy (SEM)

Cross-sections of the fractured nanocomposites in liquid nitrogen were coated with a thin layer of gold and scanned using a SERON TECHNOLOGYAIS-2100 SEM instrument at an accelerating voltage of 20 kV under argon gas at room temperature.

Mechanical and adhesion tests

Tensile, tear, and adhesion strength tests were performed using a GALDABINI Sun 2500 instrument with a 1 kN load cell at room temperature and atmospheric pressure. The sample length and width for the tensile strength test were 50 and 5 mm, respectively. The nip-to-nip distance and applied strain rate were 10 mm and 300 mm min⁻¹, respectively. In addition, a trouser tear sample was cut and gripped on the tensile machine with a 180° angle between its arms. The sample dimensions were 7.5 × 2.5 cm² with a pre-crack length of 5 cm along the middle of its width. To prevent excessive deformation of the arms and crack path deviation in the trouser tear test (essential according to ASTM D624), they were reinforced by attaching a commercial acrylic PSA, Sellotape Diamond ultra-clear tape. Symmetrical reinforcement of the arms reduced their deformation to one-tenth. Films with the same thickness as for tensile strength test were used for the trouser tear test. The nip-to-nip distance and applied strain rate were 20 mm and 300 mm min⁻¹, respectively. The tear strength was calculated from G_Tear = 2F_ave/w, where F_ave is the average tearing force and w stands for the sample thickness. Finally, the adhesion strength was measured on T-shape samples (Fig. S1†) with length and width of 150 and 25 mm, respectively. The adhesive layer thickness for the peel experiments was the same as for tensile strength test sample. The nip-to-nip distance and applied strain rate were 20 mm and 50 mm min⁻¹, respectively. The maximum standard deviations of tensile, tear, and adhesion properties, based on averaging at least two samples, were found to be 15%, 10%, and 10%, respectively.

Sample coding

MBC30 latex was dried slowly, “SD”. The nanocomposites (NCs), however, were dried from latex blends via fast, “FD”, or slow, “SD”, processes. The annealed films were also designated with “Axy”, standing for annealing followed by its time (′ for minute) and temperature (°C), respectively. Consequently, NC-SD-A90′100 °C means a slow-dried latex nanocomposite annealed at 100 °C for 90 minutes.

Results

Fig. 1 shows the AFM images of MBC30-SD, NC-FD, and NC-SD in height and phase modes. Higher modulus aggregates (brighter) were dispersed at nano-scale among the lower modulus counterparts (darker) in MBC30-SD (Fig. 1b), while a height fluctuation was noticed at micro-scale (Fig. 1a). MBC30 latex gently blended with 5 wt% three-month room-temperature aged SAN70 latex followed by fast drying, NC-FD, presented an almost similar height fluctuation image as MBC30-SD (Fig. 1c). Its phase image, however, revealed dispersion of soft nanoparticles (SNPs) along with a few micron-size agglomerates (Fig. 1d). The slow-dried nanocomposite out of the latex blend of MBC30 and 5 wt% fresh SAN70, NC-SD, showed much shallower height fluctuations than NC-FD, with a few surface holes (Fig. 1e). The phase image of NC-SD, however, implied stiffness-disparate micron-size agglomerates, presenting low-modulus (darker) and high-modulus (brighter) regions (Fig. 1f).

Fig. 1 Representative height (left) and phase (right) images of MBC30-SD (a and b), NC-FD (c and d), and NC-SD (e and f). The inset of (d) shows a 2-dimensional phase image of NC-FD, cropped to 3 μm × 3 μm.

The cross-sectional SEM image of cryo-fractured NC-FD showed a few agglomerates, 5 μm in diameter, along with engulfing shallow footprints (Fig. 2a). Replacing the aged SAN70 latex containing aggregates with the fresh one in the film-forming latex blend, NC-SD, enhanced the average diameter of agglomerates to almost 20 μm, with an encapsulating ring-shaped nonlinearly deformed matrix, 10 μm in thickness, (Fig. 2b). 45 minutes of annealing of NC-SD at 100 °C further enhanced the agglomerate size, with complementing stress-induced matrix corrugation, tens of microns in wavelength (Fig. 2c). Extension of the annealing time to 90 minutes, however, resulted in smaller agglomerates, along with massive, shallower matrix corrugation with shorter wavelengths (Fig. 2d).

Fig. 2 Cross-sectional SEM images of the nanocomposites with magnification of 3100: (a) NC-FD, (b) NC-SD, (c) NC-SD-A45′100 °C, and (d) NC-SD-A90′100 °C. The inset of (d) shows the sample image with magnification of 1200.

The stress–strain curve of MBC30-SD at 300 mm min⁻¹ showed two consecutive jumps, followed by a maximum, a decay, and final fracture (Fig. 3). Deformation of NC-FD, however, not only occurred with enhanced initial modulus but also presented amplified WoF (area under the stress–strain curve). While NC-SD showed the same modulus as NC-FD, it exhibited a much higher WoF (Fig. 3). 90 minutes of annealing of NC-SD at 70 °C reduced its WoF, but the annealing time decrease to 45 minutes resulted in a slight improvement. 45 minutes of annealing at 100 °C, however, deteriorated both the WoF and elongation at break to even lower than those of MBC30-SD. Finally, 90 minutes of annealing at 100 °C minimized the system’s WoF and elongation at break.

Fig. 3 Stress–strain curves of MBC30-SD and the nanocomposites at 300 mm min⁻¹.

The tear strength of MBC30-SD at 300 mm min⁻¹ was 10.2 kN m⁻¹ (Fig. 4a). It increased to 11.3 kN m⁻¹ in NC-FD, while it decreased to 5.4 kN m⁻¹ in NC-SD. 45 and 90 minutes of annealing of NC-SD at 70 °C enhanced its tear strength as much as 20% and 100%, respectively. Finally, 45 or 90 minutes of annealing at 100 °C raised the tear strengths of NC-SD to 9.0 and 7.7 kN m⁻¹, respectively.

Fig. 4 (a) Tear strengths of MBC30-SD and the nanocomposites at 300 mm min⁻¹ versus annealing time and temperature. (b) Adhesion strengths of the PSAs to PET at 50 mm min⁻¹ versus annealing time and temperature. Maximum standard deviations of tear and adhesion strengths, based on averaging at least two samples, were found to be 10%.

The adhesion strength of MBC30-SD as a PSA to PET was 2.6 N cm⁻¹, presenting adhesive failure (Fig. 4b). The NC-FD-made PSA, however, debonded at 3.2 N cm⁻¹. On the other hand, the NC-SD-made PSA showed an adhesion strength of 4 N cm⁻¹. Annealing the NC-SD-made PSA at 70 °C for 45 minutes approximately doubled its adhesion strength (Fig. 4b), while changing its failure mode to a mixed cohesive/adhesive type. An annealing time increase to 90 minutes magnified the peel strength as much as 50% with the same failure mode. Annealing the NC-SD-made PSA at 100 °C for 45 or 90 minutes, however, led to adhesion strengths of 10.4 and 8.5 N cm⁻¹, respectively.

Finally, intensified annealing at 150 °C for 45 or 90 minutes increased the adhesion strengths of the NC-SD-made PSA to 14.6 and 20.8 N cm⁻¹, respectively, experiencing mixed cohesive/adhesive failure. Interestingly, the MBC30-SD-made PSA annealed at 150 °C for 45 or 90 minutes presented maximized adhesion strengths of 18.2 and 25.8 N cm⁻¹, respectively, both with mixed cohesive/adhesive failure type.

Three-layer asymmetric laminates made of PSAs adhered to aluminium foil as substrate, 20 μm in thickness, resulted in lower adhesion strengths but with similar trends (Fig. S2†).

Discussion

The synthesized matrix, MBC30, was thoroughly characterized by gel permeation chromatography (GPC), differential scanning calorimetry (DSC), AFM, and rheometric mechanical spectroscopy (RMS) and the results were presented and discussed in our previous publication.¹⁰ The GPC curve exhibited three overlapping peaks with weight-average molecular weight, M_w, and dispersity of 92 kg mol⁻¹ and 2.7, respectively. Several transitions were also observed in the heat flow first-derivative curve of the DSC thermogram at −26 (with a shoulder at −9), 54, and 97 °C, with an obvious peak far from the components’ glass transition temperatures, T_g, at 155 °C, assigned to the system’s phase transition.¹⁰

Based on the obtained results, the matrix presented roughly two kinds of random copolymers, one rich in BA and the other one rich in MMA.¹⁰ In other words, each deconvoluted peak in the GPC curve and first derivative of the DSC thermogram was indicative of individual random copolymers with a specific composition (average comonomer fraction in their chains).¹⁰ The heat flow first-derivative curve of the DSC thermogram was deconvoluted into four Gaussian functions using MATLAB software (R2010b).¹⁰ The area under the deconvoluted curves was used to calculate the fraction of each copolymer portion¹⁰ (Table 2).

Table 2 The characteristics of in situ formed copolymer blend based on DSC and GPC results

MBC30 deconvoluted portion	BA composition (wt%)	Tg (°C)	Fraction (%)	Mw (kg mol^−1)
BA-rich copolymer	71	−21	87	103
MMA-rich copolymer	16	73	13	42

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Their equivalent compositions were then calculated using the Fox equation and the T_g values of pure PBA and PMMA,¹⁰ −51 and 112 °C, respectively³¹ (Table 2). Finally, for simplicity, the fraction and composition of the two copolymer portions containing a larger amount of BA and the two copolymer portions containing a smaller amount were averaged. Hence, the matrix was considered as a binary copolymer blend system composed of BA-rich and MMA-rich copolymers. The GPC curve was also deconvoluted into two main Gaussian functions and the M_w values of the resulting curves were computed using the same software (Table 2). The area under the GPC deconvoluted curves, used for calculating the fraction of each copolymer portion, was in good agreement with the DSC results.¹⁰

The dramatic peak in the heat flow first-derivative curve of the DSC thermogram, far from the components’ T_g values, was attributed to the phase transition temperature of the BA-rich/MMA-rich copolymers.¹⁰ A similar conclusion regarding such a peak far from the blend components’ T_g values was reported previously.³² The above-mentioned results, along with the nano-dispersion of high-modulus brighter fractions in the soft darker components in the AFM phase image of MBC30-SD at room temperature, implied an upper critical solution temperature (UCST) phase behaviour of the matrix.¹⁰ In other words, the BA-rich/MMA-rich copolymers were immiscible at lower temperatures, while being compatible at higher temperatures. To further confirm this conclusion, time-sweep responses of MBC30-SD to shear loads at 150 °C, corresponding to melting, close to the peak far from the components T_g values, were analyzed using RMS as a powerful tool to study the phase behaviour of polymeric systems.¹⁰ The enhancement of storage modulus, G′, toward a steady state indicated activated mixing by a temperature rise toward 150 °C (ref. 10) via reduced a = 2(χN)_c − (χN), resulting in higher G′ through G′(ω) ∼ ω²a^−5/2, introduced by Fredrickson and Larson.³³ χ, N, the subscript c, and ω are Flory–Huggins interaction parameter, the number of Kuhn segments per chain, criticality, and frequency, respectively.

The surface height fluctuations of MBC30-SD, NC-FD, and NC-SD were attributed to drying-induced Marangoni’s instability⁸ (Fig. 1a, c and e). The phenomenon was less intense in NC-SD (38 nm, based on colour gauge) (Fig. 1e) than in NC-FD (103 nm) (Fig. 1c) due to the lower modulus differentiations among its micron-size agglomerates. Slow drying of the latex blend containing singlet nanoparticles of fresh SAN70 and MBC30 latexes facilitated agglomeration with low-amplitude composition fluctuations. However, fast drying of the latex blend containing fresh MBC30 and aged micron-sized segregated SAN70 latex ended with enhanced stiffness disparity with high-amplitude composition fluctuations. The observed disparity might be assigned to rod-like SAN70 agglomerates and singlet MMA-rich aggregates, leaving the BA-rich copolymer as the matrix. MBC30-SD, with more or less uniform dispersion of tiny aggregates of the MMA-rich copolymers among their BA-rich counterparts,¹⁰ experienced a medium stiffness disparity, resulting in a corresponding height fluctuation level (52 nm) (Fig. 1a).

Cryo-fractured NC-FD showed few footprints encapsulating stiff agglomerates (Fig. 2a). In NC-SD, however, micron-size agglomerates of MMA-rich copolymer-stabilized SAN70 SNPs induced yielding of the nearby matrix (Fig. 2b). 45 minutes of annealing of NC-SD at 100 °C facilitated the system phase evolution to enlarged agglomerates due to enhanced micro-phase separation of the MMA-rich and BA-rich copolymers.¹⁰ Annealing at 100 °C reduced the ΔT_s = |T − T_Spinodal| of the MMA-rich/BA-rich copolymers blend (with T_Spinodal of UCST behaviour at about 150 °C (ref. 10)). In the meantime, it decreased the ΔT_s of the MMA-rich/SAN70 copolymers (with T_Spinodal of lower critical solution temperature (LCST) behaviour at about 150 °C (ref. 10)). Larger agglomerates induced surface corrugations with long wavelengths and deep troughs (Fig. 2c). Extending the annealing time to 90 minutes, however, reduced the size of the stable agglomerates through enhanced interfacial mixing among the MMA-rich/SAN70 copolymers due to enhanced mutual diffusion through augmented softening of the components,³⁴ while it amplified demixing among the matrix components, the MMA-rich and BA-rich copolymers, implying reduced fracture resistance (Fig. 2d). A corresponding hierarchy regarding the cryogenically fractured sample size reduction through being dipped into the liquid nitrogen was illuminating. Rough estimation of the cryo-fracture energy enhancement, namely an increase in the size of samples pieces, was allocated to NC-FD, NC-SD-A45′100 °C, NC-SD, and NC-SD-A90′100 °C,. The short elapsed time in liquid nitrogen may partition each sample into deep-quenched surface regions and shallow-quenched bulk-located regions, inducing interfacial fracturing in analogy with solvent stress cracking.

The stress–strain curves of the studied polymer films were examined under uniaxial extension as a base for their bulk toughness evaluation. The stress–strain curves of MBC30-SD and the studied nanocomposites (Fig. 3) resembled those of other rubbery acrylics,³⁵ with recorded stresses in the same range as soft materials like gels and PSAs.³⁶ The WoF of NC-SD and its mildly annealed version, with out-of-the-range deformation (arbitrarily chosen at 7000%), was higher than those of NC-FD and MBC30-SD. The augmented WoF was assigned to double-network gel-type behaviour of the BA-rich copolymers encapsulating the MMA-rich copolymer-stabilized SAN70 agglomerates.^37,38

A slight decrease in WoF through mild annealing of NC-SD was attributed to simultaneous interfacial weakening and healing of the BA-rich/MMA-rich copolymers and the MMA-rich copolymers/SAN70 SNPs, respectively (Fig. 5a). Intensified annealing, 90 minutes at 70 °C or 45 and 90 minutes at 100 °C, however, caused WoF deterioration through enhanced molecular mixing among the MMA-rich and SAN70 copolymers, leaving the BA-rich/MMA-rich copolymers segregated and inducing cavitations³⁹ (Fig. 5b). The cavities merged under stress-induced fracture when dipping the sample into the liquid nitrogen and appeared as macro-cavities (Fig. S3†). The most intense annealing, 45 or 90 minutes at 150 °C, however, led to bi-molecular dispersion of the MMA-rich/SAN70 copolymers among the BA-rich copolymers (Fig. 5c), resulting in maximum adhesion (Fig. 4b).

Fig. 5 Schematic nanostructural evolution of the studied nanocomposites as a function of annealing intensity: (a) mild annealing, (b) intensified annealing, and (c) the most intense annealing.

In other words, annealing intensification through temperature increase and/or enhanced time may simultaneously amplify the interpenetration depth among the MMA-rich and SAN70 copolymers and reduce the interfacial depths among the BA-rich and MMA-rich copolymers (Fig. 6a). The interpenetration depth of both interfaces was estimated using eqn (1):⁴⁰

l = 2(D_mt)^1/2 (1)

D_m and t are mutual diffusion coefficient and time, respectively. D_m was estimated by scaling our previously published data³ to lower molecular weights regarding the MMA-rich/SAN70 copolymers. On the other hand, D_m for the BA-rich/MMA-rich copolymers was calculated using eqn (2):⁴¹

D_m = 2D₀f(1 − f)(χ_s − χ) (2)

where f and χ_s are the volume fraction and interaction parameter at the spinodal equal to 0.87 and 0.0053, respectively,¹⁰ while D₀, the kinetic term, was assumed to be 10⁻¹² cm² s⁻¹.⁴¹ The calculated values of χ using Mayes’ compressible regular solution model⁴² and D_m for the studied systems were collected in Table 3.

Fig. 6 (a) WoF versus interpenetration depth of NC-SD-A45′70 °C (1), NC-SD-A90′70 °C (2), NC-SD-A45′100 °C (3), and NC-SD-A90′100 °C (4). (b) Interpenetration depth of the BA-rich/MMA-rich copolymers versus annealing time at different annealing temperatures. The inset depicts interfacial healing of the MMA-rich copolymers/SAN70 interface at different temperatures. Lines are guides for the eye.

Table 3 The calculated parameters applied for computing the interpenetration depths

Annealing temperature (°C)	Annealing time (min)	Dm,MMA-rich/SAN70 (nm^2 s^−1)	χBA-rich/MMA-rich
25	0	6.77 × 10^−8	0.116
	45
	90
70	0	5.47 × 10^−4	0.054
	45
	90
100	0	6.60 × 10^−2	0.044
	45
	90
150	0	42.9	0.037
	45
	90

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The predicted data confirmed the simultaneous increase and decrease of interpenetration depths regarding the nearby binary interfaces among the three components (Fig. 6b). In other words, the three-component nanocomposites require binary threshold strengths at neighbouring interfaces to achieve maximum WoF (Fig. 5a). Otherwise, any weak interface can deteriorate the performance of the whole system (Fig. 5b).

Basically, a major part of the adhesion and tear strengths of viscoelastic materials is allocated to their WoF, representing deformability through molecular disjoining in the former and frictional movements in the latter (Fig. 7). NC-FD, followed by NC-SD, showed a mild adhesion strength enhancement with respect to MBC30-SD. Annealing of the NC-SD-made PSA, however, initially magnified and then deteriorated its adhesion strength, depending on its severity: mild and harsh, respectively. The same trend was observed in the tear strength evolution, except the amplified data points of MBC30-SD and NC-FD. Their unexpected large quantities could be assigned to the fracture mode difference between the T-peel and trouser tear tests, I vs. III, respectively.

Fig. 7 Adhesion (filled circles) and tear (empty circles) strengths versus WoF: (1) MBC30-SD, (2) NC-FD, (3) NC-SD, (4) NC-SD-A45′70 °C, (5) NC-SD-A90′70 °C, (6) NC-SD-A45′100 °C, and (7) NC-SD-A90′100 °C. Lines are guides for the eye.

The addition of SAN70 SNPs into MBC30 with higher interfacial area, NC-FD, enhanced its tear and adhesion strengths. The reduced interfacial area among MBC30 and SAN70 SNPs due to agglomeration substantially reduced the tear strength, while improving the adhesion strength. Short- and long-time annealing of NC-SD at 70 °C improved both adhesion and tear strengths proportionally. Harsh annealing, however, led to proportional deterioration of adhesion and tear strengths. It seems that the lateral shear component of bulk deformation is more sensitive to the interfacial area among the matrix/dispersed phases in comparison to the T-peel deformation of constrained samples.

Mild annealing motivated dispersion of the MMA-rich copolymer-stabilized SAN70 SNPs among the BA-rich/MMA-rich copolymers blend with maximum WoF, but medium adhesion and tear strengths. An extended annealing time at mild temperature reduced the WoF but maximized the adhesion and tear strengths.

The fracture energy, G_C, of elastomers and other soft polymers is usually described by the following empirical equation, originally proposed for adhesion evaluation.^43,44

G_C = G₀(1 + ϕ(T,ν)) (3)

G₀ is material’s intrinsic fracture energy quantified at high temperatures or low strain rates, while ϕ(T,ν) is a viscoelastic dissipation term. Temperature and crack velocity-dependent ϕ has been estimated by various tan δ-related terms, such as k tan δ (ref. 5) or its empirically found complex functions from frequency-dependent linear viscoelastic tests.⁴ The stress–strain curves of the studied nanocomposites (Fig. 3) showed quite remarkable differences from rubber elasticity-based predictions. Here, yield-like behaviour at a few percent of deformation has nothing to do with yielding of the entanglement networks.⁴⁵ In other words, the nature of the emerging transient elasticity is intermolecular and thus fundamentally different from the rubber elasticity, being intrachain in nature. At high rates, the entanglement network initially undergoes affine deformation, contributing to the stress as if the melt is a crosslinked rubber. Thus, the “long-time” overall stress, σ, (Fig. 3) could be treated as being comprised of two components after the yielding of the transient intersegmental association: σ = σ_Network + σ_V. The Edward–Vilgis model⁴⁵ could be applied to represent the σ_Network and quantify the viscous component, σ_V, after separating the intersegmental elastic part from the presented data (Fig. 3). Accordingly, the area under the stress–strain curve was partitioned into three parts: intersegmental transient elasticity, rubber elasticity due to the entanglement network, and the intermolecular viscous friction. Then, the energy density ratio regarding viscoelasticity over transient elasticity was introduced as ϕ (Fig. S4† and Table 4).

Table 4 Calculated annealing intensification criterion, (t/ΔT_s)^1/3, viscoelastic dissipation, ϕ(T,ν), and active layer thickness, d, using the adhesion and tear strength results

Sample code	(t/ΔTs)^1/3 (min/°C)^1/3	ϕ(T,ν)	dAdhesion (m)	dTear (m)
MBC30-SD	0	1178	3.6 × 10^−11	5.5 × 10^−8
NC-FD	0	312	7.7 × 10^−10	9.5 × 10^−7
NC-SD	0	959	1.3 × 10^−10	2.4 × 10^−8
NC-SD-A45′70 °C	0.83	958	4.9 × 10^−10	3.6 × 10^−8
NC-SD-A90′70 °C	1.04	690	2.3 × 10^−9	1.7 × 10^−7
NC-SD-A45′100 °C	0.97	162	2.3 × 10^−8	2.2 × 10^−6
NC-SD-A90′100 °C	1.2	60	9.1 × 10^−8	1.2 × 10^−5

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Assuming the ϕ term is dependent only on the system morphology, G₀ was calculated as the prime cause of energy differentiations between adhesion and tear tests. G₀ could be calculated using the distance between crosslinks or entanglements in the unstrained state, d, using the well-known Lake and Thomas’ model:⁴⁶

where ρ, M₀, ξ, and U_C–C are the polymer density, the monomer molar mass, the monomer length (≈5 Å), and the molar energy of a C–C bond (≈350 kJ mol⁻¹), respectively.⁵ Accordingly, the only unknown parameter, d, could be estimated based on the adhesion and tear strength data points of various systems, complementing their ϕ values using combined eqn (3) and (4) (Table 4).

The calculated d values regarding the tear test were at least two orders of magnitude larger than the adhesion test counterparts, which will be discussed in detail later. In addition, the d values according to the tear test results were much larger than the unstrained distance between consecutive entanglements. Full orientation of strands crossing the crack plane was proposed to rationalize the observed disparity between the calculated and measured fracture energies of glassy polymers.⁴⁷ It may be extended regarding soft polymers through multiple connected strands in series or parallel implying fibrillation based on the viscoelastic trumpet concept.⁴⁸ Accordingly, the extracted d values could be nominated as the active layer thickness across the crack plane, namely the oriented multiple connected strands crossing the crack plane.

The domain size of a phase-separating system is proportional to time, t, and inverse quench depth, ΔT_s, both to the power 1/3 in the late regime.⁴⁹ In other words, phase separation time increases at higher annealing temperature or reduced ΔT_s leads to enhanced domain size with diminished compositional disparity among the phases. Accordingly, the active layer thickness across the crack plane was expected to increase with the estimated annealing intensification criterion (AIC), (t/ΔT_s)^1/3, for both adhesion and tear strengths (Fig. 8). The low R-squared values for the exponential correlations (base 10) were presumably due to assumed late-stage phase separation processes.

Fig. 8 Semi-logarithmic plot of the active layer thickness versus AIC using adhesion and tear strength data.

The tear test quantifies the crack growth resistance with full viscoelastic deformations, while adhesion diminishes it due to applied constraints leading to much lower viscoelastic deformation.^2,48 A less effective contribution might be assigned to the lower applied strain rate in the adhesion test. Furthermore, the calculated d based on the adhesion test might represent the intrinsic interfacial fracture energy, frequently taken equal to thermodynamic work of adhesion, which is smaller than the intrinsic cohesive fracture energy, required for stretching multiple strands and rupturing a covalent bond. The maximum WoF among the annealed nanocomposites corresponded to an active layer thickness of 33.5 nm, extracted from the tear results, roughly equal to 70% of MBC30 strand contour length between consecutive entanglements.

Conclusions

The work of failure per unit volume of an acrylic copolymer, MBC30-SD, was enhanced by addition of SAN70 SNPs followed by drying-induced agglomerations. Its WoF decreased slightly with mild annealing, while harsh annealing induced severe WoF decline. Simultaneously, the adhesion and tear strengths experienced proportional improvements followed by deterioration. The estimated active layer thickness across the crack plane based on the tear strength data was about two orders of magnitude higher than the corresponding adhesion results. Its minimum amount among the annealed nanocomposites implied an extension of 70% of MBC30 entanglement-to-entanglement strand contour length, 33.5 nm, in tearing, which declined to deformation of three consecutive C–C bonds in the adhesion test before chain rupture, achieving maximum WoF and viscoelastic loss.

Notes and references

1. S. Bhuyan, F. Tanguy, D. Martina, A. Lindner, M. Ciccotti and C. Creton, Soft Matter, 2013, 9, 6515–6524.
2. F. Saulnier, T. Ondarcuhu, A. Aradian and E. Raphael, Macromolecules, 2004, 37, 1067–1075.
3. H. Mohammadi and N. Mohammadi, Polymer, 2012, 53, 2769–2776.
4. A. Sharif, N. Mohammadi, M. Nekoomanesh and Y. Jahani, J. Adhes. Sci. Technol., 2002, 16, 33–45.
5. A. Cristiano, A. Marcellan, B. J. Keestra, P. Steeman and C. Creton, J. Polym. Sci., Part B: Polym. Phys., 2011, 49, 355–367.
6. M. B. Taub, PhD Thesis, Stanford University, Stanford, 2003.
7. S. Tobing, A. Klein, L. H. Sperling and B. Petrasko, J. Appl. Polym. Sci., 2001, 81, 2109–2117.
8. X. Sun, H. Li, S. Yan and I. Lieberwirth, J. Appl. Polym. Sci., 2013, 129, 1784–1792.
9. R. N. Li, A. Clough, Z. Yang and O. K. C. Tsui, Macromolecules, 2012, 45, 1085–1089.
10. S. Ghasemirad and N. Mohammadi, Colloid Polym. Sci., 2015, 293, 677–686.
11. A. Lindner, B. Lestriez, S. Mariot, C. Creton, T. Maevis and B. Luehmann, J. Adhes., 2006, 82, 267–310.
12. Z. Czech, J. Appl. Polym. Sci., 2005, 97, 886–892.
13. H. Tanaka and T. Araki, Chem. Eng. Sci., 2006, 61, 2108–2141.
14. M. Yousfi, L. Porcar, P. Lindner, F. Boue and Y. Rharbi, Macromolecules, 2009, 42, 2190–2197.
15. D. Bhowmik, J. A. Pomposo, F. Juranyi, V. Garcia-Sakai, M. Zamponi, Y. Su, A. Arbe and J. Colmenero, Macromolecules, 2014, 47, 304–315.
16. A. Aradian, E. Raphael and P. G. de Gennes, Macromolecules, 2000, 33, 9444–9451.
17. H. Mohammadi, N. Mohammadi and M. Kheirabadi, J. Appl. Polym. Sci., 2013, 128, 3432–3437.
18. M. Ghafoori, N. Mohammadi and S. R. Ghaffarian, J. Adhes. Sci. Technol., 2007, 21, 1059–1069.
19. A. Aradian, F. Saulnier, E. Raphael and P. G. de Gennes, Macromolecules, 2004, 37, 4664–4675.
20. M. M. Feldstein, K. A. Bovaldinova, E. V. Bermesheva, A. P. Moscalets, E. E. Dormidontova, V. Y. Grinberg and A. R. Khokhlov, Macromolecules, 2014, 47, 5759–5767.
21. G. P. Baeza, A. C. Genix, C. Degrandcourt, L. Petitjean, J. Gummel, R. Schweins, M. Couty and J. Oberdisse, Macromolecules, 2013, 46, 6621–6633.
22. J. Jancar, J. F. Douglas, F. W. Starr, S. K. Kumar, P. Cassagnau, A. J. Lesser, S. S. Sternstein and M. J. Buehler, Polymer, 2010, 51, 3321–3343.
23. D. Maillard, S. K. Kumar, B. Fragneaud, J. W. Kysar, A. Rungta, B. C. Benicewicz, H. Deng, C. Brinson and J. F. Douglas, Nano Lett., 2012, 12, 3909–3914.
24. Y. N. Pandey, G. J. Papakonstantopolpous and M. Doxastakis, Macromolecules, 2013, 46, 5097–5106.
25. V. V. Moshev and S. E. Evlampieva, Int. J. Solids Struct., 2005, 42, 5129–5139.
26. S. U. Fu, X. Q. Feng, B. Lauke and Y. W. Mai, Composites, Part B, 2008, 39, 933–961.
27. F. Deplace, C. Carelli, S. Mariot, H. Retsos, A. Chateauminois, K. Ouzineb and C. Creton, J. Adhes., 2009, 85, 18–54.
28. E. Canetta, J. Marchal, C. H. Lei, F. Deplace, A. M. Koenig, C. Creton, K. Ouzineb and J. L. Keddie, Langmuir, 2009, 25, 11021–11031.
29. J. T. Seitz, J. Appl. Polym. Sci., 1993, 49, 1331–1351.
30. J. D. Tong and R. Jerôme, Macromolecules, 2000, 33, 1479–1481.
31. F. Faghihi, N. Mohammadi and P. Hazendonk, Macromolecules, 2011, 44, 2154–2160.
32. A. Gharachorlou and F. Goharpey, Macromolecules, 2008, 41, 3276–3283.
33. G. H. Fredrickson and R. G. Larson, J. Chem. Phys., 1987, 86, 1553–1560.
34. W. Du, G. Yuan, M. Wang, C. C. Han, S. K. Satija and B. Akgun, Macromolecules, 2014, 47, 713–720.
35. I. Benedek and M. M. Feldstein, Fundamentals of pressure sensitivity, CRC Press–Taylor and Francis, Boca Raton, 2009, ch. 10, pp. 10–32.
36. M. M. Feldstein, E. E. Dormidontova and A. R. Khokhlov, Prog. Polym. Sci., 2015, 42, 79–153.
37. S. Shams Es-haghi, A. I. Leonov and R. A. Weiss, Macromolecules, 2014, 47, 4769–4777.
38. H. R. Brown, Macromolecules, 2007, 40, 3815–3818.
39. S. Joly, D. Ausserre, G. Brotons and Y. Gallot, Eur. Phys. J. E, 2002, 8, 355–363.
40. F. Brochard, J. Jouffroy and P. Leveinson, J. Phys., Lett., 1983, 44, 455–460.
41. E. L. Jablonski, R. E. Gorga and B. Narasimhan, Polymer, 2003, 44, 729–741.
42. A. V. G. Ruzette and A. M. Mayes, Macromolecules, 2001, 34, 1894–1907.
43. A. N. Gent and J. Schultz, J. Adhes., 1972, 3, 281–294.
44. D. Maugis and M. Barquins, J. Phys. D: Appl. Phys., 1978, 11, 1989–2023.
45. H. Sun, G. Liu, K. Ntetsikas, A. Avgeropoulos and S. Q. Wang, Macromolecules, 2014, 47, 5839–5850.
46. G. J. Lake and A. G. Thomas, Proc. R. Soc. London, Ser. A, 1967, 300, 108–119.
47. N. Mohammadi, A. Klein and L. H. Sperling, Macromolecules, 1993, 26, 1019–1026.
48. P. G. de Gennes, Langmuir, 1996, 12, 4497–4500.
49. M. K. Mitra and M. Muthukumar, J. Chem. Phys., 2010, 132, 184908.

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Footnote

† Electronic supplementary information (ESI) available: Fig. S1–S4. See DOI: 10.1039/c5ra21937j

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