ThreeBond Technical News
Issued July 1, 2021

98

Adhesive Analysis Using Molecular Dynamics Simulations
Introduction
Recent years have seen a shift towards the use of resin (polymeric material) as a material for
structural components of vehicles such as airplanes and automobiles with the aim of reducing
weight. As welding cannot join these resins and various inorganic materials, including iron, lightmetals and ceramics, the number of opportunities for the use of adhesives is expanding.
Automobiles, for example, contain components of various types and sizes, from large parts suchas car bodies and powertrain components to small parts such as electrical components. This
diversification of materials and parts has presented a number of challenges in terms of bonding
with adhesives. For this reason, we have been implementing multifaceted analytical methods1, 2) toprovide tailored solutions to issues faced by our customers.
However, even in 2021, it is not easy for adhesive manufacturers like ourselves to have a complete
understanding of the phenomena surrounding adhesion. Some of the many areas that are still
not fully understood include bonding mechanisms, deterioration mechanisms, adhesive bonding
compatibility prediction and inspection methods. As a result, product design often relies on
empirical knowledge.
As part of our efforts to explore a product design approach that is distinct from our empiricalknowledge, we have also commenced studies based on molecular simulations. As a proof ofconcept, this article introduces some examples of our work based on using molecular dynamics
simulations to understand phenomena relating to adhesion, including bond strength prediction andthe effect of surface contaminants.

Table of Contents
Introduction..................................................1
1. Molecular Simulations and Adhesives....2
2. Solubility Prediction.................................2
3. Mechanisms For Increased Elasticity inCured Adhesives.....................................2
4. Bond Strength Prediction........................4.

5. Adhesion to Oily Surfaces.......................4
6. Interfacial Segregation of SpecificChemical Structure..................................5
7. Gas (Water Vapor) Permeation...............6
Closing........................................................81

1.

Molecular Simulations and Adhesives

The main areas in which computer simulations are used
can be divided into electronic state level, molecular andatomic level, mesoscopic and continuum level simulations3).
The main focus of this article is molecular and atomic level
simulations. The examples covered were performed using
molecular dynamics (MD) calculations with timescales
ranging from picoseconds to tens of nanoseconds and box
sizes ranging from several angstroms to tens of nanometers.
MD calculations relating to adhesion have appeared inacademic papers and similar publications since about
2010. In recent years, examples such as the calculation ofsolubility parameters and the characteristics of crosslinking
resins have been included on the websites of software
manufacturers4-6). As a result, this method of calculation has
become more familiar, even to companies that have mainly
used experiments, including ThreeBond.
Based on the order in which they occur during the use ofadhesives, adhesion-related phenomena include “wetting”
when the adhesive is applied to the adherend, curing andassociated shrinkage of reactive adhesives, and thermal
stress (shrinkage) associated with cooling after curing in
the case of heat-curable adhesives. In addition there are arange of processes, such as stress and deterioration, that
occur during actual use after bonding. In summary, there
are a large number of parameters that can affect the strengthof a part7). It could be said that this is why the product designof actual components is often performed empirically bylooking at the overall strength and durability of parts.

Materials Studio Forcite from Dassault Systèmes K.K. wasused for MD calculations, while COMPASSII and III wereused for the force field.

2.

Adhesives are compounds of multiple resins. As a result,the solubility of these resins is an important consideration.
In addition, acrylic adhesives are often designed inconsideration of the solubility of the adhesive and theadherend. For this reason, emphasis has been placed onsolubility parameter (SP) values, which are an index ofintermolecular affinity. SP values are substance-specificvalues defined as the square-root of the cohesive energy
density of the substance. Values with closer SP values
have higher affinity with each other, meaning that they are
more soluble or more suitable for use as an adherend. SP
values are generally estimated using the group contribution
method, however, a calculation method using MD when
there is no available data on existing similar compounds has
also been established8). Using this method, we calculated
the SP value of solvent molecules and compared the results
to the values in existing literature9) (Fig. 1). As a result of
cost-saving during calculations, some slight discrepancies
were observed. However, even the largest deviations were
within 10% of the measured values and these values canbe considered sufficient for predictive purposes. These
calculations are mainly used for applications such asincreasing efficiency in the design of acrylic adhesives.
30

20

Molecular simulations provide one potential approach tosolving this issue. While current general-purpose computers
can only perform calculations covering an extremely limited
timescale and box size, MD calculations may be an effective
tool that enables users to visualize phenomena virtually andobtain prediction data.

As examples of our current work using MD calculations, thisarticle covers instances of solubility prediction, mechanisms
for increased elasticity in cured adhesives, bond strength
prediction, adhesion to oily surfaces, interfacial segregationof specific chemical structures and gas (water vapor)permeation.

2

25

Experimental(MPa)

1/2When designing adhesives, however, there are innumerable
combinations of resin materials to be prescribed, and thenumber of combinations is expanding rapidly. While there
is demand to predict results based on some form of data
before proceeding to experiments, the present reliance on
experience in many cases remains a challenge.

In addition, confirmation that the physical characteristicsof the cured adhesive are consistent with those obtained
through MD calculations can be considered an important
method of confirming the feasibility of adhesive designs.

Solubility Prediction

15

10
10

15

20

1/2

Calculated (MPa)25

30

Fig. 1 Comparison of Organic Solvent SP values
Calculated Using MD with Measured Values

3.

Mechanisms For Increased Elasticity inCured Adhesives

This section describes the use of simulations to performstudies relating to the curing properties of epoxy resins.
Epoxy resins containing phenyl glycidyl ethers (Fig.2)
have been shown to be tougher and more elastic than other

200

0.94
0.93
0.92

Density-1 (cc/g)

150

0.91

TMA (μm)

epoxy resins10). This differs from the conventional methodof adding rubber or a similar flexible molecular structure
into cured epoxy resin for the purposes of toughening theresin. This is also specific in that the added epoxy resin ismonofunctional. Believing that understanding the reason
behind this may prove useful in future adhesive design, MD
calculations were used to analyze the cause.

0.90

100

0.89
50

0.88
0.87

O

0

50

O

Fig. 2 Examples of Phenyl Glycidyl Ether
Chemical Structure

In this case, MD was used to represent the cured adhesive andthe elastic modulus was calculated based on this deformation
simulation. In order to obtain the physical characteristics ofa cured epoxy resin through simulation, the polymerization
reaction with the amine compound, which acts as the curing
agent, must first be calculated. However, MD cannot be used
to calculate chemical reactions. Therefore, the atoms relating
to the reaction were designated in advance and the bonds
were rearranged (made to react) when they came within a
set distance11, 12). In addition to distance, this methodology
also uses the reaction probability k, which takes activationenergy into consideration, to determine whether bonds are
rearranged (Formula 1). When the value of k is larger than
the random number p(0, 1), a reaction is made to occur.
When it is smaller, no reaction is made to occur. In addition,
kinetic energy equivalent to the heat of formation is added
to molecules that have undergone reactions in order topromote reactions. By repeating this process, a cured epoxy
resin model was obtained.
Formula 1: k = A exp (-Ea/RT)
A: Acceleration factor, Ea: Activation energy,
R: Gas constant, T: Temperature
When the density, elastic modulus, and glass transition
temperature of this cured material model were comparedwith experimental values, an appropriate correlation wasobserved. The glass transition temperature comparison
is shown as an example (Fig. 3). The temperature of
the inflection point estimated through calculation wasapproximately consistent with that of measurement dataobtained through thermomechanical analysis (TMA). Thisconfirms the appropriateness of the model.

100

150

200

Temperature (℃)

250

0.86

Fig. 3 Comparison of Glass Transition
Temperatures (Temperature Sweep ofReciprocal of Density) Calculated Using
MD and Measurement Data (TMA)

In addition, the radial distribution function of the functionalgroup, the stress distribution under an applied load andthe free volume when different concentrations and typesof phenyl glycidyl ether are added were calculated. Theircorrelation with the elastic modulus was then examined. As
a result, it was observed that the elastic modulus improvesas the free volume ratio inside the simulated cell decreases(Fig. 4).
3.5
3.0

Tensile Modulus (GPa)

O

0

O

2.5
2.0
1.5
1.0
0.5
0.0
0.160

0.165

0.170

0.175

0.180

0.185

Free volume ratio

0.190

0.195

Fig. 4 Relationship Between Free Volume
and Elastic Modulus When Different
Concentrations and Types of Phenyl
Glycidyl Ether are Added

In other words, this suggested that when a phenyl glycidyl
ether is added to a system containing a standard epoxy resin
and an amine compound, it acts in a similar manner to an
antiplasticizer by packing the free volume and improving
the elastic modulus. It has been reported that adding anantiplasticizer to epoxy resin increases the elastic modulus,
improves toughness and reduces water absorption13). It
appears that a similar phenomenon was observed on thisoccasion.
We believe that molecular simulation can also be applied
to building hypotheses with regards to the relationshipbetween the composition of adhesives and their physicalproperties, as is shown by this example.

3

Bond Strength Prediction

This section describes bond strength prediction.
Following on from section 3, it describes an epoxy resin
containing a phenyl glycidyl ether. It has been reported
that this formulation improves bond strength in addition to
improving bulk toughness and elasticity14).
Molecular simulations were performed in order toinvestigate whether the improvement in bond strength could
be confirmed through this method. Due to the limited box
size that can be covered by MD calculations on generalpurpose computers, these calculations were performed foran adhesive surface approximately 4 to 5 nm along eachside. The results have been included in this article because atrend towards improved bond strength was observed.
A simulation cell in which an epoxy monomer and anamine monomer are mixed were stacked onto alumina andstructural relaxation was performed. The curing simulation
described above was then carried out. Then, the temperatureof the cell was lowered to room temperature and the curing
shrinkage and heat shrinkage were calculated. Deformation
calculations were performed on the obtained model in order
to examine the stress-strain characteristics.
The area under the resulting stress-strain curve (Fig. 5)
was used to evaluate the bond strength on this occasion.
The calculated relationship between bond strength andthe concentration of added phenyl glycidyl ether is shownin Fig. 6. The results were consistent with experimental
results, as the amount of phenyl glycidylether increased, thebond strength increased.

Modulus of toughness (GPa)

4.

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

0

5

10

15

20

25

Content of Monoglycidyl ether (mol%)

30

Fig. 6 Relationship between Bond Strength andConcentration of Added Phenyl Glycidyl
Ether Calculated Using MD

In addition, MD simulation calculation limitations apply
not only to the box size, but also to time. Consequently,
the displacement per unit time may become a strain rateequivalent to or higher than the actual impact load andthere may be no impurities on the surface of the adherend,
resulting in a higher absolute value than in reality. For
this reason, the evaluation of bond strength is considered
to be a relative evaluation. Even so, there have been cases
in which these bond strength evaluation results have been
implemented in FEM as the bond strength between thefiller and matrix resin for multiscale simulations and futureapplications can be expected15).

0.40

5.

0.35

Stress (GPa)

0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.0

0.5

1.0

1.5

Strain (-)

2.0

2.5

Fig. 5 Epoxy Resin Stress-Strain Curve
Calculated Using MD

3.0

Adhesion to Oily Surfaces

This section describes how the same simulation used
above to predict bond strength has been applied to thevisualization of bond failure when foreign matter such as
oil is present on the surface of the adherend. The simulation
cell was created using the same process as above, with the
exception that oil molecules were placed on the surface of
the alumina. Snapshots of the bond failure are shown in Fig.
7. The visualization shows cracks forming around the oil,which is shown in green, before failure occurs. At this time,
the stress-strain curves at the time of failure were calculated
for cases where the molecules of the oil and adhesive wereprevented from diffusing into one another and cases where
they were allowed to diffuse for a certain period of time
(Fig. 8). Looking at the stress-strain curves, it can be seenFig. 7 Snapshots of Bond Failure Simulation

4

that when the oil and adhesive were allowed to diffuse
for a certain period of time (Oil_Mix), the area under the
curve is larger and the amount energy required for failure
to occur is larger than when diffusion was not allowed tooccur (Oil_Non_Mix). In other words, these result canbe said to reinforce the deduction that the influence of oilon the surface of an adherend can be reduced by mixing
the oil with the adhesive. Interfacial phenomena such as
adhesion to oily surfaces are difficult to observe directly
and empirical understanding has generally been based onindirect experimental data. Looking at such phenomena
from a different perspective through simulation has thepotential to enable the certainty of this understanding to befurther investigated.
0.35

Blank
Oil_Mix
Oil_Non_Mix

Stress (GPa)

0.30
0.25
0.20
0.15
0.10
0.05
0.00

0

1

2

3

Strain (-)

4

5

Fig. 8 Simulated Stress-strain Curves forDifferent Oily Surfaces

6.

Interfacial Segregation of SpecificChemical Structures

This section describes the interfacial segregation of specificchemical structures. There has been a case in which MD
calculation was been used to examine the amine segregation
mechanism at the interface when an epoxy resin and aminecompound were cured on a copper substrate16). We used thesame method to examine how the functional groups near an
alumina interface change when resin is cured in a compoundsystem with modified silicone containing methoxy groups
and a silane coupling agent.
First, a model in which modified silicone (Fig. 9) and a silane
coupling agent (Fig. 10) are mixed was created and layered
onto alumina. Relaxation calculations were then performed.
The methoxysilane curing reaction was then performed
using the same method as for the MD calculation in section
3, and changes in the segregation of functional groups that
occurred around the interface when curing took place were
examined.

H3C

O

H3C
O

CH3

O

Si
CH3

O
CH3

10

O

Si

CH3

O
H3C

Fig. 9 Chemical Structure of Modified Silicone
Used in Simulation

H3C
H3C

O
O

O

Si

NH2

CH3

Fig. 10 Chemical Structure of Silane Coupling
Agent Used in Simulation

The results showed that there was confirmed segregationof terminal methoxysilane moieties of the modified
silicone and amino groups from the silane coupling agent
at the alumina interface when the relaxation calculationis performed with the resin on the alumina, even after arelatively short relaxation calculation where the density is
not stable to a significant degree (Fig. 11). The figure showsa model in which resin is placed on alumina. The model
has been rotated 90° to the right, and is arranged so thatthe graph positions correspond to those of the model. In
addition, although it is not in the model, the calculation was
set with additional alumina to the right of the model. This
is why the same segregation can be observed at the left andright ends of the graph.
It was found that the segregation of methyl groups increased
as the curing reaction progressed. This is the reason for theenlarged peaks at the right-hand side of Fig. 12 and Fig. 11.
This suggests the presence of polypropylene glycol methylgroups aligned towards the interface. On the other hand, nochange in the amount of amino groups near the interface
were observed, even when the curing reaction occurred. In
other words, it can be seen that there is a continued presenceof the silane coupling agent containing an amino group near
the interface even when a curing reaction occurs. (Fig. 13)
Although not shown in the graph, the amount ofmethoxysilane segregation at the interface decreases as thereaction progresses. This may be because methoxy groups
are consumed by the reaction.

5

Amino group
Mass Density (g/cm3)

0.10
0.08

Curing Degree
0%
17 %
27 %
38 %

0.06
0.04
0.02
0.00
0.85

0.90

0.95

Distance ratio

1.00

Fig. 13 Changes in Segregation Behavior due toCuring Reaction of Amino Groups nearInterface

Mass Density (g/cm3)

1.2

It can be envisioned that measurement of the actual
segregation at this type of interface could be performed witha combination of readings obtained through means such as
X-ray photoelectron spectroscopy (XPS), sum-frequency
generation (SFG) and electron microscopy (TEM and SEM),
however, we believe that considering these phenomenon byadding the information obtained from the simulation willlead to a better understanding of adhesion.

Methoxysilane
Aminosilane
Amino group
Methyl group

1.0
0.8
0.6

7.

0.4
0.2
0.0

0

20

40

60

80

Distance (Å)
Fig. 11 Molecular Model of Modified Silicone
Containing Methoxy Groups and Silane
Coupling Agent Layered on Alumina
and Relaxed, and the Functional Group
Density Distribution at That Time

Methyl group
Mass Density (g/cm3)

0.8
0.7
0.6

Curing Degree
0%
17 %
27 %
38 %

0.5

0.3
0.2
0.1
0.90

0.95

1.00

Distance ratio
Fig. 12 Changes in Segregation Behavior due toCuring Reaction of Methyl Groups nearInterface

6

Moving on from the calculations related to direct adhesion
covered so far, this section describes gas permeation
simulations. The purpose of this work is to predict the gas
barrier properties of sealants and to consider to deterioration
mechanism due to water.
Our company produces sealants for gaskets for automobile
engines, LCDs and organic EL for electronic components.
These products must have liquid and gas barrier properties.
Therefore, there was a need for simulations that could beapplied to the design of these products. In particular, it was
believed that the screening of resin raw materials for use inproducts could be simplified if the permeation of gases suchas helium and hydrogen, which must be measured using
special equipment, could be predicted using simulations.
Water vapor permeation simulations are also being explored
for applications relating to the deterioration of adhesion
moisture resistance in addition to uses relating to barrier
properties. In other words, in addition to the permeation ofwater vapor into the cured adhesive, the intention in future
is to also examine the arrival of water vapor at the adhesiveinterface and the resulting deterioration of adhesion.

0.4

0.0
0.85

Gas (Water Vapor) Permeation

A method for calculating the diffusion coefficient of gas
inside a polymer using MD had already been established17).

Under this method, gas molecules are placed inside themodel in advance. The mean square displacement over time
is found and the diffusion coefficient is then calculated fromthis slope. When applied to gas permeation, however, thismethod does not take solubility into account, including
the dependence of molecular transfer on solubility to thematerial surface and internal diffusibility18). This time, thepossibility of using simulations to create a prediction that
includes solubility and diffusion was examined.
While distinct from gas permeation, there has been
an example of using MD calculations to examine themechanisms of the molecular level water transport and ion
rejection of an osmosis membrane when saltwater is used
to produce pure water19). In this case, a polymer membrane
was placed between a saltwater layer and a pure water layer.
The difference in concentration was then used as the driving
force to calculate the water permeation of the polymer.
Using this as a reference, we placed a layer of acrylic resin
cured by radical polymerization between a gas layer anda vacuum layer. The gas permeation was then calculatedusing the difference in gas pressure as the driving force (Fig.
14). The example featured in this article covers permeation
between water and helium.

Vacuumlayer

Acrylic resin
layer

Gas
layer

Fig. 14 Overview of Calculated Simulation Cell

The cured material model was based a model inwhich tetrahydrofurfuryl acrylate (THFA), dimethylol
tricyclodecane diacrylate (DCPA) and a polymerization
initiator are mixed at a molar ratio of 30:1:1. A cured
material model was then created using the same method
described in section 3, with the acrylate changed to a nonyl
phenol ethoxylate (n = 1) acrylate (NPEOA). Fig. 15 shows
a plot of the number of water molecules permeating theacrylic resin layer over time. The temperature of the system
is set to 300°C with high-pressure water, enabling results tobe obtained in a short time. Quantitative evaluation is notpossible due to the change in the pressure difference, whichis acting as the driving force. However, relative evaluation
between acrylic monomers is possible. Although this article
presents a simple comparison between two types of acrylic
monomer, it was found that the order of permeability ofdifferent monomers can be predicted effectively compared
to tests for the determination of water vapor transmission
rate (JIS K 7129-2), including with other monomers. In
addition, the order of the results when MD calculations were
performed for a longer time at 60°C was the same as thoseat 300°C.
For helium permeation, MD calculation was performed
using the same method at 25°C and 10 atm. The results
shown in Fig. 16 were obtained by comparing the same
monomers as for water molecule permeation.
While this is also a relative comparison, differences in gas
permeability derived from the chemical structure of themonomer can be predicted. Referring to this type of datawhen designing adhesives and sealants can be expected
to improve development efficiency. It also has potential
applications in confirming the feasibility of designs.

500

THFA
NPEOA

THFA
NPEOA

25

Number of transmitted He

Number of transmitted Water

30

400

20
15

300

10

200
100
0
0

200

400

600

Elapsed time (ps)800

Fig. 15 Simulation Results Showing Water
Molecule Permeation Over Time

1000

5
0
0

1000

2000

3000

Elapsed Time (ps)4000

Fig. 16 Simulation Results Showing Helium Atom
Permeation Over Time7

Closing
This article covers several examples of the use of molecular simulation in studies designed to further understanding ofphenomena related to adhesion. Although simulation technology remains in the trial and error stage, the potential for simulation
to be used in combination with results from experiments to complement their respective deficiencies and build understandingof the phenomena being studied has been demonstrated.
In future, we intend to continue to utilize our existing analytical methods and combine them with simulations as appropriate tohelp solve our customers’ problems, improve development speed, and create hypotheses.
Adhesion is an esoteric area of study that requires an interdisciplinary understanding of concepts ranging from surface
chemistry, polymer physics, and fracture mechanics to the interface and bulk phenomena predicted by the simulations in thisarticle. We continue to achieve consistent results in this field as we proceed with research and development based on input fromlarge numbers of users, suppliers, academic societies and university professors. We would like to thank all involved parties fortheir support, and we will strive to continue driving development in the field of adhesion.
<References>
1) Tanaka, Shigeo et al. Technical News 86, ThreeBond (2015)2) Ichikawa, Naoto et al. Technical News 71, ThreeBond (2008)
3) Japan Association for Chemical Innovation. Computer Simulation of Polymeric Materials: Applications of the OCTA
System (Expanded Edition), p. 5, The Chemical Daily Co., Ltd.
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5) Dassault Systèmes K.K. website: https://www.3ds.com/ja/products-services/biovia/products/molecular-modelingsimulation/biovia-materials-studio/materials-science/
6) Daikin Industries, Ltd. website: https://www.comtec.daikin.co.jp/SC/example/
7) Frank W. Reinhart, “Adhesion and Adhesives Fundamental and Practice”, p. 9, Soc. Chem. Ind. (1954)
8) M. Ishida, et al. Sumitomo Chemical Technical Review, 25 (2015)9) J. Burke, The Book and Paper Group ANNUAL, 3 (1984)
10) Y. Miyaji et al. Summary of the 55th Annual Meeting of the Adhesion Society of Japan (2017)11) T. Okabe et al., Polymer, 54, 4660 (2013)12) T. Okabe et al., European Polymer Journal, 80, 78 (2016)13) V. Sauvant et al., J.Appl. Polym. Sci, 82, 759 (2001)
14) Y. Miyaji et al. Summary of the 56th Annual Meeting of the Adhesion Society of Japan (2018)15) Dassault Systèmes K.K. website: https://www.3ds.com/fileadmin/PRODUCTS-SERVICES/SIMULIA/Resourcescenter/PDF/2018-SAoE-Multiscale_Modeling_of_Polymer_Composites_From_Atomistic_Simulation_to_Structural_
Analysis.pdf
16) Yamamoto, S. et al., Appl. Polym. Mater., 2, 1474 (2020)17) M. Meunier, J. Chem. Phys., 123, 134906 (2005)18) K. Nagai et al. Barrier Technology, p. 11, Kyoritsu Shuppan
19) T. Yoshioka et al., Membranes, 8, 127 (2018)
ThreeBond Co., Ltd. R&D Group
Technical Marketing Division, Technical Development Department
Naoya Otsuki
Masazumi Furukawa
Takashi Sugio

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Tel: +81-42-670-5333