The study described in this dissertation aims to achieve a detailed atomic-level understanding of rubber–brass adhesion through a computational approach. In particular, the following questions should be answered:
• What is the role of the functional groups of the rubber structure in interfacial interaction?
• How do copper sulfide, zinc sulfide and zinc oxide affect the interaction between rubber and brass at the adhesive interlayer?
• What is the promotional effect of cobalt as an additive in rubber–brass adhesion?
• What are the possible, more economical, and effective transition metals that can be used as alternatives to substitute for the currently used cobalt additives?
2 Models and methods 2.1 Models
2.1.1 Surfaces and dopants
Because both non-stoichiometric copper sulfide (CuxS) and stoichiometric mono copper sulfide (CuS) are formed at the adhesive interlayer of rubber and brass, two bulk models that consist of hexagonal copper(II) sulfide and ideal cubic antifluorite copper(I) sulfide are constructed37 for the adsorption studies. The usage of two idealized stoichiometric copper sulfides is a simplification that does not cover all the specific details of the complicated adhesive interlayer system. On the other hand, only one bulk model is created for zinc sulfide, where cubic zinc blende polymorph38 is used. Other than sulfide, adsorption on the oxide surface has also been studied as the presence of zinc oxide at the adhesive interlayer has been reported. The bulk model of zinc oxide is constructed from hexagonal wurtzite.39 The details of the optimized cell dimensions alongside the experimental values are tabulated in Table 1.
Table 1. Optimized cell dimensions (in Å) within the experimental space group symmetries for ZnS, Cu2S, CuS, and ZnO bulk structures. The values shown in parentheses refer to Cu2S(111) slab, are four and six atomic layers, respectively. Two slab models for zinc oxide are cleaved from the optimized bulk structure, since both ZnO(001)47 and ZnO(110)48 have been reported to be stable surfaces. A (2 x 2) supercell is created for the ZnO(001) surface, while a (1 x 1) supercell is created for the ZnO(110) surface. Both surfaces consist of four atomic layers. The corresponding surface models are visualized in Figure 6. Throughout the study, the lower halves of all sulfide and oxide surfaces are fixed at the equilibrium bulk environment, and the upper halves are relaxed.
Figure 5. Top and side view of (a) ZnS(110), (b) Cu2S(111), and (c) CuS(001) surfaces.
Figure 6. Top and side view of (a) ZnO(001) and (b) ZnO(110) surfaces.
To study the influence of different transition metals as surface dopant atoms on the adsorption of the rubber adsorbate models, the doping method is utilized, where a metal atom on the topmost of the unconstrained side is substituted with the desired dopant atom. We studied the effect of doping only on the ZnS(110) surface, since it exhibits a stronger interaction with the rubber adsorbate models than the ZnO surfaces. With similar reasoning, out of the two copper sulfide surfaces, we only focused on the Cu2S(111) surface. Doped sulfide surfaces are shown in Figure 7. Cobalt was chosen as our primary dopant atom since it has been widely used as an additive in rubber–brass adhesion. Cobalt also acted as our reference for the investigation of the effect of other transition metals as dopant atoms, such as manganese, iron, and nickel, in order to investigate their potential as cobalt substitutes in rubber–brass adhesion. For the influence of the mixed zinc-copper sulfide surface, the simplest case, which is the copper doped ZnS(110) surface, was chosen.
21 Figure 7. Top and side view of the doped sulfide surface models of (a) ZnS(110) and (b) Cu2S(111).
2.1.2 Rubber adsorbate models
The rubber adsorbate models used throughout the study were constructed based on the rubber structure (cis-1,4-polyisoprene) shown in Figure 8. During the adsorption calculations, the rubber adsorbate models were allowed to relax freely after positioned on the unconstrained side of the surfaces. Due to the complication of multiple functional groups on the rubber structure in the adsorption process, simpler prototypes of the rubber adsorbate models were created based on the functional groups present in the rubber structure. These prototypes consist of elementary functional group models that only contain one functional group, such as saturated hydrocarbons, ethene, and hydrogen sulfide. Larger models with two functional groups were constructed by replacing one of the hydrogen atoms in ethene with either a methyl or a thiol group.
We divided the chosen rubber adsorbate models into three different groups based on the functional group present in rubber structure, which include saturated hydrocarbons, unsaturated hydrocarbons, and sulfur-containing models. Each group consisted of smaller-to-larger adsorbate models, which are listed in Table 2. The use of models such as methane and hydrogen sulfide is a simplification, which does not directly represent the rubber structure.
Even so, by studying the adsorption of these models, we can predict the relationship between the smaller and larger models and the similarity between the adsorption trends with the larger models in each respective group of the rubber adsorbate models. This finding could suggest that the smaller adsorbate models are equally efficient at representing adsorption on sulfide and oxide surfaces.
Figure 8. Rubber adsorbate models constructed from cis-1,4-polyisoprene rubber structure.
Table 2. List of rubber adsorbate models
Saturated hydrocarbons Unsaturated hydrocarbons Sulfur-containing models
Methane Ethene Hydrogen sulfide
Ethane Methyl-substituted ethene Thiol-substituted ethene
2.2 Computational details
All calculations in this study are carried out using the Crystal09 program49 at the DFT level alongside the PBE0 hybrid exchange-correlation functional.50-52 DFT calculations were employed since they are suitable for modeling molecular and crystal systems as well as adsorption processes. DFT has been widely used because it provides both qualitative and quantitative insights into the structures of active surfaces and the surface reactions.53 The standard def-TZVP basis sets are used for iron, nickel, manganese, sulfur, carbon, hydrogen, and oxygen atoms,54 while for zinc, copper, and cobalt atoms, the optimized def-TZVP basis sets are applied [supplementary data in ref 55 and 56]. Spin-paired calculations are used for the adsorption study on pure sulfide and oxide surfaces while spin-unpaired calculations are employed for the doped sulfide surfaces due to the magnetic properties of the dopant atoms.
The density of the k-point is set high enough to ensure convergence. In this work, the adsorption energy (ΔEads) is calculated by ΔEads = EA/S – EA – ES, where EA/S, EA, and ES are the calculated energies of adsorption system, adsorbate, and surface, respectively. The counterpoise method has been utilized to correct the basis set superposition error (BSSE) in the calculated adsorption energies.57
3 Adsorption of rubber adsorbate models on sulfide surfaces 3.1 Adsorption on zinc sulfide surfaces
The calculated adsorption energies of various substances onto a zinc atom of a ZnS(110) surface are compiled in Table 3. The adsorption strength of elementary functional group models from the weakest to the strongest are as follows: saturated hydrocarbons < ethene <
hydrogen sulfide. This adsorption pattern is also reflected in larger models, where methyl-substituted ethene exhibits lower adsorption energy than thiol-methyl-substituted ethene. As seen from Table 3, there are only minor quantitative differences between the results obtained using smaller and larger adsorbate models in the respective adsorbate models grouping. In addition, similar adsorption trends are predicted for the different functional groups of rubber adsorbate models. Therefore, throughout our study, the same rubber adsorbate models are used, since the smaller adsorbate models are found to be as effective as the larger models in terms of the adsorption on sulfide and oxide surfaces.
Table 3. The calculated adsorption energies on the zinc and copper sulfide surfaces (in kJ mol‒
Rubber adsorbate models ZnS(110) Cu2S(111) CuS(001)
Methane –3.0 –0.5 ‒0.4
Ethane ‒4.3 ‒0.8 ‒1.1
Propane ‒3.0 ‒1.0 ‒1.8
Ethene ‒29.8 ‒48.2 ‒36.6
Hydrogen sulfide ‒61.4 ‒39.3 ‒17.4
Methyl-substituted ethene ‒39.8 ‒53.7 ‒37.4
Thiol-substituted ethene ‒50.5 ‒41.5 ‒29.4
The outward relaxation of interacting zinc atom in ethene and hydrogen sulfide cases shown in Figure 9(d) and 9(e) is not visible in the case of saturated hydrocarbons (Figure 9(a)-(c)), indicating a stronger interaction is achieved with ethene and hydrogen sulfide. Saturated hydrocarbons only undergo weak physisorption. On the other hand, ethene interacts through the carbon-carbon double bond and the hydrogen sulfide interaction occurs via the lone pair electrons in sulfur. Notable outward relaxation is also visible in the case of larger models (Figure 9(f) and 9(g)). The way that the models interact relate closely to ethene and hydrogen sulfide, since methyl-substituted ethene adsorbs via a carbon-carbon double bond while the thiol-substituted ethene interaction occurs through the lone pair sulfur electrons instead of a double bond, as hydrogen sulfide interacts stronger than ethene.
Figure 9. Side view of the optimized configurations on the ZnS(110) surface interacting with (a) methane, (b) ethane, (c) propane, (d) ethene, (e) hydrogen sulfide, (f) methyl-substituted ethene, and (g) thiol-substituted ethene.
3.2 Adsorption on copper sulfide surfaces
The obtained adsorption energies are presented in Table 3. Both copper sulfide surfaces show the same adsorption trend, with the rubber adsorbate models having a stronger interaction with the Cu2S(111) than with the CuS(001) surface. Saturated hydrocarbons still show the weakest adsorption, as seen with the ZnS(110) surface, but the adsorption strength for ethene and hydrogen sulfide on both copper sulfide surfaces are reversed when compared to ZnS(110) surface. This phenomenon is further confirmed by the interaction with larger models because of the similar adsorption strengths seen in ethene and hydrogen sulfide is reflected on both copper sulfide surfaces.
Despite the fact that the order of the adsorption strength of ethene and hydrogen sulfide is opposite of the order than on ZnS(110) surfaces, they behave similarly as on ZnS(110) surface in that they interact through a carbon-carbon double bond and the lone pair electron of sulfur, respectively. The only difference occurs in thiol-substituted ethene, where the carbon-carbon double bond dominates the interaction as opposed to the thiol group, since the adsorption strength of ethene is higher than that of hydrogen sulfide. The optimized structures of the rubber adsorbate models on both Cu2S(111) and CuS(001) surfaces are illustrated in Figure 10 and Figure 11, respectively. For both copper sulfide surfaces, stronger interactions caused by ethene, hydrogen sulfide, and substituted ethenes lead to outward relaxation of the interacting copper atom.
25 Figure 10. Side view of the optimized configurations on the Cu2S(111) surface interacting with (a) methane, (b) ethane, (c) propane, (d) ethene, (e) hydrogen sulfide, (f) methyl-substituted ethene, and (g) thiol-substituted ethene.
Figure 11. Side view of the optimized configurations on the CuS(001) surface interacting with (a) methane, (b) ethane, (c) propane, (d) ethene, (e) hydrogen sulfide, (f) methyl-substituted ethene, and (g) thiol-substituted ethene.
4 The effect of dopant atoms on adsorption of rubber adsorbate models on doped sulfide surfaces
4.1 Adsorption on doped ZnS(110) surfaces
The calculated adsorption energies for the rubber adsorbate models positioned above the dopant atom on doped ZnS(110) surfaces are tabulated in Table 4. The energies are then compared to those on the undoped ZnS(110) surface. Despite having different dopant atoms, the adsorption trend seen on the undoped ZnS(110) surface is followed, but different adsorption strengths are observed. Among the elementary functional group models, saturated hydrocarbons still show the weakest interactions, but there is a notable enhancement in adsorption due to cobalt and manganese doping. For the ethene and hydrogen sulfide cases, only copper dopant atom decreases the adsorption strength, while cobalt doping has the highest positive effect showing notable enhancement in the calculated adsorption energies. The next most effective dopant atom is manganese, while both iron and nickel doping atoms display similar adsorption strengths as the undoped ZnS(110) surface. A similar qualitative observation on the changes in the adsorption strength can also be deduced for methyl- and thiol-substituted ethenes, depending on the inclusion of the corresponding dopant atom.
Table 4. The calculated adsorption energies on the undoped and doped ZnS(110) surfaces (in kJ mol–1)
Rubber adsorbate models Undoped55 Mn doped Fe doped Co doped56 Ni doped Cu doped56
Methane –3.0 –10.2 –2.4 –27.0 –3.1 –2.0
Despite the differences in the adsorption strength, the functional group models interact similarly on all the doped surfaces, which are comparable to those on the undoped surface, with the exception of saturated hydrocarbons on cobalt and manganese doped zinc sulfide.
Optimized adsorption geometries on cobalt doped zinc sulfide are shown as an example in Figure 12. The promotional effect caused by cobalt doping in all rubber adsorbate models, including saturated hydrocarbons, is visible in the optimized adsorption geometries, where the interacting cobalt atom relaxed outward, indicating a stronger interaction. Moreover, the stronger interaction between methane and the dopant atom leads to a larger distortion of bound methane from the free geometry, as listed in Table 5. The dominant functional group that is responsible for the interaction with the ZnS(110) surface is further proved through larger model cases that have two functional groups. For methyl-substituted ethene, the interaction is dominated through the carbon-carbon double bond, while the thiol group is responsible for and dominates the adsorption with thiol-substituted ethene, rather than the carbon-carbon double bond, since the preferential binding is via sulfur containing groups.
27 Figure 12. Side view of the optimized configurations on the cobalt doped ZnS(110) surface interacting with (a) methane, (b) ethane, (c) propane, (d) ethene, (e) hydrogen sulfide, (f) methyl-substituted ethene, and (g) thiol-substituted ethene.
Table 5. Adsorption energies (ΔEads) and geometrical parameters of methane interacting with metal on the undoped and doped ZnS(110) surfaces. Included as a reference are the geometrical parameters of free methane.
Free methane Undoped Mn doped Fe doped Co doped Ni doped Cu doped
ΔEads (kJ mol‒1) - ‒3.0 –10.2 –2.4 ‒27.0 –3.1 ‒2.0
Longest C-H bond length (Å) 1.091 1.092 1.098 1.092 1.099 1.094 1.091 Largest H-C-H angle (o) 109.5 110.8 114.4 110.4 114.9 111.9 110.2 Smallest H-C-H angle (o) 109.4 108.3 106.8 108.8 106.6 107.4 108.9
4.2 Adsorption on doped Cu2
The calculated adsorption energies of the rubber adsorbate models interacting with a dopant atom on doped Cu2S(111) surfaces are presented in Table 6 and compared to those of the undoped Cu2S(111) surface. Generally, the adsorption trend on doped Cu2S(111) surfaces also follows the trend seen on the undoped Cu2S(111) surface, with the exception of methyl- and thiol-substituted ethenes on manganese and iron dopants, where the thiol-substituted ethene exhibits a slightly higher adsorption energy than methyl-substituted ethene when compared to the undoped Cu2S(111) surface. Moreover, a remarkable increase in the adsorption strength is achieved through the olefinic group interacting with the dopant atoms. The strongest effect is from the manganese and iron dopant atoms, followed by cobalt and nickel dopant atoms. This enhanced effect also results in obtaining higher adsorption energies for the methyl- and thiol-substituted ethene models.
Table 6. The calculated adsorption energies on the undoped and doped Cu2S(111) surfaces (in kJ mol–1).
Adsorbate Undoped55 Mn doped Fe doped Co doped56 Ni doped
Methane –0.5 0.0 –5.6 –0.9 0.0
Ethane –0.8 –0.1 –5.8 –1.0 –0.3
Propane –1.0 –0.2 –6.0 –1.2 –1.3
Ethene –48.2 –111.3 –104.4 –79.1 –69.0
Hydrogen sulfide –39.3 –34.3 –47.8 –43.8 –40.8
Methyl-substituted ethene –53.7 –106.5 –97.9 –79.7 –71.3
Thiol-substituted ethene –41.5 –110.1 –101.4 –69.7 –59.6
The optimized structures on cobalt doped copper sulfide are illustrated in Figure 13. The results show that rubber adsorbate models on all doped Cu2S(111) surfaces including cobalt dopant have similar interactions to those that occurred on the undoped Cu2S(111) surface.
Stronger interactions lead to the outward relaxation of the dopant atom interacting with the rubber adsorbate models. This phenomenon is clearly visible in all adsorbate models containing a carbon-carbon double bond, which includes ethene and both of the substituted-ethene models.
In addition to the relative evidence shown through the optimized structures that connect this effect to stronger interaction, the larger distortion of the ethene compared to the free ethene also indicates a stronger interaction and higher adsorption energies, as shown in Table 7.
Figure 13. Side view of the optimized configurations on the cobalt doped Cu2S(111) surface interacting with (a) methane, (b) ethane, (c) propane, (d) ethene, (e) hydrogen sulfide, (f) methyl-substituted ethene, and (g) thiol-substituted ethene
Table 7. Adsorption energies (ΔEads) and geometrical parameters of ethene interacting with metal on undoped and doped Cu2S(111) surfaces. The geometrical parameters of free ethene are included as a reference.
Free ethene Undoped Mn doped Fe doped Co doped Ni doped
ΔEads (kJ mol‒1) - ‒48.2 –111.3 –104.4 ‒79.1 –69.0
C=C bond length (Å) 1.32 1.35 1.42 1.39 1.38 1.37
Bending of CH2 groups (o) 0.0 7.3 26.9 19.5 17.0 14.9
4.3 Promotional impact of dopant atoms on sulfide surfaces
The adsorption of rubber adsorbate models on the sulfide surfaces generally show weak interactions via the saturated hydrocarbons while carbon-carbon double bonds and thiol groups of rubbers lead to stronger interactions. However, with the inclusion of different dopant atoms on both sulfide surfaces, the adsorption strength of the rubber adsorbate models can either be enhanced or reduced. Therefore, the use of different transition metals as dopant atoms on ZnS(110) and Cu2S(111) surfaces has been studied to determine their interaction with rubber adsorbate models, and the promotional impacts are presented in Figure 14 and Figure 15, respectively.
Figure 14. The effect of doping on interaction of the rubber adsorbate models and the doped ZnS(110) surfaces. Saturated and unsaturated hydrocarbons present an average effect on the adsorption of methane, ethane, and propane, and ethene and methyl-substituted ethene, respectively.
Figure 15. The effect of doping on the interaction of the rubber adsorbate models and the doped Cu2S(111) surfaces. Saturated and unsaturated hydrocarbons present an average effect on the adsorption of methane, ethane, and propane, and ethene and methyl-substituted ethene, respectively.
In the case of the ZnS(110) surface (Figure 14), the copper dopant notably weakens the adsorption strength of all the functional groups of rubber. On the other hand, the iron and nickel dopants on the ZnS(110) surface display little or no effect on the adhesion. Manganese and cobalt doping not only enhance the adsorption strength of the carbon-carbon double bonds and thiol groups of the rubber adsorbate but also trigger the saturated hydrocarbon groups, leading to higher adsorption energies. These positive effects are more significant in the case of cobalt doping than when manganese is used for doping.
The enhancement of the adsorption strength of all the functional groups of rubber by cobalt and manganese doping on the ZnS(110) surface is not shown on the doped Cu2S(111) surfaces.
Only the adsorption involving the carbon-carbon double bonds of rubber is initiated on all the doped Cu2S(111) surfaces. Even so, the effect is significantly stronger, as shown in the case of manganese and iron doping when compared to the doped ZnS(110) surfaces (Figure 15). While the highest promotional effect is shown through cobalt doping on the ZnS(110) surface, this is not in the case on the Cu2S(111) surface, since the manganese and iron doping on the Cu2S(111) surfaces have a higher promotional effect than the cobalt doping. On the other hand, while the nickel dopant does not show a promotional effect on the ZnS(110) surface, the adsorption strength of rubber to Cu2S(111) surface is also increased through carbon-carbon double bond when the nickel dopant is used.
5 Adsorption of rubber adsorbate models on zinc oxide surfaces
The calculated adsorption energies on both the ZnO(110) and ZnO(001) surfaces are tabulated in Table 8. Even though the most stable polymorph of ZnO and ZnS are different, the results obtained from the adsorption of rubber adsorbate models on the ZnS(110) surface is being used as a reference. The adsorption trend between functional group models and the ZnO(110) surface follow the same trend seen on the ZnS(110) surface, in which saturated hydrocarbons exhibit the weakest interaction, followed by ethene while hydrogen sulfide had a slightly stronger interaction than ethene. Even so, the adsorption energies are slightly enhanced, by approximately 4-7 kJ mol-1 through the saturated hydrocarbons and ethene but are reduced by 20 kJ mol-1 when interacting with hydrogen sulfide. The adsorption strength for larger adsorbate models is also shown to be similar to that on the ZnS(110) surface, where thiol-substituted ethene shows a stronger interaction than methyl-thiol-substituted ethene, but the adsorption energies are lower compare to ZnS(110) surface.
On the other hand, the adsorption is noticeably stronger on the ZnO(110) surface than on the
On the other hand, the adsorption is noticeably stronger on the ZnO(110) surface than on the