Multi-scale modelling of interfacial phenomena in acrylic adhesives undergoing deformation

Información del proyecto

MODIFY

Identificador del acuerdo de subvención: 228320

Proyecto cerrado

Fecha de inicio 1 Junio 2009

Fecha de finalización 31 Mayo 2012

Financiado con arreglo a

• Specific Programme "Cooperation": Nanosciences, Nanotechnologies, Materials and new Production Technologies

Coste total € 4 269 113,42

Aportación de la UE € 2 863 126,00

Coordinado por

PANEPISTIMIO PATRON
Greece

Final Report Summary - MODIFY (Multi-scale modelling of interfacial phenomena in acrylic adhesives undergoing deformation)

Executive Summary:
In soft nanostructured materials containing polymers (such as acrylic adhesives), interfaces pose specific challenges since they are usually diffuse and can transfer stress through chain entanglements. The equilibrium structure of soft polymer interfaces is well-known, but their mechanical strength remains poorly understood. Yet many new nanostructured materials contain internal interfaces and important
applications involve a contact between the soft polymer and a hard substrate. The detailed understanding and modelling of the mechanical response of these interfaces is challenging and currently prevents the use of modelling as a screening tool for new materials in important applications.

In MODIFY we addressed all these problems through a specific example of application where interfaces dominate materials performance, i.e. soft nanostructured adhesives. The objectives of the project was to obtain a fundamental understanding of the complex interfacial structure-related interactions in these materials through sophisticated multi-scale modeling by developing new knowledge about: (i) The mechanism(s) of stress transfer at internal interfaces between soft latex particles; this was done at different scales from the molecular entanglement to the finite element level. (ii) The mechanism of stress transfer at hard/soft interfaces between the substrate and the soft adhesive. (iii) The effect of the presence of multiple internal interfaces on the macroscopic rheological properties of the material, and (iv) The respective role played by the polymer rheology.

Major achievements include:
• Synthesis of nine model polymer dispersions having monomer compositions of 98.1 weight% n-butyl acrylate / 1.9 weight% acrylic acid in two sets. The polymers were synthesized by gradual addition emulsion polymerization processes. Radicals were generated continuously throughout the polymerization by the combination of oxidants and reductants in the presence of a transition metal salt. Samples identified with XMM were polymerized at 40° C using a mixture of t-amyl hydroperoxide (tAHP) and ammonium or sodium persulfate as oxidants (APS, NaPS). Samples identified with DAK were polymerized at 60° C using only NaPS as the oxidant.
• Thorough rheological characterization of their linear and non-linear rheological properties at different temperatures and construction of time-temperature superposition (TTS) master curves over a broad frequency range by combining small-amplitude oscillatory (SAOS) and creep data using a single shift factor.
• Collection of a unique and complete set of rheological data in the non-linear regime using two rheometers: the commercial MCR 300 one for the linear viscoelastic characterization in oscillation and the MTR 25 rheometer developed at ETH Zürich for the non-linear step shear rate and continuous lubricated squeeze flow tests.
• A new method to fabricate multilayer adhesives having a gradient in viscoelastic properties, leading to a new strategy to optimize adhesion of PSA layers.
• A new methodology to characterize quantitatively the crack propagation velocity and contact angle at the interface between a soft viscoelastic layer and a hard surface as a function of applied energy release rate.
• A new method, based on the detection of image contrast, to statistically analyze the kinematics of cavity growth during the deformation of an adhesive, allowing also to extract the average mean tensile stress on the fibrils.
• Development of a new theory for the thermodynamic description of nonequilibrium multiphase systems, including the interfaces. We implemented the GENERIC framework for systems such as pressure sensitive adhesives (PSA’s) with fixed and moving surfaces. This helped us extract relevant boundary conditions for the bulk phases bounded by moving interfaces. The new theory expresses the interplay between bulk material and interfaces, by essentially introducing extra terms in the transport equation that account for a "moving interface normal transfer" (MINT).
• GENERIC formulation of the so called RaPiD (Responsive Particle Dynamics) model, a very efficient method to account for the transient forces present in complex fluids, which allowed us to determine its consistency from a mechanistic and thermodynamic point of view.
• Execution of detailed atomistic simulations of PSA samples adsorbed on amorphous silica and ferrite which allowed us to compute: a) the work of adhesion at the two surfaces, the entanglements network at the interface, and the response of the system to tensile stretching with an emphasis on the molecular mechanisms behinds slip and failure
• Development of a new differential constitutive law for highly elastic viscoelastic materials and parameterization on the experimentally measured rheological data
• Development of a mesoscopic, coarse-grained network simulation model capable of accessing sufficiently large time and length scales by modeling latex particles by just six degrees of freedom, and by introducing transient forces to capture the effect of slow changes in the degree of chain intermixing and in the number of sticker groups shared between pairs of latex particles. The model can nearly quantitatively predict the shear and extensional nonlinear rheology by careful tuning of only a few parameters to the linear rheology.
• Development of new phase-field models capable of simulating the time evolution of bubbles and fingers within the viscoelastic PSA material. Also, compressible two-phase flows, where the bubbles are modeled as a fluid with high compressibility.
• Development of several new 3D finite element codes capable of simulating the debonding of model adhesives containing deformable bubbles according to the probe tack experiments. The simulations use either differential constitutive models and structured meshes or integral constitutive models and unstructured meshes. Multiple (up to 100) bubble simulations have thus been carried out thereby successfully simulating the dynamics of the entire adhesive, its deforming side-surfaces and the preformed bubbles in it, as observed in well-controlled experiments.
Project Context and Objectives:
Acrylic pressure sensitive adhesives (PSAs) are based on complex formulations employing random copolymers of a long-chain acrylic (e.g. n-butyl acrylate, BA) characterized by a low glass transition temperature (Tg) with a short side-chain acrylic (such as methyl acrylate) to adjust Tg and acrylic acid (AA) to improve adhesion and optimize elongational properties. They are materials which overwhelm the modern adhesives industry (valued at ca 1.4 Billion Euro) due to a spectrum of unique properties such as excellent control on glass transition temperature, low plateau modulus, competitive cost, superior stability, and greater resistance to oxidation (because of their saturated backbone) compared to rubber-based analogues. Within these materials, interfaces pose specific challenges since they are usually diffuse and can transfer stress through chain entanglements. When they are prepared by emulsion polymerization in water, acrylic PSAs result from the drying and coalescence of separate latex particles so that the memory of the original interface is retained. Although the equilibrium structure of these soft polymer interfaces is well-known, their mechanical strength remains poorly understood. Owing to the small separation of the latex particles, the structure of acrylic PSAs is characterized by extended interface regions whose effect today is only empirically assessed. In applications involving a contact between the soft polymer and a hard substrate, interfacial bonding also constitutes a fundamental problem, since it is at the root of the mechanisms governing failure upon deformation.

When the soft adhesive undergoes large non-linear deformations, additional interfacial interactions arise due to formation, elongation, and ultimate breakage of internal cavities leading to thin, highly elastic filaments. For example, the debonding process of a PSA from its adherent (represented schematically by the stretching deformation of a thin film between two parallel plates being separated from each other at constant rate) is characterized by a force-displacement curve which typically exhibits a characteristic peak in the stress due to a process of cavity growth from the interface with the probe, mostly controlled by the elastic modulus of the adhesive. The subsequent widespread presence of the cavities causes the force to drop, a process followed by a third stage, that of fibril formation.

The detailed mechanical understanding and modeling of the mechanical response of these interfaces is challenging and currently prevents the use of modeling as a screening tool for new adhesive materials in many applications. As a result, the industrial approach is today limited to trial-and-error efforts and loose cooperative thinking rather than based on deep understanding. Companies manufacturing adhesives, such as DOW and Rhom and Haas, are in need of improving the performance of existing products or in developing new ones by tailoring the chemical constitution, architecture, molecular weight distribution and relative concentrations of their homo- and copolymeric main components, as well as the resins and solid fillers they may contain. This is true also for large petrochemical companies with business in pipe coating. For example, a ~10% part of LBI’s products [LBI is a global leader in polyolefin technology, production and marketing: globally 1st in polyolefin compounding, 1st in polyolefin licensing, 1st in polypropylene catalysts, 1st in polypropylene and 3rd in polyethylene] in Europe and USA is related to pipes and pipe coating comprising ~50 million €/year business. Pipe coating, as referred to, consists of film casting and coating of metal pipes with polyolefin and epoxy layers. LBI commercializes both the external polyethylene (PE) “jacket” but also the adhesive between the external and the epoxy layer, consisting of PE, PE blends or copolymers.

Using as a model system the wide variety of available acrylic adhesives, the main objective of MODIFY was to build a fundamental understanding of the role of such interfaces in the performance of advanced adhesives by developing sophisticated hierarchical models addressing:
• the mechanism(s) of stress transfer at internal interfaces between soft latex particles containing polymers with different topologies; this needs to be addressed at different scales from the molecular to entanglement network level
• the mechanism of stress transfer at hard-soft interfaces between the substrate and the soft adhesive, as a function of chemical composition of the PSA formulation and the chemistry of the substrate
• the effect of the presence of multiple internal interfaces on the macroscopic deformation behavior of the adhesive
• how cavitation and the development of the fibrillar structure in the final adhesive product are affected by changes in the properties of the initial formulation
• the respective role played by the polymer rheology
• the correct type of boundary conditions (b.c.’s) at the polymer/substrate interface; this needs to be derived from non-equilibrium statistical mechanics
• a more representative constitutive law for the finite isotropic and anisotropic elastic behavior of these materials

We deliberately addressed a specific class of PSAs only (acrylics), since we consider it at present more useful to achieve an in-depth understanding of a given type of material where a spectrum of interfacial interactions determine final properties rather than adding to the large amount of poorly connected knowledge that is accumulating in the field recently. We stress, however, that the same approach can address blends of existing PSAs or the use of fillers (e.g. CNT) and that it can be extended to other important areas such as the cosmetics, the food, the paints, and the coatings sectors.

The interface modeling pursued in the course of the MODIFY project aimed at explaining the role of a number of molecular and physicochemical parameters (nature, composition and architecture of chains, particle-particle degree of inter-entanglement, latex particle size and particle size distribution, concentration, molecular weight between crosslinks and degree of crosslinking, viscosity, elastic modulus, and type of substrate) on the thermodynamic, mechanical and transport properties of this class of materials. By having molecular-level control over their properties and nanostructures in the 100-300nm scale, the goal was to guide the two participating industrial partners (DOW and LBI) toward several specific targets of direct technological and economic relevance:
• knowledge-based methods to optimize the peel/shear/tack PSA balance onto a particular substrate (depending upon the class of PSA: permanent or removable)
• development of new PSA products based on filmic-on-filmic combinations
• development of new substrates with well-controlled roughness and physical chemistry for controlling adhesion; this can lead ultimately to linerless adhesives (no backing paper to initially protect them)
• design of controlled release adhesives with enhanced recyclability

Understanding the role of internal (between particles and between cavities inside the adhesive) and external (between the adhesive and the substrate) interfacial interactions in soft adhesives is clearly the key to designing better formulations with improved or even drastically new performance properties. Before MODIFY, there was no model addressing these interactions; there were no computational tools developed for predicting the behavior of a PSA material in each elementary stage of the bonding/debonding process from the molecular parameters of the material. A quick literature survey quickly revealed only a few highly segregated efforts based on simple (and sometimes rather heuristic) mechanical models, fracture mechanics arguments, scaling models, and macroscopic numerical calculations which relied on the use of simplistic purely viscous or viscoelastic constitutive equations or treated highly elastic materials as solids. But the transition from viscoelastic fluid to viscoelastic solid (i.e. to a “fluid” with a very large, non-measurable Newtonian viscosity) is a known limitation in simulation techniques, while treating an adhesive using solid mechanics is not sufficient. For example, the debonding deformation, which can be compared at an entirely different length scale with the oriented structure found in polymer crazes, cannot be approximated by a simple elastic fracture mechanics approach; a more microscopic understanding is required. Existing numerical algorithms also fail to address cavitation phenomena or to correctly treat interfacial stresses.

In MODIFY, our goal was to address the acrylics PSA design problem through a hierarchical approach: We worked with two representative formulations of acrylics: (a) Systems with homogeneous composition but possibly internal dynamic heterogeneities (partially crosslinked random copolymers), and (b) systems with compositionally heterogeneous materials (“core-shell” systems from water-based latexes). The former are compositionally homogeneous but can be heterogeneous at the level of crosslinking density (which results into heterogeneities in their microscopic dynamics). The latter are inherently compositionally heterogeneous with very slow to vanishing dynamics in the core. We divided the whole process of their bonding and debonding on a slid substrate into elementary steps: initial contact formation, emergence of defects at the interface or in the bulk of the adhesive, nucleation of cavities, growth of cavities, interaction between cavities and formation of fibrils, and ultimate fracture of fibrils. The surface of the hard substrates was systematically modified by changing it via modifications of its chemical structure or its topography (roughness). The resulting b.c.’s was quantified experimentally during deformation experiments and their coupling with the deformation of the soft material was studied. Through nine coordinated workpackages (1: Synthesis, fabrication and characterization of model emulsion PSA polymer systems; 2: Experimental characterization of the rheological properties and debonding mechanisms of soft adhesives; 3: Atomistic modeling of adhesion – beyond equilibrium atomistic simulations of interfacial slip; 4: Nonequilibrium thermodynamics for mixed three- and two-dimensional systems; 5: Mesoscopic modeling of rheological behavior in the bulk and at interfaces; 6: Phase-field and finite-element macroscopic computations; 7: Micro-macro integration for materials design; 8: Project management; 9: Results management) and by bringing together the most advanced experimental and modeling tools available today, we modeled each one of these debonding steps and developed a fundamental understanding of how they are affected by the molecular parameters of the adhesive.

The atomistic modeling allowed us to understand the degree to which the compatibility of the PSA-substrate interface is affected by subtle changes in the chemical constitution of the base polymer and the chemistry of the substrate, since this affects directly the interfacial bonding of the two phases. At the mesoscopic level, we developed specific network models for compositionally homogeneous partially crosslinked random copolymers and compositionally heterogeneous core-shell based adhesives. In the latter, the main dynamic phenomena occur in the interaction zones between the shells which form the internal interfaces. For the homogeneous systems, the network models provided a statistical description of the underlying network structure obtained by radical polymerization techniques, forming the base of the fabricated model acrylic PSAs. The models explicitly accounted for the joining areas between microgel particles and/or the transition zones between crosslinked and non-crosslinked polymer considered as internal interfaces. For the heterogeneous systems, the models were refined to account for the large spectrum of relaxation times characterizing their dynamics, modifications in the inter-particle potential, and effects due to particle overlapping processes resulting in “sticky” phenomena between different particles. The theoretical component of the multi-scaling approach addressed two issues: (a) a new type of b.c. and (b) a new family of constitutive equations for PSAs from a non-equilibrium thermodynamics perspective. On the macroscopic level, computations were executed with the new constitutive equation as wella s with integral ones capable of predicting morphology development and cavity evolution (fibrillation and fingering) in the volume of the PSA and along the substrate surface. Two distinct numerical techniques were used: the first, a phase-field method, offered a detailed study of individual cavity and finger growth; the second, a finite-element method, helped simulate the entire system with many cavities and fingers.

The modeling was extensively validated by appropriate experimental studies of the model acrylic PSAs. We started with structural investigations using SEM and TEM to look at the structure of the particles and the adhesive film, AFM to resolve contrasts in mechanical properties (between hard and soft domains) on the 10-20 nm scale, and X-ray diffraction to characterize the crystallinity of the PE substrates, and continue with adhesive and rheological testing. Some of the techniques were standard (but very useful) while others such as the probe tack geometry onto which an optical technique was mounted allowed for in situ 3D visualization and are considered to be state-of-the-art. The direct characterization of the model materials in the probe tack geometry, specific for testing of adhesive properties, gave important insights on possible applications of the tested materials for the development of commercial adhesives. The rheological characterization assessed the linear viscoelastic properties, the strain rate dependence at large deformations, and the temperature dependence of the fabricated model PSAs.

MODIFY went beyond the state-of-the-art in the field in many respects:
• It focused on a model system (water-based acrylic PSAs based e.g. on butyl acrylate and 2-ethyl hexyl acrylate) with the advantage of a complexity which is somewhat controllable.
• It divided the full problem to sub-problems by distinguishing between particle-particle (internal soft/soft interfaces) and adhesive-substrate (external soft/hard) interactions; we expect the simplified sub-problems to be easier to adapt to experimental data.
• It employed a hierarchy of state-of-the-art tools ranging from atomistic interface modeling, to mesoscopic network models, to phase-field and finite-element approaches for calculating diffuse interfacial patterns, to continuum mechanics theories for crack propagation and finite elasticity, to strict non-equilibrium statistical mechanics treatments of interfaces.
• It proposed and actually carried out well-designed experiments which provided information for direct comparison with and validation of the outcome of the modeling. In many cases, the experiments critically guided the modeling efforts; for example, it was realized that one of the key aspects of the problem is the dynamics of the contact line at the adhesive-substrate interface which should be understood on the basis of detailed non-equilibrium dynamics simulations.
• It integrated sound statistical-mechanics theories to the multi-scale modeling approach, and validated how different levels can be interfaced through targeted experiments at different levels for different adhesive/substrate combinations.
• It generated several state-of-the-art codes and algorithms with potential applications to several systems in Soft Matter where interfacial interactions shape their behavior.

Project Results:
As mentioned above, MODIFY was structured around 9 highly inter-related, highly interconnected work packages (WPs):
WP1: Synthesis, fabrication and characterization of model emulsion PSA polymer systems
WP2: Experimental characterization of the rheological properties and debonding mechanisms of soft adhesives
WP3: Atomistic modeling of adhesion – beyond equilibrium atomistic simulations of interfacial slip
WP4: Nonequilibrium thermodynamics for mixed three- and two-dimensional systems
WP5: Mesoscopic modeling of rheological behavior in the bulk and at interfaces
WP6: Phase-field and finite-element macroscopic computations
WP7: Micro-macro integration for materials design
WP8: Project management
WP9: Results management

The key achievements of our research work in the 7 technical WPs (WP1 through WP7) is summarized in the following paragraphs of this report

WP1: Synthesis, fabrication and characterization of model emulsion PSA polymer systems: Nine polymer dispersions having monomer compositions of 98.1 weight% n-butyl acrylate / 1.9 weight% acrylic acid were provided to the Consortium in two sets. The polymers were synthesized by gradual addition emulsion polymerization processes. Radicals were generated continuously throughout the polymerization by the combination of oxidants and reductants in the presence of a transition metal salt. Samples identified with XMM were polymerized at 40° C using a mixture of t-amyl hydroperoxide (tAHP) and ammonium or sodium persulfate as oxidants (APS, NaPS). Samples identified with DAK were polymerized at 60° C using only NaPS as the oxidant. For all samples the reductant used was Bruggolite® FF6. In all cases, to reduce free monomer in the final products, an additional quantity of tAHP and Bruggolite® FF6 was added after completion of the gradual addition portion of the polymerization. Particle size was controlled by polymerizing monomers in the presence of 1.3 weight%, based on total weight of monomers, of a butyl acrylate / methyl methacrylate latex having a Tg of ~20°C and particle diameter of ~100nm. The polymerization was performed in the presence of 0.2 weight%, based on total weight of monomers, sodium dodecylbenzene sulfonate. 9.2 equivalent% basic sodium (from sodium carbonate), based on acrylic acid was used to regulate polymerization pH. Final pH of the emulsions was adjusted by the addition of ammonium hydroxide.

Molecular weight was regulated by the addition of 0 to 0.2 weight % of the chain transfer agent (CTA) n-dodecylmercaptan (n-DDM), based on the total weight of monomers, continuously throughout the gradual addition/ polymerization of monomers. When the n-DDM level is expressed as 0.05%, 0.5 parts by weight n-DDM was added to 981 parts butyl acrylate and 19 parts acrylic acid.

Aspects of many of the techniques used to do more detailed characterization of the polymers are considered to be proprietary to The Dow Chemical Company; as a result, detailed may not be disclosed here. Absolute molecular weight was determined by gel permeation chromatography using coupled refractive index (RI) and multi-angle light scattering (MALS) detectors. GPC recovery % is used as an estimate of the percentage of a polymer sample included in the molecular weight calculations and is based on the known mass injected onto the column, the refractive index of p-BA, RI detector response factor and the area under the curve of the RI detector chromatogram. Values of less than 100% indicate the presence of gel polymer, polymer too high in molecular weight or too crosslinked to adequately dissolve in the mobile phase and be recovered in the analysis. With the exception of DAK4027, and possibly XMM19305, it should be considered for all samples that 100% of the polymer was soluble in the mobile phase and included in the analysis of molecular weight. The error involved in the estimate of recovery has not been determined, but the overall pattern of the data in the XMM samples suggests that XMM19305 is essentially 100% soluble. The theoretical molecular weight was calculated by the simplistic assumption of 100% chain transfer efficiency leading to 1 mole of polymer chains / mole n-DDM.

13C NMR was used to estimate the absolute frequency of branches in exemplary polymers from each of the XMM and DAK series. XMM polymers were determined to have approximately 7.5 branch points / 1000 backbone carbons and DAK series polymers were closer to 15 branch points / 1000 backbone carbons, consistent with the difference in polymerization temperature. The NMR technique does not differentiate between long and short chain branches.

Analysis of GPC data provided more information with regard to relative levels of long and short chain branching. These data were used to construct the Mark-Houwink-Sakurada (M-H-S) plots of absolute molar mass vs. intrinsic viscosity as determined by on-line viscometry for both the DAK and XMM sample series of polymers. The plots of log (intrinsic viscosity) vs log (MW) were not linear in the entire sample molecular weight range, the slopes decreasing towards higher molecular weight. By fitting the data with second order polynomial and subsequently taking the derivative of that function, the “a” value as a function of molecular weight could be determined. The “a” value was found to decrease with the increasing of molecular weight in the main peak region. Since higher “a” values are indicative of less compact, less branched chains, the conclusion reached was that the higher molecular weight chains are more branched than the lower molecular ones. The “a” value at weight average molecular weight of each sample was used as an index to probe the average polymer chain compactness, with more highly branched polymers being more compact. For the DAK series, higher CTA levels generally correlate with higher “a” values. The exception to this trend was DAK4027. It should be noted that the data showed only 67% recovery for this sample. It is probable that the resultant “a” value calculated from the MW distribution of the recovered material was not representative of the entire polymer sample, with branched material being selectively excluded from the analysis. The correlation of higher “a” value with higher CTA level held true for the XMM series samples made with NaPS, where all samples showed essentially quantitative recovery.

The tacticity of the polymers was determined by directly dissolving the emulsions into deuterated THF. The 1H, 13C, and diffusion NMR spectra were acquired on a Bruker AV III 600 MHz NMR spectrometer. Based on literature and previous tacticity study done by K. Beshah (Makromol. Chem. 194, 3311, 1993), the acrylic backbone methine carbon (-CH, ~42.4 ppm) was used to analyze pBA tacticity. In comparison, the two polymer samples (XMM19301, 40 °C polymerization temperature; DAK4027, 60 °C polymerization temperature) showed very similar multiplicity patterns (overlapped nicely), indicating similar tacticity for the two polymers. Specifically, the isotactic (mm) CH signal was shifted slightly up-field at ~42.2 ppm and accounted for ~21 % . The syndiotactic (rr) and heterotactic (mr) CH peaks were overlapping at ~42.6 ppm and accounted for ~79 %. The carbonyl (C3) and –OCH2CH2- (C4-C5) signals in pBA were also sensitive to polymer tacticity. The comparison of their relative integral ratios and multiplicity signals suggested similar tacticity for XMM19301 and DAK4027. In a similar manner, the two polymers displayed very similar backbone (–CH2-CH-) proton signals and multiplicity patterns, again indicating similar tacticity between them.

Also determined was the total quantity of acrylic acid residues in the emulsions, as well as the quantity present in polymer in the aqueous phase of the emulsion. Particle bound acid was determined by subtraction. Data about the acid content in terms of milliequivalents / gram of polymer solids, along with Mn and Mw values for representative samples, exhibited little variability across polymers within a series; so an average of the values within a series for all samples in that series was used.

For the DAK series of polymers serum polymer was determined to be nearly 100% acrylic acid with end groups of predominately sulfonate and sulfate (~ 1:0.6 ratio) on one chain end, and a mixture of saturated and unsaturated monomer residue on other (~ 2:1 ratio) . Compositions appeared to be very similar in the XMM polymers. Analysis of the serum phase polymers sampled during the polymerization suggested the presence of oligoradical species having one sulfate end-group and 1, 2, or 3 acrylic acid units in a ratio of approximately 10:1:0.1. For the DAK series possible oligoradical species having one sulfate end-group and only 1 or 2 acrylic acid units were identified. These species represent possible end-groups for the polymer chains in the particles.

Ion chromatography found evidence of only sodium and sulfate ions in any significant concentration. Representative samples of the XMM and DAK series polymers were analyzed by Transmission Electron Microscopy. For both the XMM and DAK examples the 4,000X images showed clear residues of particle boundaries at the appropriate scale. This observation provided no estimation of the degree of diffusion of particle chains across particle-particle interfaces, but did suggest that the particles fail to completely coalesce in the dry film. Images of the same polymers at 10,000X appeared to have lost enough contrast to make the inter-particle boundaries less clear.

WP2: Experimental characterization of the rheological properties and debonding mechanisms of soft adhesives

2.1 Rheological studies. We have carried out a thorough rheological characterization of the XMM and DAK-series of samples, both in non-linear shear and continuously lubricated squeeze flow (CLSF).
Two rheometers were used in these studies: a) the commercial MCR 300 for the linear viscoelastic characterization in oscillation, and b) the MTR 25 developed at ETH Zürich for the non-linear step shear rate and continuous lubricated squeeze flow tests. A special feature of the latter is the partitioned plate, which allowed very precise viscosity measurements and the simultaneous determination of both normal stress differences from a single test. It has been used with cone-plate-geometry (cone angle 0.15 rad) and a radius Ri of the inner tool of 8 mm. The test temperature was 50°C. Contrary to the MCR 300 with plate-plate-geometry, the sample was squeezed during loading. This led to a strongly bulged rim which could not be flattened due to the yield stress of the samples or the very long relaxation times.

The results of the rheological measurements can be summarized as follows:
• Time-temperature superposition (TTS) master curves were constructed over a broad frequency range by combining small-amplitude oscillatory (SAOS) and creep data using a single shift factor.
• The PSAs studied exhibited an elastic dominated behavior over a wide frequency range and show no terminal flow regime in the accessible time/frequency regime. Rheological properties of PSA were strongly affected at temperatures above 90°C where TTS did not any longer hold.
• In the non-linear regime (uniaxial elongational flow), the PSAs showed a strong strain-hardening behavior which was almost independent from strain-rate in the broad range of several decades investigated.
• A molecular weight influence on the strain-hardening factor was observed at intermediate strain rates close to the transition from a polymeric to a sticker-group dominated flow behavior.
• Sample DAK 4027 is different from 4029-4037, since it contains ~30% insoluble gel fraction (DOW analysis). On the other hand, sample DAK 4037 showed an extremely good reproducibility even for -?2 (the quantity most sensitive to flow instabilities). DAK 4037 was the sample with the lowest branching content and the lowest viscosity.
• A comparison of the two most extreme samples without large gel content (DAK 4029 and DAK 4037) showed that: Both the steady state viscosity ?ss and first normal stress coefficient ?1,ss decrease, in accordance with the decreasing molecular weight MW. The shear hardening, viz the ratios ?max/?ss and ?1,max/?1,ss both increase. Since MW decreases, this effect - improving the creep resistance - has to be attributed to the modification of the branching structure by the n-DDM.
• The maximum of the viscosity was at a shear rate independent strain of about ? = 16 for DAK 4029 and ? = 20 for DAK 4037. The maximum of ?1 independent of the sample increased with shear rate from about ? = 25 at D = 0.1s-1 to ? = 30 at D=3s-1.
• Contrary to the viscosity, the first normal stress coefficient ?1 showed a very slow relaxation when the shear flow was stopped after 30 shear units.

2.2 Adhesive tests. In WP2 we characterized the debonding mechanisms of model PSA layers and in particular we studied the effect of internal and external interfaces on the debonding mechanisms. The quantitative characterization of the adhesive/substrate contact angle and crack dynamics was a specific target. A secondary objective was the characterization of the rheological properties of the PSA materials in elongation with a uniaxial tensile test, characteristic of the behavior of adhesives during debonding. The results of ESPCI had then to be passed to UPatras, CNRS and UCL within WP6 and 7 for the mesoscopic and macroscopic simulation.

A good deal of time was spent in characterizing the tensile and adhesive properties of the two model adhesive series provided by DOW, in developing a method to prepare multilayer films with internal interfaces, and in developing a new experimental setup to characterize the contact angle. The major achievements can be summarized as follows:
• We adapted the Phan-Thien/Tanner (PTT) constitutive equation to simulate the extensional behavior of adhesive materials in simple uniaxial extension and at constant strain rate extension. This equation can be used in full 3D macroscopic simulations and provides physically meaningful parameters.
• We developed a new strategy to optimize adhesive properties of multilayer films by a proper choice of the viscoelastic properties of the layers.
• We developed a new methodology to characterize quantitatively the crack propagation velocity and contact angle at the interface between a soft viscoelastic layer and a hard surface.
• We characterized the crack propagation velocity and contact angle as a function of applied energy release rate for two model adhesives on six different surfaces.
• We developed a new and very promising method, based on the detection of image contrast, to statistically analyze the kinematics of the adhesive deformation during debonding developed in collaboration with the CNRS group. The following parameters were extracted for three model adhesives: average mean tensile stress on the fibrils, average cavity size and growth rate and average eccentricity of the cavities as a function of time.

WP3: Atomistic modeling of adhesion – beyond equilibrium atomistic simulations of interfacial slip
The starting point for the successful implementation of an atomistic MD algorithm was the development of a reliable molecular model describing interactions in the system under study. In MODIFY, we aimed at utilizing an all-atom force-field for the model PSAs and the corresponding PSA-substrate systems that could accurately reproduce their conformational, structural and dynamical features. The successful implementation of such a forcefield opened the way to predicting several important properties of the model PSA-substrate systems addressed in MODIFY: a) the work of adhesion, b) the entanglement network at the interface, and c) the response of the adhesives to an applied uniaxial stretching deformation, and d) the molecular mechanisms behind slip phenomena at the substrate.

3.1. The work of adhesion. Owing to the large requirements in CPU time, we computed the work of adhesion only for the XMM19301 sample on an amorphous silica (a-silica) substrate. The calculation was carried out with two different ways: a) from the interactions between the polymer molecules and the surface atoms using a method that utilizes the concept of the van der Waals contact area, and b) through the polymer stresses which are developed near the substrate under investigation. Let us call the first Method I and the second Method II. Method I gave the following estimate for the work of adhesion of XMM19301 on amorphous silica: WA = (1.79±0.50) J/m2. The corresponding estimate from Method II was WA = (2.23±1.40) J/m2. We observe that the two Methods give slightly different estimates; given the last statistical uncertainty with which the stress tensor components are calculated from the virial theorem, we trust more the prediction from Method I. That is, our simulation estimate for the work of adhesion of XMM19301 on amorphous silica is: WA = 1.79 J/m2. This value should be compared against the experimentally measured value obtained from the team of Prof. Creton at ESPCI which for typical substrates is usually reported to be in the range 0.05-0.1 J/m2. We also mention that a very similar value at the one we obtained here has been reported in the literature for acrylic polymers on a copper surface by Kisin et al. (J. Chem. Mater. 2007): WA = 1.68 J/m2 for an oxygen-content on the copper surface equal to 0.143 oxygen atoms/Å2. As explained by Kisin et al., the value of the work of adhesion WA increases as the Oxygen content of the substrate increases. Given the high Oxygen content of the a-silica employed in our simulations, the agreement between simulation and laboratory measurements is very-very encouraging.

3.2. The entanglement network at the interface. Based on the idea of Tzoumanekas and Theodorou (Macromolecules, 2005) we developed the CReTA algorithm capable of reducing atomistic configurations of polymer melts to entanglement networks of primitive paths (PPs). The PPs provide a coarse-grained representation of chains characterizing their topology. In the context of the reptation theory, a PP is regarded as the shortest path generated by keeping chain ends fixed and at the same time shrinking chain’s contour. This procedure is applied simultaneously for all chains and its capability lies in the fact that it uncovers the network of entangled PPs underlying the large-scale topological superstructure of a high-molecular weight (MW) polymer melt. For each polymeric system of interest, the results of such a topological analysis should be reported as average values over a large number of statistically independent atomistic samples. In the present case, these material samples (thermodynamically and topologically equilibrated at all length scales) were provided by the detailed atomistic Molecular Dynamics (MD) simulations executed in our team for the model MODIFY acrylics both in the bulk and near a hard substrate. Using CReTA, them, we were able to reduce them to configurations to PP networks, which were next analyzed to extract their topological properties, with an emphasis on the formation of uncrossability points near the substrate.

We applied CReTA to four (4) different (statistically independent) configurations of XMM19301/a-silica interfacial system which was generated in the course of MD simulations specifically for the purposes of this work at two different temperatures (T=700K and T=300K). At the highest temperature (T=700K), this was easy because we simply sampled four different configurations at different (separated long enough) configurations collected in the course of the corresponding MD run (25ns, 28ns, 30ns, and 33ns). At room temperature (T=300K), statistically independent confirgurations were obtained by cooling each one of the above mentioned configurations at 700K down to 300K and waiting for their density to reach a constant value. The computed topological networks revealed that the generated PPs for the rather short acrylic polymers studied here consist of a small number of short pair-wise blocked chain segments (topological constraints or kinks) which are connected through straight sections of beads.

An interesting point of our work is that, in the way CRETA is implemented, we did not destroy the polymeric structure of the strongly adsorbed acrylic chains on the hard substrate (a-silica). This was achieved by considering atoms deeply inside the interfacial region as immobile, i.e. as topologically uncrossable points. This explains the parallel arrangement of chains that was observed on the two a-silica surfaces and the richness of the corresponding domain in kink points. This is precisely the desired entanglement network at the interface that we wanted to uncover in the course of MODIFY. It is this network that carries all the stress when the material is subjected to stretching deformations normal to the substrate.

3.3 Molecular mechanisms of wall slip. To understand the molecular mechanisms behind slip phenomena during the uniaxial stretching of adhesive polymers, we resorted to a generalized non-equilibrium molecular dynamics (NEMD) algorithm capable of following the stretching deformation of an adhesive polymer above a solid substrate. The relevant statistical ensemble is the so called NPxxLyPzzT ensemble, where N denotes the number of interacting atomistic units in the system, Pii the normal pressure in the i-direction, Ly the box dimension along the stretching (y-) direction, and T the temperature. Such an ensemble allows one to simulate a sample of the material of interest confined between two parallel substrates under conditions of uniaxial deformation, since one has full control on the length of the simulation cell along the y direction and on the stress or pressure tensor components in the two lateral directions; as a result, the dimensions of the simulation cell along x and z are allowed to vary (to fluctuate) in response to the applied field along the y direction.

For validation purposes, we first applied the new algorithm in a simulation with a significantly simpler system, that of a linear polyethylene (PE) adsorbed between two graphite surfaces. Typical results from these simulations revealed a continuous decrease of the size of the simulation cell in the two lateral dimensions as the material was stretched along the y direction, indicative of slip of the melt at the interface with the graphite substrate. The slip was rather fast in the beginning (up to the first 50 ps) and then slowed down somewhat. Next, we proceeded to apply the new algorithm to the MODIFY XMM samples adsorbed on a-silica. As far as the size of the simulation cell in the three directions x, y and z is concerned, the results were qualitatively very similar to those obtained for the PE melt on graphite; however, the rate with which the two lateral components (x and z) decreased was much slower. To shed light into this, we monitored the response of individual XMM chains to the applied field. These chains were chosen to lie next to the a-silica substrate. Our analysis revealed that, in contrast to PE chains above graphite, XMM chains above a-silica are so strongly adsorbed (mainly by their SO4 end groups) that can hardly detach from it. As a result, the material exhibits practically no slip at the wall or an infinitesimal one. The adsorption of SO4 groups on a-silica is so strong that even at Wi numbers as high as 10,000 no detachment was observed.

To check the effect of the substrate on the response of the XMM sample, we repeated the stretching experiments by using now a ferrite substrate. The simulation results showed again a rather limited interfacial slip, especially at low values of the Wi number. However, at very high Wi numbers, chain detachment was observed, which was accompanied by significant slip. To elucidate this, we monitored again the response of individual XMM chains adsorbed on ferrite to the applied deformation. Interestingly enough, for two randomly adsorbed chains in the simulation cell, the results obtained revealed chain detachment at deformation levels above approximately 100% for the largest Wi numbers studied (Wi=5000 and 10000).

Our conclusion therefore is that slip phenomena are intimately connected with the ability of chains to withstand the tensile force along the y direction through the strong specific forces that develop with the substrate atoms. The result is consistent with the corresponding calculations of the work of adhesion of the XMM sample on a-silica and ferrite (it is smaller in the ferrite). Clearly, the driving force for slip phenomena is the detachment of the SO4 groups (as well as the rest of the specific bonds developing between the XMM chain and the substrate) from the substrate at high enough deformation loads,. Slip occurs whenever the energy keeping these groups adsorbed is overcome by stretching.

WP4: Nonequilibrium thermodynamics for mixed three- and two-dimensional systems
We developed a new theory for the thermodynamic description of nonequilibrium multiphase systems, including the interfaces. We implement the GENERIC (“general equation for the nonequilibrium reversible-irreversible coupling") framework of nonequilibrium thermodynamics for systems, such as pressure sensitive adhesives (PSA’s), with fixed and moving surfaces. We ultimately wanted to extract relevant boundary conditions for the bulk phases bounded by the said interfaces. We first understood how the general thermodynamic theory of 2D interfacial systems can be rigorously extended to nonequilibrium situations. To do so, we analyzed the local equilibrium assumption for interfaces from the perspective of gauge transformations, which are the small displacements of Gibbs' dividing surface. The gauge invariance of thermodynamic properties turns out to be equivalent to conditions for jumps of bulk densities across the interface of the Clapeyron type. We further verified these properties using nonequilibrium molecular dynamic simulations and statistical mechanics of a coexisting liquid-vapor system. This insight further strengthened the foundations of the local equilibrium assumption for interfaces and was used to characterize nonequilibrium interfaces in a compact and consistent way, with a clear focus on gauge invariant properties.

We then identified the variables that fully characterize the system in the bulk phases, and onto which the boundary conditions will be applied. A particularly relevant choice for the MODIFY project about PSA’s was the coarse grained RaPiD (Responsive Particle Dynamics) model. The RaPiD model is a very efficient method to account for the transient forces present in complex fluids, such as solutions of entangled polymers. This coarse-grained model considers a solution of particles, that are made of a core and a corona. The cores typically interact through conservative interactions, while the coronae transiently penetrate each other to form short-lived temporary interactions, typically of entropic origin. We formulated this rheological model within the GENERIC framework to determine its consistency, from a mechanistic and thermodynamic point of view. Finally, we developed the generalized GENERIC theory that expresses the interplay between bulk and interfaces, by essentially introducing extra terms in the transport equation that account for a "moving interface normal transfer" (MINT).

WP5: Mesoscopic modeling of rheological behavior in the bulk and at interfaces
Given that the performance of pressure sensitive adhesives (PSA) in real applications is primarily determined by substrate-adhesive interactions, which are strongly influenced by the bulk rheology of the material, in WP5 small amplitude oscillatory shear (SAOS) and creep compliance tests were used to study the linear rheological properties in shear at different temperatures. Time-temperature superposition (TTS) master curves were constructed over a broad frequency range by combining SAOS and creep data using a single shift factor. The PSA studied were found to exhibit an elastic dominated behavior over a wide frequency range and to show no terminal flow regime in the accessible time/frequency regime. Rheological properties of PSA were also found to be strongly affected at temperatures above 90°C where TTS does no longer hold. In the non-linear regime, the uniaxial elongational flow was measured using an extensional rheometry device at different strain rates to observe the response of the PSA in extension, and they all showed a strong strain-hardening behavior which was almost independent from strain-rate in the broad range of several decades investigated. A molecular weight influence on the strain-hardening factor was observed at intermediate strain rates close to the transition from a polymeric to a sticker-group dominated flow behavior.
In a 2nd stage, and in order to overcome difficulties in the design problem of novel pressure sensitive adhesives formed by drying of a polymer latex emulsion due to a lack of understanding of the relation between microscopic details and large-scale rheology, we introduced a coarse-grained computer simulation model aimed at providing such a link. To reach sufficiently large time and length scales each latex particle in the new model was represented by just six degrees of freedom, and transient forces were introduced to capture the effect of slow changes in the degree of chain intermixing and in the number of sticker groups shared between pairs of latex particles. We showed that this model can nearly quantitatively predict the shear and extensional nonlinear rheology by careful tuning of only a few parameters to the linear rheology. We found a complex transient viscosity, with multiple inflection points and maxima under shear flow and a strong strain hardening under extensional flow, all in agreement with experimental observations. We also investigated the influence of each of the model’s parameters on the linear and nonlinear rheology.

WP6: Phase-field and finite-element macroscopic computations
The overall objective of WP6 was to model the debonding process of pressure-sensitive adhesives (PAS) on the macroscopic scale. Two very different numerical methods were proposed for this task: a) a phase-field model in which the interfaces are represented as a certain level set of a scalar function, the so-called phase field (a function that indicates in which phase each point in space is located), and b) a finite element code that works on an evolving (deforming) adaptive grid.

6.1 Phase Field Modeling
In phase-field models, surfaces and interfaces are represented by supplementary scalar fields, the so-called phase fields, which take different constant values in the two bulk materials and vary between these values across a well-defined front region which constitutes a diffuse interface. The time evolution of the interface position is described through an equation of motion for the phase field that reflects the physics of the problem at hand.

6.1.1. The Saffman-Taylor problem in three dimensions. In the course of MODIFY, we performed simulations of three-dimensional fingers, with quite surprising results. In cells with square cross section, the finger did not converge to the steady-state axisymmetric finger solutions predicted by Levine and Tu (Phys. Rev. A, 1992), but with time becomes thinner and thinner behind the tip and eventually pinches off. This was a surprising result and rather unknown in the pattern formation community; but it can actually be understood by a linear stability analysis of an infinitely long liquid cylinder enclosed by a second liquid. We have found that such a cylinder indeed undergoes an instability analogous to the Rayleigh-Plateau instability of a liquid jet. This offered us the opportunity to validate (successfully) the 3-d code by direct comparison to the linear stability calculation for this problem.

After validation, we performed extensive numerical simulations in the tube geometry in axisymmetric coordinates and found good agreement with the boundary integral results of Levine and Tu, which concern only steady states. Remarkably, the critical velocity beyond which no steady-state finger solutions exist was reproduced with excellent precision. Beyond this point, we observe that the interface between the two fluids undergoes a tip-splitting instability.

6.1.2. Phase-field models with tensorial mobility. Since the numerical simulation of phase-field models in 3-d is quite demanding in computing resources, it was important to explore all possible means to increase efficiency. Given, in particular, that the required discretization is set by the thickness of the diffuse interfaces of the phase field, it was desirable to work with interfaces that are as thick as possible. However, the diffuseness of the interfaces also induces spurious effects that scale with the thickness and that are often called “thin-interface effects”. The elimination of such effects can hence drastically increase the efficiency of a phase-field model since it makes it possible to increase the interface thickness.

In all phase-field models for two-phase flow in which incompressibility is enforced, the pressure field is obtained by solving a Poisson equation, with a source term that represents the capillary pressure. Since the viscosity is different in the two fluids, a suitable interpolation through the interface was needed. The standard approach is to make the viscosity a simple function of the phase field. We analyzed the precision of the solutions obtained with this method, that is, the difference between the result of the phase-field method and a sharp-interface solution. It was found that two effects linked to the finite thickness of the interface are present: an additional transport along surfaces and an interface resistance. Each of these effects could be eliminated for arbitrary interface thickness by a specific interpolation function, but the two interpolation functions are different, such that both of these effects cannot be eliminated at the same time. We showed that if the inverse viscosity (the mobility in Darcy’s law) is allowed to become a tensor inside the interfaces, both effects can be eliminated at the same time since components of the pressure gradient parallel and perpendicular to the interface can be treated separately. We thus obtained a drastically improved convergence with interface thickness in numerical simulations of some simple test geometries.

6.1.3 Phase-field model for bubble growth. During the debonding of a PSA, in most cases numerous bubbles form by cavitation at the substrate surface (the surface of the tack probe) and grow during further extension of the material. The bubbles are probably filled with a small quantity of residual gas, but the pressure remains so low that it can safely be neglected in comparison with the atmospheric pressure. Consequently, the bubbles can be considered as voids. In almost all the phase-field models for two-phase flow that can be found in the literature, both phases are considered as incompressible. Whereas this is still a good approximation for the PSA material, the bubble volume grows with time, which implies that the “bubble phase” must be compressible. However, since in phase-field models all physical properties have to be interpolated through the diffuse interfaces, it is difficult if not impossible to combine an incompressible fluid with one that has infinite compressibility. A possible solution for a convenient formulation of a phase-field model for the growth of bubbles is to consider both phases (material and bubbles) as compressible fluids, with a strong contrast in compressibility. Then, the physically realistic situation can be recovered – at the price of an increasing numerical effort – by increasing the contrast between the two compressibilities.

In the course of the MODIFY project, a new phase-field formulation of two-phase compressible flows was implemented, which implies that the density is a new independent variable. In both fluids, the pressure and the density are linked by an equation of state, specific for each phase. We validated this model by several test simulations with increasing geometrical complexity. The simplest case was actually a 1-d simulation, in which two layers of viscoelastic material are separated by a “gap” of void. Of course, in this situation there should be no adhesion of the upper layer on the substrate, and the force needed to strech the “sandwich” should be zero. However, due to the finite compressibility contrast in our model, a small residual force is transmitted by the bubble, which increases with the extension of the bubble. We studied the dependence of this residual force on the various parameters of the model, and then chose a set of parameters where this force was as small as possible. We emphasize that it is possible to reduce this residual force by increasing the contrast between the compressibilities. However, this leads to stronger conditions on the choice of the time step and therefore increases the computation time.

The next step was to carry out direct comparisons of the phase model predictions against finite-element simulations in the same geometry and for the same constitutive equation (an Oldroyd B fluid, for which the strength of capillary and elastic forces is characterized by the values of the capillary number Ca and the Deborah number De, respectively). A single bubble was enclosed between two plates, and the upper plate was lifted up at a constant velocity. The non-circular shape of the bubble was captured by both methods, and the shapes of the contour lines for the velocity field were very similar. Overall, the agreement between the results obtained by the phase-field simulations and the finite-element computations was very satisfactory, which opened the way to use the new method to explore the dynamics of the debonding process.

6.2 Finite elements
Several new finite element codes were developed to simulate the deformation of model adhesives in the usual tack experiments. New mesh generation codes were developed both in 2 & 3 dimensions which couple the elliptic-mesh generation methodology with domain decomposition and local mesh refinement around the deforming interfaces. In this way, large adhesive and bubble deformations leading to fibrillation can be followed accurately. The viscoelastic models mentioned in the Annex I of the Grant Agreement (Upper-Convected Maxwell, KBK-Z type, Oldroyd-B, PTT, FENE-CR) were used. Additionally we used the elasto-viscoplastic, elastic and hyperelastic models proposed to us during this project by the other participating teams (Neo-Hookean, Arruda-Boyce, Mooney-Rivlin, etc., carefully coupled or not with some of the previously mentioned viscoelastic models).

The differential models were used either in 2D or 3D simulations which focused on a cell of orthogonal parallelepiped shape, containing a single bubble, which is placed either inside it or in contact with its lower surface. Its upper surface can be removed at a constant velocity to simulate the tack experiments. On the side surfaces of the cell, symmetry conditions were used so that its repetition in both directions can reconstruct the entire film with the bubbles in it. The equations were discretized in a structured mesh and were solved using (a) the mixed Galerkin/finite element method for the velocities, pressure and location of mesh nodes and (b) the DEVSS-G with streamline upwinding method for the stress components. The numerical results demonstrated that the bulk debonding mechanisms during stretching of PSAs depend mainly on a velocity independent ratio between elastic, viscous and capillary forces. The 3-phase contact line formed by the intersection of the adhesive/air interface with the substrate may be fixed or a Navier-type slip condition may be applied on it.

The integral models were exclusively used in 3D simulations with an unstructured mesh. These simulations either focused on a cell, also of orthogonal parallelepiped shape, containing up to 10 bubbles, which are placed either inside it or in contact with its lower surface or up to 100 bubbles which were in contact with the lower substrate, when the entire adhesive is modeled. This allowed us to directly compare our predictions with the experimental observations from the well-controlled experiments conducted in ESPCI.

WP7: Micro-macro integration for materials design
A key aspect of MODIFY has been the clever and efficient bridging of the different scales through the pasing of information from one to the other. For the bridging of the experimental efforts with the macroscopic finite-element studies, we developed a new constitutive equation which was fully parameterized on the basis of the linear and non-linear rheological data collected under WP2. The new constitutive equation originated from principles of non-equilibrium thermodynamics by postulating an expression for the stress tensor that has contributions from two terms, one that captures the elastic behavior of the MODIFY materials and one that describes their viscoelastic behavior. For the elastic component, we made use of the molecular constitutive equation typically proposed in the literature for materials with a behavior that resembles rubber elasticity. It accounts for contributions from cross-links and virtual tube constraints around network chains. The viscoelastic component, on the other hand, was taken to be described by the Stephanou et al. model (J. Rheology, 2009) which has been shown to compare well both with rheological data obtained from non-equilibrium Molecular Dynamics simulations and experimentally measured rheological data for high density polyethylene (HDPE) resins. The model has been derived from the Generalized Brackets formalism of non-equilibrium thermodynamics, so it is thermodynamically admissible (it fully complies with the 1st and 2nd law of Thermodynamics). The model was capable of capturing the actual rheological data obtained in WP2 for the XMM samples extremely satisfactorily both qualitatively and quantitatively.

On the basis of non-equilibrium thermodynamics principles, we also derived a new slip boundary condition (b.c.) for adhesives on solid substrates. The resulting equation relates the slip velocity at the surface with the wall shear stress and involves 3 parameters:
• The relaxation time of tethered chains
• The equilibrium density of tethered chains
• The equilibrium average squared end-to-end distance of tethered chains

In the course of the 2nd period of the MODIFY project, we obtained the values of all these three parameters for the XMM19301 acrylic adhesive adsorbed on a-silica by resorting to detailed interfacial molecular dynamics (MD) simulations. We also carried out a detailed analysis of the structure of the adsorbed XMM19301 molecules on the substrate by computing the statistics of conformations formed by adsorbed segments in the interfacial area and are widely known in the literature as trains, loops, and tails.
The trains are defined as successive bonds along the main chain backbone with their atoms located inside the adsorbed layer, i.e. at a distance less than 6Å from the a-silica substrate. The loops are defined as sequences of backbone atoms connecting two trains, with centers, however, outside the adsorbed layer. Finally, the tails are defined as sequences of backbone bonds terminated at one side with a non-adsorbed chain end and at the other side by an atom connected to a train.

The final results of our atomistic simulations for the mean-values of the three parameters entering the new b.c. were thus reported as a function of the chain conformation (train, loop, and tail) developing at the wall. The corresponding b.c. was next employed in the macroscopic FE calculations of tensile deformation (under WP6).
Potential Impact:
D1) Potential Impact
The MODIFY project aimed at developing detailed knowledge and modelling of the mechanical response of Pressure Sensitive Adhesives (PSA). It implied the detailed physicochemical understanding of interfaces in relation to the selected materials composition. Furthermore, a simplified but sufficiently accurate mathematical representation of molecular structure, capturing its key physicochemical features, was required in combination with meso and macroscopic simulation approaches to ultimately describe adhesive behaviour. Such a multiscale modelling approach was extremely challenging from a scientific and computational perspective but essential to commence a rational design of PSA to address specific performance needs beyond experience based trial-and-error product developments.

Based on the set forth project objectives, the final results generated by the different partners, and the industrial relevance of these results into various fields, the potential impact of MODIFY expands beyond the usual academic horizons as eventually captured in scientific publications, lectures, and future research.

At the socio-economic level, we mention that the European PSA market itself is valued at ca 1.4 Billion Euro. If products made with PSA are considered, the figure is at least three times higher. Energy costs and regulatory compliance pressure are increasing the need for more energy efficient, environmentally friendly and easy to recycle systems. The successful modelling of the interactions at the interface(s) of PSA formulations of direct relevance to industrial and technological applications, such as the family of Lucalen (ethylene/acrylic-acid or ethylene/acrylic-acid/butyl-alcohol) copolymers which are produced by the high pressure polymerization technology Lupotech TTM from Lyondellbasell will lead to new products for extrusion coating purposes with cleaner (no residual adhesive transferred between interfaces) easy peel-off from the target surface combined with easy disassembly of the product at the time of disposal/recycle.

In this direction, MODIFY has provided a significant step forward towards understanding the adhesion process of polymer to various surfaces and the failure mechanism. Furthermore, the developed tools to characterize polymers with respect to non-linear rheological and adhesive properties, that were developed and optimized throughout the project, are valuable for developments in the field. Specifically, we are a significant step further on the way to being able, from input on the polymer structure and chemistry, to predict the final product performance and properties. We mention, for example, that today, incineration or recycle systems are generally employed at the end of the life cycle of the PSA label product. Incineration has limitations and negative environmental impact regarding the by-products produced and the resulting composition of the emission to the environment, since the PSA acts as a contaminant in the separation process either in the film or in the paper label system. Ideally the material of construction of the label should match that of the labeled substrate with minimal additional contamination of the PSA and other formulation components. MODIFY has helped develop systems mimicking the performance of current adhesives but with enhanced recyclability and overall lower system raw material and energy costs due to better adhesive efficiency. This is extremely important given that the estimated recycling costs associated with paper and filmic PSA label are today in the 0.5-1.0 Billion Euro range, implying enormous savings that could be globally leveraged in the industry through simplification or cost reduction in the recycling process.

Overall, the research carried out in the course of the MODIFY project is such that allows us now to make specific and extremely helpful recommendations for the design of new PSA’s with optimized performance properties. A significant part of the MODIFY project was spent developing methodologies for how best to study PSA’s. The method enabled the identification of the most important parameters defining adhesion and allowed an optimization process for characterizing and comparing individual PSA formulations with one another. In the later stages of the project, the methodology was extrapolated toward commercially relevant PSA. This helped us realize PSA formulations with improved properties in relation to standard tests such as the tack, shear and peel ones as well as overall processability; these tests play also the role of the critical variables for differentiated PSA material development. The MODIFY methodologies provide a finer analysis of the PSA structure and by being much more sensitive to small changes in formulation or synthesis conditions offer tremendous advantages to future PSA materials design strategies.

Given the above successes and considering that PSAs are ubiquitous in the everyday life of citizens and they are increasingly used today due to their simple and safe handling properties, the impact of MODIFY will also be important at the social level. The new knowledge will help expand even more the applications domain of PSA materials, especially in areas where they can displace more hazardous types of glues such as solvent based or curing type glues as described below. MODIFY will contribute significantly also to the training of young European scientists in modern, state-of-the-art modelling, computational, and experimental (materials synthesis, characterization, product design) skills. By putting more science into the business of making adhesives, it will help upgrade the skill requirements of the work force employed in the business. This is particularly important given that computing skills are increasingly becoming an essential part of tomorrow’s society; our project will train several young scientists to the most modern computational techniques.

Finally, MODIFY will have a tremendous environmental impact considering that it directly addresses the need for progressively replacing products manufactured with hazardous technologies (European Directives 67/548/EEC and 79/831/EEC dealing specifically with the classification and labelling of solvents) with a new generation of high-performance nanostructured and cleaner materials requiring less hazardous and more energy efficient technologies. In the PSA area, high energy costs (due to the drying process), hazardous waste disposal requirements and restrictions on pollution have contributed to the shift from solvent-based PSA to water-based and hot-melt PSA which do not use any solvent during processing and are manufactured with more energy efficient processes. This shift has started in the late 1980’s and is continuing now. The market share of solvent-based adhesives was however still 50% for packaging tapes in 1998 (data from DOW); in labels, the solvent based PSAs represent only 10% of the market and a further decrease of that proportion will require a clear improvement in performance of water-based or of hot-melt PSAs which cannot be achieved by empirical optimisation of existing products. Our advanced understanding of the behaviour of acrylic PSAs will greatly help in devising strategies for the design of water-based acrylics (which are easier to handle and safer than many conventional adhesives) with sufficiently good performances to replace currently used solvent-based acrylics.

D2) Main Dissemination Activities
Overall, the main deliverable items of MODIFY are a set of methodologies and state-of-the-art design tools with many potential applications. To achieve their dissemination in the best possible way, measures were taken in the course of the project at two levels:
• Industrial dissemination: Students and experienced researchers of the academic partners were invited to stay at the DOW and LBI sites and implement the newly developed tools
• Academic dissemination: Scientific papers are being written in international, high-profile science and engineering journals. Partners attended and (will continue to) attend top-level scientific and technical conferences in the general areas of adhesion and computational materials science and engineering, for the purpose of providing the work performed in MODIFY the highest visibility. Given the richness of physical phenomena addressed (interfacial interactions between colloidal particles in emulsion PSAs, adhesion to the substrate, deformation during debonding from the substrate, fracture) and the breadth of scientific experimental, theoretical and modeling tools to be developed – this included both methodologies and results – dissemination across discipline boundaries was also pursued. The MODIFY efforts were presented in a wide area of conferences: (a) AERC, SOR, ACS, APS, AIChE, and MRS; (b) meetings of the Adhesion Society; (c) Conferences on the Thermodynamics of complex fluids, (d) International Symposia and Conferences on Macromolecules, Fracture, Surfaces and Interfaces, and Polymers in dispersed media colloids, (e) the International Congress on Rheology and the IUPAC World Polymer Congress, and (f) International Workshops on the Multiscale Modelling of Materials.

D3) Exploitation Plan
Based on the set forth project objectives and the final results generated by the different partners, the exploitation plans break down into a number of specific fields. The focus for these various fields is on the industrial relevance and thus expands beyond the academic exploitation of the generated knowledge as eventually captured in scientific publications, lectures, and future research, addressed elsewhere in the final report. The two industrial partners, Dow and LBI, are aiming to maximize the knowledge leverage in their specific fields of interest.

Resin design. Several PSA structures have been synthesized and characterized to the extent of the state-of-the-art experimental tools available. Linear and branched structures as well as commercial PSA formulations were provided for further analysis and adhesion testing. Quickly it became clear that these structures either in a pure or formulated form are difficult to characterize molecularly. Drawing direct correlation of a structure – performance nature remains therefore to a large extend a holistic exercise. Nevertheless a number of insights have been gained at a macroscopic level (i.e. rheology and adhesion behavior). Accordingly the next steps will entail:
• Resin synthesis and formulation design using a Design of Experiment approach to tailor and capture the operational performance window in relation to the PSA materials composition – Plan: 2nd Half 2012 – 2013
• Identification of the right experimental tools and relevant methodologies that enabled the elucidation of the meso- and macroscopic behavior of PSA’s. Rheological methodologies in the linear and non-linear viscoelastic regimes indicated operational shear or elongational windows characterizing interesting PSA features. In addition, novel adhesion characterization tools were developed more aligned to the industrial use of PSA and more readily providing scientific measures accessible for modeling purposes.
Accordingly, the immediate future actions will include:
• Acquiring of novel adhesion test equipment – Plan: 2013
• Implementation of the shear and extensional rheology characterization methodology as a standard test for commercial PSA’s. This will require expanding the rheological characterization equipment - Plan: 2012: standard test; 2013: dedicated rheometer purchase.
• Generation of structured data and representation through user friendly interfaces – Plan: 2014

Multi-scale modeling. A significant body of work was developed in terms of the physical theory building and efficient computational algorithm definition. At each scale - atomistic, mesoscopic, and macroscopic – efforts were put in place to either expand existing procedures or develop novel theories and concepts that could capture as accurate as possible the essential physics of PSA’s. The complexity and time consuming nature of these tasks however left a very important work for completion. Connecting the computational results obtained at the different time and length scales will be essential for the implementation and use of the present algorithms in an industrial environment. In addition the user friendliness of the eventual tool combined with the ability to generate the necessary input parameters is detrimental for an optimal use. A significant effort will need to be put in place to achieve this target and will require further research covering the mathematical and computational aspects of this challenge. New funding mechanisms will need to be sought for as the challenge has now become more of an ICT nature versus the physics and industrial applicability oriented project MODIFY.
Accordingly the next steps will entail:
• Inventorisation of the state-of-the-art computational algorithms at each scale level of the multi-scale modeling space – Plan: 2013
• Definition of performance prediction criteria and alignment of capabilities that are able to accomplish this requirement – Plan: 2013
• Developing connector software bridging in-output – Plan: 2014
• Optimization of computational algorithms – Plan: 2014
• User interface design – Plan: 2015
• Computational infrastructure integration – Plan: 2015

Intellectual property. Modeling is an exercise in developing tools that, provided the correct input parameters are used, and the underlying algorithms capture the physicochemical nature of the phenomena of interest sufficiently well, enables a prediction of potential options. In the present case the options reflect critical synthesis variables defining a desired molecular architecture, which can be related to a PSA performance criterion in a specific application. Intellectual property (IP) will be mainly developed based on the defined resin compositions. Besides the IP consequences of a modeling effort for resin composition and performance, additional IP is envisioned in the algorithms themselves. These are of particular interest of SME’s focusing on polymer modeling software commercialization. The partner developers need to consider the feasibility of pursuing this avenue. Further IP is to be captured for the novel adhesion equipment and associated experimental devices as developed in the course of the project.
Accordingly the next steps will entail:
• Capture IP for potential novel PSA materials as based on the simulated and experimental performance evaluations - Plan: Aligned to experimentation plan
• Capture IP for significant algorithms - Plan: 2012
• Capture IP for novel analytical tools - Plan: 2012

Further Research & Development. As indicated above a 3 year project enables a significant progress in a focused area but often leave a number of open ended topics that require further research or development as well as pragmatic translation of knowledge into tools relevant for industrial users. A number of topics have been indicated as to requiring further efforts:
• The computational physico-chemistry theories need constant improvement to refine their accuracy and include additional structural features – Plan: ongoing research
• Connectivity of various modeling techniques and approaches used for the simulations at different length and time scale need working out further – Plan: funding for 2013-2015 requested
• Computational Interfacing implies the translation of academic codes into robust user friendly but relevant simulation tools for specific users. It implies ICT` focus as well as training and close interaction with the final users to fulfill their specific needs – Plan: funding for 2013-2015 requested
• Continued collaboration will be sought between various partners for new projects including specific alliances tailored to specific needs as arisen from the project – Plan: 2012 - 2013 EU and national funding mechanisms are explored.

In conclusion, project MODIFY has provided a significant step forward towards the development of simulating the performance of complex PSA’s. A number of further steps are planned by the industrial partners to exploit the findings. The modeling implementation still requires a significant effort to achieve the industrial practice but the steps to be taken are clear. Of immediate relevance are the experimental tools and methodologies developed during the project. They provide a basis for refining understanding and creating a data driven modeling approach.