The adhesion between two immiscible polymers stitched together via mobile promoters is studied with large scale molecular simulations employing a coarse-grained bead-spring model. An adhesion model is presented that enables both connector molecular slipping out viscously and bulk dissipation in two dissimilar glassy polymers, in which one is dense melt and another is loose. The contributions to the separation work from thermodynamics and chain suction are studied in dependence of the connector areal density, at constant temperature, and at fixed basic molecular parameters. It is shown that high connector coverage, but below saturation areal density, can enhance the adhesion toughness and interfacial strength. Bulk dissipation is not considerable with low connector areal density in mushroom regime, while becomes more evident in the loose block when the coverage density is increased up to overlapping brush regime. With increasing connector length, both bulk melts are enhanced by the segments of connector chains that penetrated in. The results provide insight into the structure evolution of adhesion interface coupled with promoter molecular, which are useful for future developments of continuum cohesive models for fracture of polymer- polymer interfaces.

Immiscible polymers are usually jointed together by adhesive promoters dissolved into either bulk, and miscible polymers can be adhered by self-adhesion through weak van der Waals interactions. Above glass transition temperature Tg, promoter molecules can adhere or penetrate into either polymer as bridges, while molecules from miscible polymers interact with each other directly, and chains will be entangled or cross-linked with each other, thus the macroscopic interface becomes interdiffused. Adhesion toughness is then largely determined by the rearrangement or restructuring of surface molecules to enhance the contacting bonds (e.g., interdigitating chain segments) across the interface. Under mechanical loading, the surface chains could be sucked out and/or undergo scission, which is known as adhesive fracture. Adhesion between any pair of polymers can be well enhanced if the interface can sustain sufficient stress to induce dissipation, such as flow, yield or crazing, in the bulks. To evaluate adhesion strength of weak interface, chemical bonding, chain entanglement, areal density of connectors, mismatch of bi-materials, mechanical roughness, and loading rates etc. should be considered to bridge the gap between polymer science and fracture mechanics. However, the microscopic mechanism of fracture or debonding of polymer adhesion is still open due to the complexity of the real situation of molecular level coupling at the interface with/without connectors and the energy dissipation process in the bulks adjacent to the interface, despite of existed excellent two-dimensional models.1–5 

For studying polymer systems, one of the main unresolved problems is the time-scale and length-scale gaps between computational and experimental methods. Coarse-grained molecular dynamics simulations (CG-MD) representing a system by a reduced number of degrees of freedom and elimination of fine interaction details become a powerful tool,6–8 and goes faster than that for the same system in all-atom representation. As a result, an increase of orders of magnitude in the simulation time and length scales can be achieved.

Previous CG-MD simulations mainly focused on the adhesion between a glassy polymer and a rigid substrate chemically attached with end-grafted chains. However, real adhesion junctions often contain two polymer blocks and promoters that are free at both ends and can wander into the polymer matrix, which is extremely sensitive to the polydispersity of mobile connectors,1 Figure 1 describes the situation. The pullout/scission of connector chains from bulk melts and dissipation taking place on either melt cannot be ignored. It was also shown that the areal density and molecular weight of the copolymer chains played important roles on the fracture mechanism at PS/PVP interfaces reinforced with PS-PVP block copolymers in experiments.9,10

FIG. 1.

Adhesion models of two immiscible glassy polymers with connector promoters. (a) Mobile connector molecules (red) with a areal density of 0.008σ-2 (or 0.024σ-2) enter freely into (b) one dense melt (green) and another loose melt (blue) to form a (c) 2D (y view) / (d) 3D model in a MD cell (black) with initial dimensions of Lx0 ≈ 32σ, Lx0 ≈ 32σ and Lx0 ≈ 65σ before equilibration. Each chain of either polymer melt contains 500 beads with a density of ρ ≈ 0.85σ-3, each chain of connector has 100 (150 or 200) beads, all the length of chain are well chosen relative to the entanglement length (estimated in the range 40∼80). We then vary the interaction 12-6 LJ potential between beads among blue melts, i.e., by setting cutoff radius rc = 1.3 × 21/6σ, and green melts rc = 1.5 × 21/6σ, and connectors rc = 21/6σ to mimic different materials. For each connector-bead and melt-bead interaction, connector chains as adhesion promoters are compatible with blue melt rc = 1.3 × 21/6σ and green melt rc = 1.5 × 21/6σ, and make interdiffusion possible, therefore can strengthen the interface. The melts themselves repel each other described by a repulsive 12-6 LJ potential (i.e., rc = 0.85σ), thus weak van der Waals interactions between two interfacial surfaces are not involved. The top plane (virtual wall) is displaced upward along the z-axis, while the bottom is fixed and lateral deformation is restrained.

FIG. 1.

Adhesion models of two immiscible glassy polymers with connector promoters. (a) Mobile connector molecules (red) with a areal density of 0.008σ-2 (or 0.024σ-2) enter freely into (b) one dense melt (green) and another loose melt (blue) to form a (c) 2D (y view) / (d) 3D model in a MD cell (black) with initial dimensions of Lx0 ≈ 32σ, Lx0 ≈ 32σ and Lx0 ≈ 65σ before equilibration. Each chain of either polymer melt contains 500 beads with a density of ρ ≈ 0.85σ-3, each chain of connector has 100 (150 or 200) beads, all the length of chain are well chosen relative to the entanglement length (estimated in the range 40∼80). We then vary the interaction 12-6 LJ potential between beads among blue melts, i.e., by setting cutoff radius rc = 1.3 × 21/6σ, and green melts rc = 1.5 × 21/6σ, and connectors rc = 21/6σ to mimic different materials. For each connector-bead and melt-bead interaction, connector chains as adhesion promoters are compatible with blue melt rc = 1.3 × 21/6σ and green melt rc = 1.5 × 21/6σ, and make interdiffusion possible, therefore can strengthen the interface. The melts themselves repel each other described by a repulsive 12-6 LJ potential (i.e., rc = 0.85σ), thus weak van der Waals interactions between two interfacial surfaces are not involved. The top plane (virtual wall) is displaced upward along the z-axis, while the bottom is fixed and lateral deformation is restrained.

Close modal

The mechanism of interface failure has been found to depend on the molecular weight of the coupling chains. Short chains can be pulled out of bulk materials at a force that increases with the length of the pulled-out section. As the length of the chains increases to somewhere between one and four times the length required to form an entanglement in the melt, the force required for pullout becomes greater than the force to break chains, so they fail by scission. However scission failure is not expected for a tough interface, elastic and capillary forces during pull-out of connectors are desired to strengthen the adhesion.

We here conduct large amounts of CG-MD simulations on adhesion of two glassy polymers (One dense melt and another loose) jointed together by mobile connector chains, considering the deformations and dissipations of both bulks and connectors. The complicated viscous process involving chain pulling out, crazing and scission are strongly dependent on the separation strain rate dγzz/dt, the areal density of connector Σ, and the length of connector chain n. This parameter space is more abundant than one can investigate at the same time, however we only focus attention to the effects of Σ = 0.008σ-2 (mushroom regime) to 0.032σ-2 (overlapping brush regime), with n = 100, 150, 200 at a fixed temperature T = 0.1ɛ/kB, while another possibility of chemical scission for the connectors is not incorporated presently for our loose system at relative slow strain rate dγzz/dt = 0.5 × 10-5τ-1 (the LJ units will be noted below). In fact, for most loose systems, the force on the connectors is far below the chemical rupture forces.1 Thus, in the low-velocity regime, scission is indeed negligible for loose systems of unbranched connectors.

Our simulations follow the methodology described in previous literatures. A generic bead-spring model that describes the coarse-grained behavior of polymers is used. The polymer chains (either belonging to the bulks or a connector) are treated as sequences of beads interconnected by springs, using a representation based on the Kremer-Grest model,8 but extended to account for stiffness along the chain backbone and attractive interaction as well. The connectors penetrate sequentially into both bulks: each successive connector is immersed in a different polymer bulk while only one-stitch is made at the interface, and uniformly distributed at the interface between the two melts at a specific areal density Σ. Each chain of polymer melt contains N = 500 spherical beads with a bead density of ρ = 0.85σ-3 that interact with a truncated and shifted Lennard-Jones (LJ) potential

\begin{equation}U_{LJ} \left( r \right) = 4\varepsilon \left[ {\left( {\frac{\sigma }{r}} \right)^{12} - \left( {\frac{\sigma }{r}} \right)^6 - \left( {\frac{\sigma }{{r_{\rm c} }}} \right)^{12} + \left( {\frac{\sigma }{{r_{\rm c} }}} \right)^6 } \right], \quad r < r_{\rm c},\end{equation}
ULJr=4ɛσr12σr6σrc12+σrc6,r<rc,
(1)

where r is the distance between any two beads. The binding energy ɛ and molecular diameter σ are used to define our units in dimensionless values relative to the LJ units. The unit of time τ = (mσ2/ɛ)1/2, where m is the bead mass. LJ units can be conversed with SI units for a particular material in which the bead is a possible group of polymer units, e.g. σ ≈ 0.5 nm, τ ≈ 1.9ps for PMMA (m = 1.660 × 10-25 kg). Inside individual polymer bulk, the interaction between any two bulk beads is with the same σ and ɛ. Two beads from dissimilar bulks repel each other directly, the LJ interaction is repulsive. However, to realize the adhesion, the attractive part of the LJ potential is incorporated for connector-bead and bulk-bead interaction by setting rc > 21/6σ. Adjacent beads along the chain are coupled with the finitely extensible nonlinear elastic (FENE) potential

\begin{equation}U_{{\rm FENE}} \left( r \right) = - kR_0 ^2 \ln \left[ {1 - \left( {\frac{r}{{R_0 }}} \right)^2 } \right],\quad r < R_0.\end{equation}
U FENE r=kR02ln1rR02,r<R0.
(2)

The standard values k = 30u0/σ2 and R0 = 1.5σ are employed. The ULJ+UFENE combination is asymmetric with respect to the equilibrium bond length ∼0.96σ.8 This bond interaction ensures the chain connectivity and, coupled with the excluded volume interaction between unconnected beads, prevents the chains from crossing each other, thus yielding an entangled polymer ensemble. Consequently, extension of bonds is more favorable than their compression. Overall, the bonds are slightly stretched and a non-zero average tension exists in the bonds. Bonding forces in connectors are derived from reflected-FENE potentials, which control both the elongation as well as the compression of the polymer bonds symmetrically around the equilibrium bond length 1.0σ.

The entanglement density is varied by the stiffness along the polymer chain that is enhanced by using a bending potential and a torsion potential acting on three, respectively four, consecutive connected beads. The bending potential maintains the angle between adjacent pairs of bonds close to the equilibrium value 109.5°. The torsion potential constrains the dihedral angle to three possible equilibrium values 180°, 60° and 300°. We use a form of the torsion potential that depends also on bending angles, such that the force cancels when the dihedral angle becomes undefined as two consecutive bonds align. For all simulations presented here our semiflexible chains have bending and torsion stiffness: kθ = 25ɛ, kφ = 1ɛ (Rotational Isomeric State chains, RIS).11,12

In addition, each bead from the polymer bulks interacts with the virtual upper and lower rigid walls of MD simulation box via an integrated Lennard-Jones (LJ) potential

\begin{equation}U_{{{\rm LJ}} }^{{\rm wall}} \left( z \right) = \frac{{2\pi \varepsilon _{{\rm wall}} }}{3}\left[ {\frac{2}{{15}}\left( {\frac{\sigma }{z}} \right)^9 - \left( {\frac{\sigma }{z}} \right)^3 } \right], \quad z < z_{{\rm c} }^{{\rm wall}},\end{equation}
U LJ wall z=2πɛ wall 3215σz9σz3,z<zc wall ,
(3)

with |$z_{{\rm c} }^{{\rm wall}}$|zc wall = 2.2σ, the binding energy ɛwall = 2.0ɛ. Strongly attractive walls are employed to prevent adhesive failure between bulk melts and walls during stretching.13 

The MD-samples are prepared carefully prior to the debonding simulations. The polymer chains from the bulks are generated as random walks with constraints for the bond lengths, bending and torsion angles around their equilibrium values needed for the specific potentials. The connector chains are generated such that they have a predefined conformation at the interface with a certain number of stitches and a certain number of beads between the stitches. The two polymer bulks are placed on top of each other and the preformed connectors are uniformly distributed at the interface according the desired areal density of the connectors. The resulted intertwining between connector chains and bulk chains, which cannot cross each other, consequently establishes the adhesive junction. A packing procedure is used after generation to make the initial distributions of particles in the two melts as uniformly as possible.11 Two short MD stages are employed next in order to bring the whole system to equilibrium: a slow push-off stage uses capped LJ potentials to eliminate the bead overlaps, followed by a brief MD run when the full potentials are turned on and the system is taken to the desired temperature.14 Two polymers with connectors randomly penetrating across the interface are placed in one MD-box, see Figure 1.

Prior to tension, the system is weakly coupled with first-order kinetics to an external heat bath with given temperature and a first-order kinetic relaxation of the pressure, thus both the pressure and temperature approach our desired values.15 During the NPT ensemble, we raise the temperature to 1.0ɛ/kB giving an increased efficiency for several million time steps in order to equilibrate and fasten interdiffusion of the adhesion system, viz., thermal welding. After that, the temperature was cooled down to 0.1ɛ/kB and the overall pressure P ≈ 0. The temperature is kept constant by coupling the system to a Langevin thermostat with the friction coefficient 0.5τ-1 and the strength of the Gaussian white-noise force 3kB-1. The majority of the experiments are performed at 0.1ɛ/kB that is below the glass transition temperature of polymer bulks with RIS chains, estimated as TgRIS = 0.7ɛ/kB.12 The equations of motion are integrated using the velocity-Verlet algorithm16 with a time step Δt = 0.01τ.

We then impose vertical deformation to the MD cell by quasistatically moving the top virtual LJ-wall in the z-direction (increase Lz) while fixing the bottom wall, i.e. applying separation strain γzz = (LzLz0)/Lz0 simultaneously, and periodic boundary conditions are supplemented in the x and y directions (i.e. without lateral strain maintaining constant Lx and Ly), see Figure 1.

The virial stress is commonly used to find the macroscopic (continuum) stress in molecular dynamics computations. Although virial expression shows unphysical oscillations in the region of an atomic-level inhomogeneity, it can average through the overall volume, thus suitable for describing inhomogeneous polymer adhesions. The macroscopic stress tensor T in a macroscopically small, but microscopically large, volume Ω is typically taken to be

\begin{equation}T_{{\rm ij}} = \frac{1}{\Omega }\sum\limits_\alpha ^\Omega {\left( { - m^{( \alpha )} \big( {v_{\rm i} ^{( \alpha )} - \bar v_{\rm i} } \big)\big( {v_{\rm j} ^{( \alpha )} - \bar v_{\rm j} } \big) + \frac{1}{2}\sum\limits_\beta {\big( {x_{\rm i} ^{( \beta )} - x_{\rm i} ^{( \alpha )} } \big)} f_{\rm j} ^{( {\alpha \beta } )} } \right)}\end{equation}
T ij =1ΩαΩm(α)vi(α)v¯ivj(α)v¯j+12βxi(β)xi(α)fj(αβ)
(4)

where m(α) is the mass of the α-th molecule in Ω, vector x(α) its position, with Cartesian components (x1(α), x2(α), x3(α)) = (x(α), y(α), z(α)), v(α) its velocity, |$\bar v$|v¯ the local average velocity which approach zero in static loading, and f(αβ) is the force on molecule α exerted by another molecule β.

During the simulations we measure the total integrated work (per unit of cross-sectional area) exerted at t

\begin{equation}W\left( t \right) = \int_0^t {T_{{{\rm zz}} }^{\rm n} } \dot \gamma _{{\rm zz}} L_{{\rm z0}} d\tau,\end{equation}
Wt=0tT zz nγ̇ zz Lz0dτ,
(5)

where |$T_{{{\rm zz}} }^{\rm n}$|T zz n is the magnitude of the vertical traction stress measured in a Lagrangian section across the center of MD cell.17 The final limit of integrated work is known as measured adhesion energy G that is strongly influenced by the viscoelastic nature of the adhesive.

The above expressions of virial stress (Eq. (4)) and integrated work (Eq. (5)) are incorporated in our simulation codes.

We first examine evolutions in failure mode with connector chain length n = 100, 150 and 200 varying areal density from 0.008σ-2 to 0.032σ-2 in systems. After equilibration, the virtual walls are separated at strain rate dγzz/dt = 0.5 × 10-5τ-1. Figure 2 illustrates the stress needed to stretch the adhesive melts as a function of the vertical strain applied. Due to the limit of relaxing time and inhomogeneous interface in simulations, the lateral stresses cannot be fully relaxed in the geometry of model within a fixed spacing, thus the initial vertical component of viral stresses (volume average) Tzz are not exactly zero.

FIG. 2.

Variation with vertical strain of stress needed to deform the MD cell at strain rate dγzz/dt = 0.5 × 10-5τ-1, adhesion with connector chain length n = 100 (a), 150 (b) and 200 (c) respectively, and areal density of Σ = 0.008σ-2, 0.016σ-2, 0.024σ-2 and 0.032σ-2.

FIG. 2.

Variation with vertical strain of stress needed to deform the MD cell at strain rate dγzz/dt = 0.5 × 10-5τ-1, adhesion with connector chain length n = 100 (a), 150 (b) and 200 (c) respectively, and areal density of Σ = 0.008σ-2, 0.016σ-2, 0.024σ-2 and 0.032σ-2.

Close modal

In Figure 2, the adhered polymers respond elastically, viz., there is a linear increase in stress with strain initially. The stress continues to rise until it reaches a peak value and then drops sharply. This initial peaks and drops (Σ > 0.008σ-2) are dependent on Σ. The constant Hookean response for Σ = 0.008σ-2 shows that no considerable internal viscosity occurred during connector pull-out within mushroom regime, and the pulling force is predominantly elastic.

In Figure 2, as connector density is increased up to overlapping brush regime (Σ > 0.008σ-2), the adhesion becomes arrested presumably by entanglements. The adhesive interface is strengthened by the connector molecules that immerse into either bulk, thus the system is well jointed together as a whole polymer. Hyperelastic polymer will initially be linear, but at a certain point (initial peak), the stress-strain curve will reach a plateau due to the release of energy as heat while straining the material. After a short dip, the slope of stress-strain curve (modulus) increases again. This hyperelasticity is often observed in early stage. Cross-linked (entanglements between chains act like chemical crosslink, see Figure 5–7) polymers will act in this way because initially the polymer chains can move relative to each other when a stress is applied, and thus flow resulting in strain softening. However, at a certain point the polymer chains will be stretched to the maximum that the covalent cross links will allow, and this will cause a dramatic increase in the elastic modulus of the material, say strain hardening. The stress at large deformations can be decomposed into two separate contributions: a viscous component usually referred to as the flow stress, related to intermolecular interactions on segmental scale, and a neoHookean strain hardening component originating from an entropic-elastic response of the entangled molecular network. After plastic flow, a craze usually develops via the initiation of a cavity, the growth of instabilities and finally the coalescence of holes.18,19 This viscous process is evident for long connector n = 200, see Figure 2(c) and Figure 7, the final tails in the stress curves is lengthened and stress fluctuates about a plateau value, and more external work is needed until final detachment. These tails occur after yielding, when connector chains pull free of each other, and increase the dissipation during this process. While for Σ = 0.024σ-2 and 0.032σ-2 with n = 200, Σ = 0.032σ-2 with n = 200, the adhesion interfaces are strong enough that melts detach from walls resulting in a suddenly drop of stress-strain curve, see Figure 6(h) and Figure 7(g) and 7(h).

FIG. 5.

Snapshots of adhesion configurations for chain length of connector n = 100, and areal density of connector Σ = 0.008σ-2 (a), 0.016σ-2 (b), 0.024σ-2 (c) and 0.032σ-2 (d) respectively at peak stresses; (e), (f), (g) and (h) at failures during tensile deformation with vertical strain rate dγzz/dt = 0.5 × 10-5τ-1. Partial views of green melts above dash lines are placed on the top for comparison of bulk deformation, while no obvious dissipation can be observed there.

FIG. 5.

Snapshots of adhesion configurations for chain length of connector n = 100, and areal density of connector Σ = 0.008σ-2 (a), 0.016σ-2 (b), 0.024σ-2 (c) and 0.032σ-2 (d) respectively at peak stresses; (e), (f), (g) and (h) at failures during tensile deformation with vertical strain rate dγzz/dt = 0.5 × 10-5τ-1. Partial views of green melts above dash lines are placed on the top for comparison of bulk deformation, while no obvious dissipation can be observed there.

Close modal
FIG. 7.

Snapshots of adhesion configurations during tension for chain length of connector n = 200, other notations for the scheme are the same as Figure 5.

FIG. 7.

Snapshots of adhesion configurations during tension for chain length of connector n = 200, other notations for the scheme are the same as Figure 5.

Close modal

The total work per unit area (Eq. (5)), given by the total integral of stress vs. separation displacement, is shown in Figure 3(a). External work increases with time and reaches a plateau that gives the toughness G at failure, W(t) is measured for a sufficiently long time such that each connector chain has been completely pulled off from either melt or lapping chain bundles (Figure 5(g) and 7(h)). Both adhesion toughness G and peak stress have strong dependence on the connector coverage density Σ. As T is lowered well below the glass transition temperature, the thermodynamics are dominated by the increased monomeric friction with n.

FIG. 3.

(a) Total exerted work for the indicated connector coverage density Σ in systems varied with time. (b) The final value of the work gives the toughness of adhesion G that increases with Σ except for Σ = 0.032σ-2 and Σ = 0.024σ-2 (n = 200) in which too high density might induce phase separation in the melts and weaken the adhesion.

FIG. 3.

(a) Total exerted work for the indicated connector coverage density Σ in systems varied with time. (b) The final value of the work gives the toughness of adhesion G that increases with Σ except for Σ = 0.032σ-2 and Σ = 0.024σ-2 (n = 200) in which too high density might induce phase separation in the melts and weaken the adhesion.

Close modal

At zero separation velocity (quasistatic limit), the adhesion energy is no other than the work to pull out connector chains at a constant stress over a distance. Above a characteristic velocity, viscous loss dominates and the fracture energy increase linearly with the velocity.1,4 Toughness G shows a jump for Σ = 0.008-0.024σ-2, and 2D scaling laws3GΣ2 fitted with current data are depicted as solid lines for comparisons, the tendency is apparent. But phase separation20 might occur somewhere, e.g. Σ = 0.032σ-2, especially for long connectors (n = 200) which depresses the enhancement of G, see Figure 3(b), and G for Σ = 0.032σ-2 converge to a constant value.

Peak stress somehow is a measurement of adhesion strength and increases significantly with Σ from 0.008σ-2 up to 0.032σ-2, in Figure 4. At each Σ, peak stresses increases with connector length n from 100 to 200, however, it is saturated as the interface is well enhanced by the connector chains that dissolved into the adjacent bulks, especially for Σ = 0.024σ-2 and 0.032σ-2 with n = 200, Σ = 0.032σ-2 with n = 200 (in dash rectangle), where loose melts are detached from the wall and peak stress yields similar value of detaching stress, see Figure 6(h) and Figure 7(g) and 7(h).

FIG. 4.

Peak stress Tzz varies with connector areal density Σ for indicated connector length n.

FIG. 4.

Peak stress Tzz varies with connector areal density Σ for indicated connector length n.

Close modal

Configurations of polymer-polymer adhesion under tension at peak stresses and failures are depicted in Figure 5–7. The pulling force reaches a maximum at peak stress, and connector chains are pulled taut. Failure occurs by simple chain pullout for short connector n = 100, e.g. Figure 5, bulk deformations become more evident in blue loose melts with increasing areal density. One end of promoter molecule entangled with melts is still grafted within green dense melts, and another end is almost pulled out from blue loose melts for its disentanglement. Once connectors slipped out of bulk surface, segments between entanglements are expanded from their equilibrium random-walk configurations to nearly straight lines, viz., the entropy of the thread is reduced and elastic energy is stored in the bonds of connectors. Further stretching aligns connector chains to form fibrils that transmit stress, and the interface becomes irregular, i.e. zigzag. Therefore, interfacial dissipation occurred during the sucking out process of connectors. The areal density of connector Σ has significant contributions to the bulk dissipation as the deformation is noticeable for loose melts. Meanwhile, both bulk polymers are modified by the connector molecular and the work for separation of adhesion rise with increase of Σ from 0.008σ-2 to 0.032σ-2. The final state consists of several main fibrils. These bundles of highly aligned chains are nearly parallel to the vertical axis along which strain is applied. A series of lateral lain and cross-tie fibrils are generated that can be most clearly seen. However, the overlapped connectors (bundles) are not easy to be completely pulled off from each other, which lengthen the tail of stress-strain curve and promote the adhesion energy, see Figure 2(c), Figure 5(g) and Figure 7(f).

With higher areal density and longer connectors dissolved in melts, bulk deformation in blue loose melts become significant during tension in Figure 6 and Figure 7, which is localized in a narrow active zone at the boundary of the growing craze network. After cavitations and crazing, the entangled chains formed bundles (fibrils) and thickened the polymers. However, this is not noticeable in green dense melts. The connector chains well entangled with melts can sustain sufficient stress, and are sucked out viscously, which fibrillates with much energy dissipated in drawing out the fibrils.

FIG. 6.

Snapshots of adhesion configurations during tension for chain length of connector n = 150, other notations for the scheme are the same as Figure 5.

FIG. 6.

Snapshots of adhesion configurations during tension for chain length of connector n = 150, other notations for the scheme are the same as Figure 5.

Close modal

The virtual walls act as rigid substrates, and cavities grow in blue loose melts first leading to crazing that detaches melts from the bottom. The force of individual fibril increase dramatically when more chains detached from the wall, therefore, adhesive failures at the wall/polymer interface occurred finally, see Figure 6(h), 7(g), and 7(h). The strength of adhesion interface reinforced by high Σ connectors is so strong that loose polymer can be separated from the wall. This is similar to the surface tension of polymer glasses pulled off from rigid wall. If the interactions between walls and polymers are strong enough, melts would deform further or chains of fibrils would break (chain scission) as an alternative, although the last is not expected for a tough adhesion.

Two immiscible polymers stitched by mobile connector molecules in a realistic 3D model are investigated by coarse-grained MD simulations. The adhesion interface can be strengthened by increasing the connector areal density, thus the toughness is enhanced. However, this adhesion enhancement is saturated as high connector areal density is beyond a certain value that phase separation might occur. With the low areal density of connector in mushroom regime, the failure of the interface is mainly chain pulling-out, and bulk melt dissipation is not considerable. Increasing the areal density to overlapping brush regime, connectors gathered to form bundles after being slipped out of bulk polymers, the interface become tough enough that adhered polymers would deform, cavitations and crazing formed therein, and cohesive failure between loose melts and rigid substrates occurred instead mitigating adhesion failure.

Further work to investigate the dependences of other parameters, e.g. connector length and separation strain rate etc., and chain scission on the failure of adhesion via mobile connectors is ongoing.

The calculations were performed at the Zernike Institute for Advanced Materials. The author has benefited from very helpful exchanges with Professor Erik Van der Giessen and Dr. Monica Bulacu, and he gratefully acknowledges supports from Newton International Fellowship (NF080039) and Newton Alumni Follow-On of UK's Royal Society hosted by University of Glasgow and Newcastle University, and Aeronautical Science Foundation of China (2012ZF52074), NSFCs (10602023, 11172130 and 11232007), the Fundamental Research Funds for the Central Universities, the Program for Changjiang Scholars and Innovative Research Team (IRT0968) and National Basic Research Program (973, 2011CB707602) of China.

1.
F.
Brochard-Wyart
,
PG
De Gennes
,
L.
Leger
,
Y.
Marciano
, and
E.
Raphael
,
The Journal of Physical Chemistry
98
(
38
),
9405
(
1994
).
2.
PG
De Gennes
and
L.
Leger
,
Annual Review of Physical Chemistry
33
(
1
),
49
(
1982
).
3.
H. R.
Brown
,
Annual Review of Materials Science
21
(
1
),
463
(
1991
).
4.
H.
Ji
and
PG
De Gennes
,
Macromolecules
26
(
3
),
520
(
1993
).
5.
E.
Raphael
and
PG
De Gennes
,
The Journal of Physical Chemistry
96
(
10
),
4002
(
1992
).
6.
K.
Yokomizo
,
Y.
Banno
, and
M.
Kotaki
,
Polymer
53
(
19
),
4280
(
2012
).
7.
M.
Doi
and
S. F.
Edwards
,
The theory of polymer dynamics
(
Oxford University Press
,
USA
,
1988
).
8.
K.
Kremer
and
GS
Grest
,
The Journal of Chemical Physics
92
,
5057
(
1990
).
9.
C.
Creton
,
E. J.
Kramer
,
C. Y.
Hui
, and
H. R.
Brown
,
Macromolecules
25
(
12
),
3075
(
1992
).
10.
J.
Washiyama
,
C.
Creton
, and
E. J.
Kramer
,
Macromolecules
25
(
18
),
4751
(
1992
).
11.
M.
Bulacu
and
E.
van der Giessen
,
The Journal of chemical physics
123
,
114901
(
2005
).
12.
M.
Bulacu
and
E.
van der Giessen
,
Europhysics Letters
93
,
63001
(
2011
).
13.
S. W.
Sides
,
G. S.
Grest
, and
M. J.
Stevens
,
Physical Review E
64
(
5
),
050802
(
2001
).
14.
R.
Auhl
,
R.
Everaers
,
G. S.
Grest
,
K.
Kremer
, and
S. J.
Plimpton
,
The Journal of Chemical Physics
119
,
12718
(
2003
).
15.
H. J. C.
Berendsen
,
J. P. M.
Postma
,
W. F.
Van Gunsteren
,
A.
Di Nola
, and
J. R.
Haak
,
The Journal of Chemical Physics
81
,
3684
(
1984
).
16.
W. C.
Swope
,
H. C.
Andersen
,
P. H.
Berens
, and
K. R.
Wilson
,
The Journal of Chemical Physics
76
,
637
(
1982
).
17.
B.
Liu
and
X.
Qiu
,
Journal of Computational and Theoretical Nanoscience
6
(
5
),
1081
(
2009
).
18.
E.
Kramer
,
Advances in Polymer Science
52–53
,
1
(
1983
).
19.
R. N.
Haward
and
G.
Thackray
,
Proceedings of the Royal Society of London. Series A.
302
(
1471
),
453
(
1968
).
20.
Y.
Xue
,
H.
Liu
,
Z.
Lu
, and
X.
Liang
,
J. Chem. Phys.
132
,
044903
(
2010
).