Towards the Multiscale Design of Pressure Sensitive Adhesives

Abstract

Pressure-sensitive adhesives (PSAs) are soft polymeric materials that exhibit complex rheological and mechanical behavior gov- erned by the interplay between polymer architecture, crosslink density, and entanglement constraints. Predicting their rheological properties from underlying microstructure remains a central challenge in adhesive design. In this work, we adopt a multiscale com- putational framework based on the Lagrangian Heterogeneous Multiscale Method (LHMM), coupling a macroscopic continuum description with a mesoscale polymer network model featuring breakable bonds embedded in a viscous medium. The approach enables consistent information transfer across scales and captures both elastic network response and viscous dissipation. The framework is calibrated using experimental rheological data and tensile measurements for four PSA formulations with varying gel fractions and crosslink densities. The simulations reproduce key experimental trends in storage modulus (G'), loss modulus (G"), and tensile stress-strain behavior under planar extension, while differentiating the distinct mechanical signatures of each formula- tion. The results elucidate how crosslink density and effective network connectivity control stiffness, stress localization, and failure characteristics. Overall, the proposed multiscale methodology provides a predictive platform for linking microstructural design pa- rameters to macroscopic mechanical properties and offers a rational basis for the formulation and optimization of next-generation PSAs.

Figures (6)

• Figure 1: Schematic of multiscale features of tensile test experiments and adhesives manufactured. a) Schematic of the tensile test experiments. The sample is deformed at a constant elongation rate, while the stress is recorded as a function of strain. At the microscale, the properties of the polymeric network (e.g. degree of crosslinking, molecular weight distribution, etc) will determine the response of the material to the deformation, and thus the macroscopic stress-strain response. b) The four samples (AD1 to AD4) were synthesized with varying amounts of chain transfer agent (CTA) and crosslinker (AMA). Addition of CTA leads a reduction in the overall molecular weight of the polymer compared to AD1, and overall degree of crosslinking, whereas addition of AMA favors the crosslinking of the polymer chains, while keeping the length of the polymer chains relatively unchanged compared to the blank sample (AD1). Mixtures of CTA and AMA (AD4) lead to microstructural features that are intermediate between the two extremes, depending on the formulation.
• Figure 2: a) LHMM sketch, b) Schematic mapping approach. The polymeric network is discretized as interconnected gel blobs (red) and low molecular weight fractions as sol blobs (grey). The gel volumetric fraction determines the total amount of gel blobs in the system. Stretchable bonding potentials (blue springs) are used to capture network connectivity, whereas all the blobs (gel and sol) in the system interact via viscous forces (green dashpot); c) Illustration of the cross-linking degree for two different systems with $c_d=3$ and $c_d=5$.
• Figure 3: Experimental characterization of the different samples. a) Differential molecular weight fraction, b) SAOS rheological characterization. Continuous and dashed lines corresponds to experimental measurements of $G^\prime$ and $G^{\prime\prime}$, c) Normalized stress vs strain tensile experiments
• Figure 4: a) $G^{\prime}$ linear correlation with $K_s$ and b) exponential correlation with $c_d$, $G^{\prime} \sim K_s{c_d}^{1.4}$. $G^{\prime}$ measured at maximum frequency ($\bar{\omega}=1$) at SAOS test for $\phi_{gel}=69\%$ and normalized with the corresponding value at $K_s=50$ and $c_d=2$.
• Figure 5: $G^{\prime}$ and $G^{\prime\prime}$ as a function of frequency for experimental (lines) and numerical ($\bullet,\times$) results for the different adhesive formulations. The values of $\phi_{\text{gel}}$, $K_s$, and $c_d$ used to simulate the gels are indicated. a) AD1, b)AD2, c)AD4, d)AD3. A visualization of the G particles forming the network is shown for each sample. Particles of type S are omitted for clarity.