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Polymer – Polymer interaction at the nanoscale: An atomic force microscopy study of interaction stress
Polymer Testing 77 (2019) 105902
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Short Communication: Test Method
Polymer – Polymer interaction at the nanoscale: An atomic force microscopy study of interaction stress
T
Meysam Rahmata,*, Pascal Hubertb a b
Aerospace, National Research Council Canada, 1200 Montreal Road, Ottawa, ON K1A 0R6, Canada Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC H3A 0C3, Canada
A R T I C LE I N FO
A B S T R A C T
Keywords: Atomic force microscopy Interaction stress Polyethylene UHMWPE Interface
A new method of polymer-polymer interaction characterization through atomic force microscopy (AFM) is presented. Unlike previous interaction characterization methods such as light scattering, and differential scanning colorimetry, the current method generates the interaction strength in terms of interaction stress. This method is based on previously developed stepwise discretization technique, and is demonstrated here through studying the interaction between polyethylene (PE) and three compatible polymers including high density polyethylene (HDPE), ultra-high molecular weight polyethylene (UHMWPE), and polyethylene high density grafted with glycidyl methacrylate (PE-g-GMA). The results showed that PE-g-GMA had the strongest interaction of 1.5 MPa with PE in air; whereas UHMWPE offered the weakest interaction (i.e. 1 MPa) and HDPE had the shortest interaction distance of 4.3 nm at the peak interaction. The outcome was shown to be in agreement with previously demonstrated principle of polymer-polymer interaction, demonstrating the new method as a simple but powerful option in polymer-polymer interaction studies.
1. Introduction Interactions between different types of polymer determine the compatibility of the components in a polymer mixture and define the blend characteristics, including mechanical properties and transparency [1]. Optimization of the desired properties in a polymer blend is usually achieved by understanding and adjusting intermolecular and intramolecular interactions within the components. In recent years, nanocomposites have encouraged significant research on functionalization and grafting techniques between the matrix and nano-reinforcements [2–5]. It has been shown that the matrix at the vicinity of the nano-reinforcements shows different properties when compared to the bulk matrix [6–9]. The properties of this reign, called the interphase, play an important role in the nanoreinforcement-matrix interaction [10]. Establishing a strong interaction between the interphase and the matrix, which may or may not be the same polymer used in the interphase region, helps effectively harness the outstanding properties of the nano-reinforcement at the macroscale [11]. Extensive studies on properties of multicomponent polymer systems were previously performed by using techniques such as light scattering [12], inverse gas chromatography [13,14], and differential scanning colorimetry [15,16]. Atomic force microscopy (AFM), as a powerful technique in atomic/molecular scale studies has shown promising
*
capabilities [17,18]. Particularly, AFM has been used as a tool for mechanical characterization of material systems, from a single covalent bond strength measurement [19] to manipulating nanoscale objects [20] and carbon nanotube pull-out experiments [21,22]. However, three major drawbacks have been identified with AFM interaction measurements (1) measuring parameters (e.g. attraction forces): without a clear understanding of the interaction mechanism; (2) reporting geometry dependent results, which cannot be used to compare different studies; and (3) limiting the AFM capabilities by using ineffective procedures. Therefore, Rahmat and Hubert [23] proposed “interaction stress” as a new interaction parameter and defined it as “the state of stress (i.e., a tensor) at any given point of an object as a result of its vicinity to a secondary object”. They showed that interaction stress does not have the limitations of Hamaker constant [24] (i.e., restriction to simple geometries) or Lennard-Jones potential [25] (i.e., limited to particles). They developed a procedure called stepwise discretization method to capture the interaction stress as a function of objects’ distance by using the entire range of a single AFM force-displacement curve. The interaction stress only depends on the pair of materials and the environment, and is independent of the geometry. Therefore, once it is calculated for a pair of materials in an environment such as water or air, it can be employed as raw data to obtain various interaction parameters. The results of this interaction characterization
Corresponding author. E-mail address: [email protected] (M. Rahmat).
https://doi.org/10.1016/j.polymertesting.2019.105902 Received 25 July 2018; Received in revised form 13 December 2018; Accepted 11 May 2019 Available online 13 May 2019 0142-9418/ © 2019 Elsevier Ltd. All rights reserved.
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were directly used to understand the reinforcement mechanism in a nanocomposite [26]. Furthermore, the interaction stress concept was applied to various nanoscale material interaction scenarios including modelling local matrix properties surrounding a nano-reinforcement (i.e. interphase characterization) [6], coarse grain simulations of nanocomposites [27], and even nanoscale contact mechanics [28–30]. In the current work, we follow the stepwise discretization method to extract polymer-polymer interaction stresses between polyethylene, and three other polymers of the same family: high density polyethylene (HDPE), ultra-high molecular weight polyethylene (UHMWPE), and high density polyethylene grafted with glycidyl methacrylate (PE-gGMA). These polymers are candidates to be used as nanotube grafting interphase in polymer nanocomposites with polyethylene matrix. Furthermore, polymer composites with polyethylene matrix and polymer fibres such as UHMWPE (i.e. Dyneema and Spectra) will benefit from studying the interaction studies of these materials.
Table 1 Experimental setup parameters and geometric dimensions of the AFM probe. Parameter (unit)
Value
Tip radius (nm) Flattened height (nm) Natural frequency in air (Hz) Deflection sensitivity Quality factor Force ramp frequency (Hz) No. of data points Cantilever width (μm) Cantilever length (μm)
50 30 366,644 37.97 377 1 19,455 31.0 81.4
k = 0.1906ρf b2LQf Γi (ωf ) ωf2 where L is the cantilevers length, Qf is the quality factor in the fluid, and ωf is the fundamental mode resonant frequency of the cantilever. Table 1 lists the experiment parameters as well as geometric dimensions of the cantilever beam and the probe. Based on the values listed in Table 1, a spring constant of 25.4 N/m was obtained for the AFM probe. Scanning Electron Microscopy: Scanning electron micrographs were captured by a Hitachi S-4700 FE-SEM to measure the characteristics of the AFM probes. The system was operated at a voltage of 10 kV and a current of 20 μA. The AFM probes were fixed on the stage by conductive carbon tape. The diameters of the PE-tip probes were measured without further coating. Substrate Preparation: A hot press and a pair of silicon wafers were used to manufacture flat substrates with smooth surfaces from polymer pellets/powder. Processing temperature for all HDPE, PE-gGMA and UHMWPE was 149 °C (300 °F). Stepwise Discretization Method: Based on the interaction stress definition, if one of the objects is in the form of an infinite plane, all components of the interaction stress tensor, except the normal stress in the direction perpendicular to the plane, are zero. The value of this nonzero stress component can be determined as the interaction force per unit area, which is applied from the infinite plane to a flat crosssection of the other object (parallel to the infinite plane) at a given distance. The interaction stress, which is a function of the materials of the flat substrate, the other object, and the environment, varies with the object-substrate distance. Therefore, parallel sections within an arbitrary-shaped object experience different interaction stresses based on their distances from the substrate. Knowing the interaction stress versus distance for an object-substrate system, one can predict the amount of force that is applied from the substrate to any parallel section of the object. The stepwise discretization method works based on the fact that for distances larger than the cut-off distance (step 0), the substrate applies negligible forces to the AFM tip, leading to zero interaction stress. After a tip displacement ΔD1 towards the substrate (step 1), a fraction of the tip is now within the cut-off distance and an interaction force F1 is measured. The AFM tip cross-section area A11, located at an average distance D1 from the substrate surface, is used to compute the interaction stress σ1 as σ1 = F1/A11. As the tip moves down by a displacement ΔD2 (step 2), a larger portion of the tip is exposed to the interaction force. This portion can be divided into two sections: section 1 has an area A12 at an average distance D1, and section 2 has an area A22 at an average distance D2. The interaction force F2 is the resultant of the forces applied to both sections: F2 = σ1A12 + σ2A22; where σ1 and σ2 are the interaction stresses at the distance D1 and D2 from the substrate, respectively. The stress level at D1 was calculated in step 1; hence, the interaction stress at the distance D2 can be obtained in this step (step 2) as σ2 = (F2 - σ1A12)/A22. Similarly at step n, all parameters in the equation are known from previous steps and σn can be determined. It should be noted that the cross-section area is a function of the tip geometry. In this way, the stepwise discretization method
2. Materials and methods HDPE: Sclair® 19G Homopolymer HDPE was obtained from Nova Chemical (Calgary, Canada). According to the manufacturer, it had a melting temperature of 200–230 °C, density of 958 kg/m3, hardness Shore D of 68, Young's modulus of 840 MPa, tensile Strength of 42 MPa and elongation at break of 560%. PE-g-GMA: LOTADER® AX8840 polyethylene high density grafted with glycidyl methacrylate (PE-g-GMA) was acquired from Arkema (Colombes, France). Based on the provided data sheet, this material had a melting temperature of 105 °C, density of 940 kg/m3, hardness shore D of 50, Young Modulus of 104 MPa, tensile Strength of 8 MPa, and elongation at break of 420%. LOTADER® AX8840 resin is a random copolymer of ethylene (E) and glycidyl methacrylate (GMA). It is produced by a high pressure radical polymerization process and can be processed on equipment used for polyethylene (LDPE) and ethylene copolymers. It is not corrosive and reacts with maleic anhydride and acid containing polymers. UHMWPE: Ultra-high molecular weight polyethylene was purchased from Sigma Aldrich (St. Louis, United States). It had a melting temperature of 138 °C, density of 940 kg/m3, and average molecular weight of 3–6 million Da. Atomic Force Microscopy: The surface roughness images, measurements, and the force curves were obtained using a Veeco Dimension V atomic force microscope from Veeco Metrology Group. The images and roughness studies were performed in air and at room temperature. Veeco DNP-10 probes were used for the surface roughness study. These probes are made of silicon nitride and have four cantilevers with a nominal tip radius of 20 nm and nominal spring constants in the range of 0.06–0.12 N/m for the longer cantilevers and 0.32–0.58 N/m for the shorter ones. The force curve measurements were carried out under distilled and deionised water and at room temperature. These curves were obtained using silicon cantilever with attached polyethylene particle (diameter: 5 μm) probes from Novascan (Ames, IA, U.S.A.) with nominal spring constants of 4.5, 7.5, and 14 N/m. Since all force curves were obtained under water the appropriate reflective coating on the back side of the cantilevers was considered. Spring constant of the cantilevers were obtained using thermal tuning method [31]. The first step in this method is to calculate the Reynolds number, Re,
Re = ρf ωb2 /(4η) where ρf is the density of the fluid, ω is the fundamental mode resonant frequency, b is the cantilever width, and η is the viscosity of the surrounding fluid. Then from the curve presented by Sader et al. [31] the parameter Γi (ωf ) is determined (i.e. 0.72 in this case), and finally the spring constant, k, is calculated from 2
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M. Rahmat and P. Hubert
Fig. 1. HDPE substrate topography; (a) three-dimensional surface, (b) height profile of a random line on the surface.
jump to contact did not happen, and the force readouts demonstrate an acceptable precision and sensitivity. Three regimes of noncontact, semicontact, and contact are distinguishable on the graph at 0–200, 200–275, and 275–300 nm, respectively. The reproducibility of the force curve measurements was examined by performing tens of force curve experiments on different locations of the substrate. The sudden jump at 200 nm, is due to the unsteady inflation point when the attraction force towards the substrate goes beyond the resistance force in the cantilever (due to bending), resulting in the cantilever to bend down towards the surface even more, which consequently causes the attraction forces to increase. In this situation the cantilever gains its force balance again at the semi-contact region. At this point, due to close proximity of some regions of the probe to the substrate, some repulsion forces are generated which help the probe regain static equilibrium. The interaction force field asymptotically goes to zero by increasing the distance between the objects. Hence, defining a cut-off distance beyond which there is assumed to be zero attraction force is fundamentally inaccurate, but practically useful with negligible errors. It should be noted that the non-zero interaction force shown in Fig. 2 for separation distances between 0 and 200 nm is the summation of all attractive forces that are applied to every small element of the AFM probe locating outside the cut-off distance; and the summation of negligible, but no-zero, forces applied to the entire probe (from the entire substrate) has resulted to 10 nN attraction. The maximum attraction force in the approach section of the force curve between the polyethylene tip and different substrates is shown in Fig. 3. The attraction force is a function of tip geometry and substrate surface roughness; and hence, cannot be used as a direct comparison index of the interaction between different pairs of materials. However, in this case the same tip was used to obtain force curves and the substrates were completely flat, so it can be concluded that the PE-g-GMA has the strongest interaction with polyethylene. The interaction force
determines the interaction stress as a function of tip-substrate distance, while the AFM tip moves toward the substrate. The stepwise discretization method is explained in detail in Ref. [23]. 3. Results and discussion A set of AFM force measurements was performed to obtain the interaction between polyethylene tips and substrates manufactured from HDPE, PE-g-GMA, and UHMWPE. The substrates were flat and the AFM tips were spherical. Jaiswal et al. [32] demonstrated the effect of surface roughness and geometry on the measured interaction forces between the AFM probe and various samples such as an alumina particle. In another study, Serro et al. [33] showed that the substrate roughness significantly affected the difference between the maximum attraction force in air and under water. For a rough substrate, the maximum attraction force in air was almost equal to the value under water; whereas for a smooth substrate, the value under air was almost an order of magnitude higher. Therefore in this work, the substrates were prepared by employing a pair of silicon wafers to achieve nanoscale level flatness and eliminate the effect of substrate topology on the results [32–34]. Fig. 1 shows an AFM image of the substrate surface, along with the surface topography on a random line. Random locations on the substrate were selected to acquire the interaction force curves under distilled water in order to eliminate the effect of capillary forces due to the humidity level in the air [35]. Small ramps of up to 300 nm were applied to the cantilever [18] and the data from the approach regime were captured. The contact deformation and viscoelastic behaviour of the polymer play important roles in the retrace regime and the value of the sticktion force [36,37]. Therefore, in the current work, only the approach section of the force curve was investigated. AFM probe characteristics, especially the combination of the cantilever spring constant and tips radius, define the shape of the force curves. Fig. 2 illustrates a sample of the force curves obtained with a polyethylene tip and PE-g-GMA substrate under water. As a direct result of proper AFM probe selection, it is evident that a sudden
Fig. 2. The approach section of force curve measurements for a system of polyethylene tip – PE-g-GMA substrate under water.
Fig. 3. Maximum attraction force between polyethylene tip and different substrates under water. 3
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respectively, show longer cut-off distance compared to HDPE with higher density. It should be highlighted that the interaction stress results presented in Fig. 4 were calculated based on experiments under water. The nature of the forces under liquids [38] and the interaction between water and carbon based structures [39,40] are well-understood. In water, the velocity of the electromagnetic waves is lower compared to the vacuum or air and the dipole-dipole interaction, and consequently the van der Waals forces are smaller [32]. According to Goodman and Garcia [41], there is a great increase (by factors of up to 10 and more) in the van der Waals forces, when the medium is air or vacuum, as opposed to water or other liquids. Therefore, a corresponding increase in the magnitude of the interaction stress is expected when considering the interaction under vacuum or air. Considering the scale factor of 10 to convert the stresses shown in Fig. 4, interaction stress values on the order of 1 MPa are still lower than tensile strength of the tested materials, which is 4, 8 and 42 MPa, for UHMWPE, PE-g-GMA, and HDPE, respectively. Previous studies on Poly(methyl methacrylate) (PMMA) showed a PMMA-PMMA interaction stress of 12 MPa in vacuum, while the tensile strength of this material is 70 MPa [6]. This higher interaction stress for PMMA is due to higher charge density in the chain. These results show that an interaction based only on weak van der Waals forces is not sufficient for an effective polymer nanocomposite, and mechanical interlocking (e.g. wrapping and grafting) and chemical functionalization are required. The AFM probes and substrate materials were commercially acquired and were not synthesised in house, so the possibility of the presence of low molar mass compounds cannot be denied without further analysis and chemically characterizing the probe and substrates. However, this characterization cannot be performed before the test due to the risk of interfering with the geometry or characteristics of the probe, and the essential SEM characterization of the probe which determines its geometric dimensions perhaps affects the surface chemistry of the probe, which makes the chemical characterization of the probe after the experiments irrelevant. Therefore, the results presented in this work should be considered with the possibility of measuring interaction between polymers including lower molar mass compounds, which may be close to real situations in some cases. Previous Polymer-polymer interaction studies, particularly in polymer blends, were using a variety of methods and parameters including phase diagrams and miscibility maps, phase separation diagrams, and interaction energy density. Also theoretically, interaction models were developed to relate interaction energy for blends of copolymers based on the interaction energies between monomer unit pairs. However, the current work proposed a direct mechanical interaction stress measurement as a function of distance, which is significantly more advanced than a single interaction energy number between a pair of polymers.
Fig. 4. Interaction stress curves between polyethylene and different polymers under water.
between the polyethylene tip and PE-g-GMA, HDPE, and UHMWPE were 25.5 ± 1.8, 21.7 ± 3.7, and 17.6 ± 3.7 nN, respectively. The error bars show the standard deviation of more than ten measurements. Following the procedure explained previously by Rahmat and Hubert [23], the interaction stresses between polyethylene and three substrates were calculated from the noncontact regime of the raw force curves. The data-processing procedure involved discretizing the continuous force curve into values at different steps along the force curve, defining different cross-sections for the AFM tip, and allocating the amount of force applied to each of these cross-sections. As a result of the stepwise discretization method, the stress level at each of these cross-sections was obtained. Fig. 4 shows the interaction stress results between polyethylene and three polymers of PE-g-GMA, HDPE, and UHMWPE under water. Form these curves, the amount of stress induced in polyethylene matrix as a result of its vicinity with these types of polymers (in polymer blends, or as reinforcement grafting interphase) can be determined as a function of distance. Maximum attraction stresses (negative value) of 0.147, 0.126, and 0.104 MPa were calculated for PE-g-GMA, HDPE, and UHMWPE, respectively. These values were obtained at distances of 7.0, 4.3, and 10.4 nm for PE-g-GMA, HDPE, and UHMWPE, respectively. The maximum interaction stresses follow the same trend observed in Fig. 3 for maximum attraction forces. The cut-off distances for PE-g-GMA, HDPE, and UHMWPE were measured at 63, 21, and 56 nm, respectively, meaning that outside these ranges polyethylene has negligible interaction with these polymers. The positive interaction stresses (data points at the top left corner) represent repulsion stresses. Closer than the distance of maximum interaction stress When the polyethylene tip gradually moves towards the three polymers surface, the magnitude of the attraction stress decreases to reach zero, in which the three polymers and polyethylene attain the equilibrium state. At this point there is no attraction or repulsion between them. A strong repulsion was observed when the polyethylene tip was further lowered toward the polymer substrates. The inflection point in the force curve (Fig. 2) indicates the beginning of semi-contact regime and therefore was assumed as the contact point. The separation distances in Fig. 4 were calculated according to contact point defined as such. As shown in Fig. 4, UHMWPE has the weakest interaction with polyethylene, and that is in agreement with the concept of critical molecular weight in blends miscibility studies. It's been shown that for a polymer pair with unfavourable heat of mixing, immiscible blends are formed when the components have high molecular weights. However, by decreasing the molecular chain length of either component, the combinational entropy can become the more dominant term in the free energy [1]. Furthermore, PE-g-GMA presents the highest negative charge density centres (compared to HDPE and UHMWPE) at its glycidyl methacrylate section and therefore offers the strongest interaction with polyethylene. Also, it is noticeable that UHMWPE and PE-g-GMA with their long molecular chains and grafted glycidyl methacrylate,
4. Conclusion Polymer-polymer interaction characteristics play an important role in polymer mixture compatibility and nano-reinforcement grafting optimization in polymer nanocomposites. A comprehensive methodology was presented in this work to use AFM for polymer interaction characterization purposes. The methodology was based on previously developed stepwise discretization technique and provided interaction stress between a pair of polymers, as an example between polyethylene and three compatible polymers including HDPE, UHMWPE and PE-gGMA. The attraction forces under water were measured and it was found that the interaction stresses under vacuum or in air for all these options were lower than the strength of the corresponding polymers. It was shown that PE-g-GMA offered the strongest interaction stress with a value of 1.5 MPa (in vacuum or air), while UHMWPE and HDPE provided the weakest (i.e. 1 MPa) and shortest interaction distance (i.e. 4.3 nm at the peak stress), respectively. The smallest interaction stress 4
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in the case of UHMWPE was attributed to its high molecular weight and was according to the concept of critical molecular weight in blends miscibility studies. The lowest interaction distance in case of HDPE was perhaps due to the higher density of this polymer which resulted in a packed surface. These findings are in agreement with the polymer interaction principles demonstrated in the literature, demonstrating the validity of the proposed method and the obtained results in characterizing polymer-polymer interactions.
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Polymer Testing journal homepage: www.elsevier.com/locate/polytest
Short Communication: Test Method
Polymer – Polymer interaction at the nanoscale: An atomic force microscopy study of interaction stress
T
Meysam Rahmata,*, Pascal Hubertb a b
Aerospace, National Research Council Canada, 1200 Montreal Road, Ottawa, ON K1A 0R6, Canada Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, QC H3A 0C3, Canada
A R T I C LE I N FO
A B S T R A C T
Keywords: Atomic force microscopy Interaction stress Polyethylene UHMWPE Interface
A new method of polymer-polymer interaction characterization through atomic force microscopy (AFM) is presented. Unlike previous interaction characterization methods such as light scattering, and differential scanning colorimetry, the current method generates the interaction strength in terms of interaction stress. This method is based on previously developed stepwise discretization technique, and is demonstrated here through studying the interaction between polyethylene (PE) and three compatible polymers including high density polyethylene (HDPE), ultra-high molecular weight polyethylene (UHMWPE), and polyethylene high density grafted with glycidyl methacrylate (PE-g-GMA). The results showed that PE-g-GMA had the strongest interaction of 1.5 MPa with PE in air; whereas UHMWPE offered the weakest interaction (i.e. 1 MPa) and HDPE had the shortest interaction distance of 4.3 nm at the peak interaction. The outcome was shown to be in agreement with previously demonstrated principle of polymer-polymer interaction, demonstrating the new method as a simple but powerful option in polymer-polymer interaction studies.
1. Introduction Interactions between different types of polymer determine the compatibility of the components in a polymer mixture and define the blend characteristics, including mechanical properties and transparency [1]. Optimization of the desired properties in a polymer blend is usually achieved by understanding and adjusting intermolecular and intramolecular interactions within the components. In recent years, nanocomposites have encouraged significant research on functionalization and grafting techniques between the matrix and nano-reinforcements [2–5]. It has been shown that the matrix at the vicinity of the nano-reinforcements shows different properties when compared to the bulk matrix [6–9]. The properties of this reign, called the interphase, play an important role in the nanoreinforcement-matrix interaction [10]. Establishing a strong interaction between the interphase and the matrix, which may or may not be the same polymer used in the interphase region, helps effectively harness the outstanding properties of the nano-reinforcement at the macroscale [11]. Extensive studies on properties of multicomponent polymer systems were previously performed by using techniques such as light scattering [12], inverse gas chromatography [13,14], and differential scanning colorimetry [15,16]. Atomic force microscopy (AFM), as a powerful technique in atomic/molecular scale studies has shown promising
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capabilities [17,18]. Particularly, AFM has been used as a tool for mechanical characterization of material systems, from a single covalent bond strength measurement [19] to manipulating nanoscale objects [20] and carbon nanotube pull-out experiments [21,22]. However, three major drawbacks have been identified with AFM interaction measurements (1) measuring parameters (e.g. attraction forces): without a clear understanding of the interaction mechanism; (2) reporting geometry dependent results, which cannot be used to compare different studies; and (3) limiting the AFM capabilities by using ineffective procedures. Therefore, Rahmat and Hubert [23] proposed “interaction stress” as a new interaction parameter and defined it as “the state of stress (i.e., a tensor) at any given point of an object as a result of its vicinity to a secondary object”. They showed that interaction stress does not have the limitations of Hamaker constant [24] (i.e., restriction to simple geometries) or Lennard-Jones potential [25] (i.e., limited to particles). They developed a procedure called stepwise discretization method to capture the interaction stress as a function of objects’ distance by using the entire range of a single AFM force-displacement curve. The interaction stress only depends on the pair of materials and the environment, and is independent of the geometry. Therefore, once it is calculated for a pair of materials in an environment such as water or air, it can be employed as raw data to obtain various interaction parameters. The results of this interaction characterization
Corresponding author. E-mail address: [email protected] (M. Rahmat).
https://doi.org/10.1016/j.polymertesting.2019.105902 Received 25 July 2018; Received in revised form 13 December 2018; Accepted 11 May 2019 Available online 13 May 2019 0142-9418/ © 2019 Elsevier Ltd. All rights reserved.
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were directly used to understand the reinforcement mechanism in a nanocomposite [26]. Furthermore, the interaction stress concept was applied to various nanoscale material interaction scenarios including modelling local matrix properties surrounding a nano-reinforcement (i.e. interphase characterization) [6], coarse grain simulations of nanocomposites [27], and even nanoscale contact mechanics [28–30]. In the current work, we follow the stepwise discretization method to extract polymer-polymer interaction stresses between polyethylene, and three other polymers of the same family: high density polyethylene (HDPE), ultra-high molecular weight polyethylene (UHMWPE), and high density polyethylene grafted with glycidyl methacrylate (PE-gGMA). These polymers are candidates to be used as nanotube grafting interphase in polymer nanocomposites with polyethylene matrix. Furthermore, polymer composites with polyethylene matrix and polymer fibres such as UHMWPE (i.e. Dyneema and Spectra) will benefit from studying the interaction studies of these materials.
Table 1 Experimental setup parameters and geometric dimensions of the AFM probe. Parameter (unit)
Value
Tip radius (nm) Flattened height (nm) Natural frequency in air (Hz) Deflection sensitivity Quality factor Force ramp frequency (Hz) No. of data points Cantilever width (μm) Cantilever length (μm)
50 30 366,644 37.97 377 1 19,455 31.0 81.4
k = 0.1906ρf b2LQf Γi (ωf ) ωf2 where L is the cantilevers length, Qf is the quality factor in the fluid, and ωf is the fundamental mode resonant frequency of the cantilever. Table 1 lists the experiment parameters as well as geometric dimensions of the cantilever beam and the probe. Based on the values listed in Table 1, a spring constant of 25.4 N/m was obtained for the AFM probe. Scanning Electron Microscopy: Scanning electron micrographs were captured by a Hitachi S-4700 FE-SEM to measure the characteristics of the AFM probes. The system was operated at a voltage of 10 kV and a current of 20 μA. The AFM probes were fixed on the stage by conductive carbon tape. The diameters of the PE-tip probes were measured without further coating. Substrate Preparation: A hot press and a pair of silicon wafers were used to manufacture flat substrates with smooth surfaces from polymer pellets/powder. Processing temperature for all HDPE, PE-gGMA and UHMWPE was 149 °C (300 °F). Stepwise Discretization Method: Based on the interaction stress definition, if one of the objects is in the form of an infinite plane, all components of the interaction stress tensor, except the normal stress in the direction perpendicular to the plane, are zero. The value of this nonzero stress component can be determined as the interaction force per unit area, which is applied from the infinite plane to a flat crosssection of the other object (parallel to the infinite plane) at a given distance. The interaction stress, which is a function of the materials of the flat substrate, the other object, and the environment, varies with the object-substrate distance. Therefore, parallel sections within an arbitrary-shaped object experience different interaction stresses based on their distances from the substrate. Knowing the interaction stress versus distance for an object-substrate system, one can predict the amount of force that is applied from the substrate to any parallel section of the object. The stepwise discretization method works based on the fact that for distances larger than the cut-off distance (step 0), the substrate applies negligible forces to the AFM tip, leading to zero interaction stress. After a tip displacement ΔD1 towards the substrate (step 1), a fraction of the tip is now within the cut-off distance and an interaction force F1 is measured. The AFM tip cross-section area A11, located at an average distance D1 from the substrate surface, is used to compute the interaction stress σ1 as σ1 = F1/A11. As the tip moves down by a displacement ΔD2 (step 2), a larger portion of the tip is exposed to the interaction force. This portion can be divided into two sections: section 1 has an area A12 at an average distance D1, and section 2 has an area A22 at an average distance D2. The interaction force F2 is the resultant of the forces applied to both sections: F2 = σ1A12 + σ2A22; where σ1 and σ2 are the interaction stresses at the distance D1 and D2 from the substrate, respectively. The stress level at D1 was calculated in step 1; hence, the interaction stress at the distance D2 can be obtained in this step (step 2) as σ2 = (F2 - σ1A12)/A22. Similarly at step n, all parameters in the equation are known from previous steps and σn can be determined. It should be noted that the cross-section area is a function of the tip geometry. In this way, the stepwise discretization method
2. Materials and methods HDPE: Sclair® 19G Homopolymer HDPE was obtained from Nova Chemical (Calgary, Canada). According to the manufacturer, it had a melting temperature of 200–230 °C, density of 958 kg/m3, hardness Shore D of 68, Young's modulus of 840 MPa, tensile Strength of 42 MPa and elongation at break of 560%. PE-g-GMA: LOTADER® AX8840 polyethylene high density grafted with glycidyl methacrylate (PE-g-GMA) was acquired from Arkema (Colombes, France). Based on the provided data sheet, this material had a melting temperature of 105 °C, density of 940 kg/m3, hardness shore D of 50, Young Modulus of 104 MPa, tensile Strength of 8 MPa, and elongation at break of 420%. LOTADER® AX8840 resin is a random copolymer of ethylene (E) and glycidyl methacrylate (GMA). It is produced by a high pressure radical polymerization process and can be processed on equipment used for polyethylene (LDPE) and ethylene copolymers. It is not corrosive and reacts with maleic anhydride and acid containing polymers. UHMWPE: Ultra-high molecular weight polyethylene was purchased from Sigma Aldrich (St. Louis, United States). It had a melting temperature of 138 °C, density of 940 kg/m3, and average molecular weight of 3–6 million Da. Atomic Force Microscopy: The surface roughness images, measurements, and the force curves were obtained using a Veeco Dimension V atomic force microscope from Veeco Metrology Group. The images and roughness studies were performed in air and at room temperature. Veeco DNP-10 probes were used for the surface roughness study. These probes are made of silicon nitride and have four cantilevers with a nominal tip radius of 20 nm and nominal spring constants in the range of 0.06–0.12 N/m for the longer cantilevers and 0.32–0.58 N/m for the shorter ones. The force curve measurements were carried out under distilled and deionised water and at room temperature. These curves were obtained using silicon cantilever with attached polyethylene particle (diameter: 5 μm) probes from Novascan (Ames, IA, U.S.A.) with nominal spring constants of 4.5, 7.5, and 14 N/m. Since all force curves were obtained under water the appropriate reflective coating on the back side of the cantilevers was considered. Spring constant of the cantilevers were obtained using thermal tuning method [31]. The first step in this method is to calculate the Reynolds number, Re,
Re = ρf ωb2 /(4η) where ρf is the density of the fluid, ω is the fundamental mode resonant frequency, b is the cantilever width, and η is the viscosity of the surrounding fluid. Then from the curve presented by Sader et al. [31] the parameter Γi (ωf ) is determined (i.e. 0.72 in this case), and finally the spring constant, k, is calculated from 2
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Fig. 1. HDPE substrate topography; (a) three-dimensional surface, (b) height profile of a random line on the surface.
jump to contact did not happen, and the force readouts demonstrate an acceptable precision and sensitivity. Three regimes of noncontact, semicontact, and contact are distinguishable on the graph at 0–200, 200–275, and 275–300 nm, respectively. The reproducibility of the force curve measurements was examined by performing tens of force curve experiments on different locations of the substrate. The sudden jump at 200 nm, is due to the unsteady inflation point when the attraction force towards the substrate goes beyond the resistance force in the cantilever (due to bending), resulting in the cantilever to bend down towards the surface even more, which consequently causes the attraction forces to increase. In this situation the cantilever gains its force balance again at the semi-contact region. At this point, due to close proximity of some regions of the probe to the substrate, some repulsion forces are generated which help the probe regain static equilibrium. The interaction force field asymptotically goes to zero by increasing the distance between the objects. Hence, defining a cut-off distance beyond which there is assumed to be zero attraction force is fundamentally inaccurate, but practically useful with negligible errors. It should be noted that the non-zero interaction force shown in Fig. 2 for separation distances between 0 and 200 nm is the summation of all attractive forces that are applied to every small element of the AFM probe locating outside the cut-off distance; and the summation of negligible, but no-zero, forces applied to the entire probe (from the entire substrate) has resulted to 10 nN attraction. The maximum attraction force in the approach section of the force curve between the polyethylene tip and different substrates is shown in Fig. 3. The attraction force is a function of tip geometry and substrate surface roughness; and hence, cannot be used as a direct comparison index of the interaction between different pairs of materials. However, in this case the same tip was used to obtain force curves and the substrates were completely flat, so it can be concluded that the PE-g-GMA has the strongest interaction with polyethylene. The interaction force
determines the interaction stress as a function of tip-substrate distance, while the AFM tip moves toward the substrate. The stepwise discretization method is explained in detail in Ref. [23]. 3. Results and discussion A set of AFM force measurements was performed to obtain the interaction between polyethylene tips and substrates manufactured from HDPE, PE-g-GMA, and UHMWPE. The substrates were flat and the AFM tips were spherical. Jaiswal et al. [32] demonstrated the effect of surface roughness and geometry on the measured interaction forces between the AFM probe and various samples such as an alumina particle. In another study, Serro et al. [33] showed that the substrate roughness significantly affected the difference between the maximum attraction force in air and under water. For a rough substrate, the maximum attraction force in air was almost equal to the value under water; whereas for a smooth substrate, the value under air was almost an order of magnitude higher. Therefore in this work, the substrates were prepared by employing a pair of silicon wafers to achieve nanoscale level flatness and eliminate the effect of substrate topology on the results [32–34]. Fig. 1 shows an AFM image of the substrate surface, along with the surface topography on a random line. Random locations on the substrate were selected to acquire the interaction force curves under distilled water in order to eliminate the effect of capillary forces due to the humidity level in the air [35]. Small ramps of up to 300 nm were applied to the cantilever [18] and the data from the approach regime were captured. The contact deformation and viscoelastic behaviour of the polymer play important roles in the retrace regime and the value of the sticktion force [36,37]. Therefore, in the current work, only the approach section of the force curve was investigated. AFM probe characteristics, especially the combination of the cantilever spring constant and tips radius, define the shape of the force curves. Fig. 2 illustrates a sample of the force curves obtained with a polyethylene tip and PE-g-GMA substrate under water. As a direct result of proper AFM probe selection, it is evident that a sudden
Fig. 2. The approach section of force curve measurements for a system of polyethylene tip – PE-g-GMA substrate under water.
Fig. 3. Maximum attraction force between polyethylene tip and different substrates under water. 3
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respectively, show longer cut-off distance compared to HDPE with higher density. It should be highlighted that the interaction stress results presented in Fig. 4 were calculated based on experiments under water. The nature of the forces under liquids [38] and the interaction between water and carbon based structures [39,40] are well-understood. In water, the velocity of the electromagnetic waves is lower compared to the vacuum or air and the dipole-dipole interaction, and consequently the van der Waals forces are smaller [32]. According to Goodman and Garcia [41], there is a great increase (by factors of up to 10 and more) in the van der Waals forces, when the medium is air or vacuum, as opposed to water or other liquids. Therefore, a corresponding increase in the magnitude of the interaction stress is expected when considering the interaction under vacuum or air. Considering the scale factor of 10 to convert the stresses shown in Fig. 4, interaction stress values on the order of 1 MPa are still lower than tensile strength of the tested materials, which is 4, 8 and 42 MPa, for UHMWPE, PE-g-GMA, and HDPE, respectively. Previous studies on Poly(methyl methacrylate) (PMMA) showed a PMMA-PMMA interaction stress of 12 MPa in vacuum, while the tensile strength of this material is 70 MPa [6]. This higher interaction stress for PMMA is due to higher charge density in the chain. These results show that an interaction based only on weak van der Waals forces is not sufficient for an effective polymer nanocomposite, and mechanical interlocking (e.g. wrapping and grafting) and chemical functionalization are required. The AFM probes and substrate materials were commercially acquired and were not synthesised in house, so the possibility of the presence of low molar mass compounds cannot be denied without further analysis and chemically characterizing the probe and substrates. However, this characterization cannot be performed before the test due to the risk of interfering with the geometry or characteristics of the probe, and the essential SEM characterization of the probe which determines its geometric dimensions perhaps affects the surface chemistry of the probe, which makes the chemical characterization of the probe after the experiments irrelevant. Therefore, the results presented in this work should be considered with the possibility of measuring interaction between polymers including lower molar mass compounds, which may be close to real situations in some cases. Previous Polymer-polymer interaction studies, particularly in polymer blends, were using a variety of methods and parameters including phase diagrams and miscibility maps, phase separation diagrams, and interaction energy density. Also theoretically, interaction models were developed to relate interaction energy for blends of copolymers based on the interaction energies between monomer unit pairs. However, the current work proposed a direct mechanical interaction stress measurement as a function of distance, which is significantly more advanced than a single interaction energy number between a pair of polymers.
Fig. 4. Interaction stress curves between polyethylene and different polymers under water.
between the polyethylene tip and PE-g-GMA, HDPE, and UHMWPE were 25.5 ± 1.8, 21.7 ± 3.7, and 17.6 ± 3.7 nN, respectively. The error bars show the standard deviation of more than ten measurements. Following the procedure explained previously by Rahmat and Hubert [23], the interaction stresses between polyethylene and three substrates were calculated from the noncontact regime of the raw force curves. The data-processing procedure involved discretizing the continuous force curve into values at different steps along the force curve, defining different cross-sections for the AFM tip, and allocating the amount of force applied to each of these cross-sections. As a result of the stepwise discretization method, the stress level at each of these cross-sections was obtained. Fig. 4 shows the interaction stress results between polyethylene and three polymers of PE-g-GMA, HDPE, and UHMWPE under water. Form these curves, the amount of stress induced in polyethylene matrix as a result of its vicinity with these types of polymers (in polymer blends, or as reinforcement grafting interphase) can be determined as a function of distance. Maximum attraction stresses (negative value) of 0.147, 0.126, and 0.104 MPa were calculated for PE-g-GMA, HDPE, and UHMWPE, respectively. These values were obtained at distances of 7.0, 4.3, and 10.4 nm for PE-g-GMA, HDPE, and UHMWPE, respectively. The maximum interaction stresses follow the same trend observed in Fig. 3 for maximum attraction forces. The cut-off distances for PE-g-GMA, HDPE, and UHMWPE were measured at 63, 21, and 56 nm, respectively, meaning that outside these ranges polyethylene has negligible interaction with these polymers. The positive interaction stresses (data points at the top left corner) represent repulsion stresses. Closer than the distance of maximum interaction stress When the polyethylene tip gradually moves towards the three polymers surface, the magnitude of the attraction stress decreases to reach zero, in which the three polymers and polyethylene attain the equilibrium state. At this point there is no attraction or repulsion between them. A strong repulsion was observed when the polyethylene tip was further lowered toward the polymer substrates. The inflection point in the force curve (Fig. 2) indicates the beginning of semi-contact regime and therefore was assumed as the contact point. The separation distances in Fig. 4 were calculated according to contact point defined as such. As shown in Fig. 4, UHMWPE has the weakest interaction with polyethylene, and that is in agreement with the concept of critical molecular weight in blends miscibility studies. It's been shown that for a polymer pair with unfavourable heat of mixing, immiscible blends are formed when the components have high molecular weights. However, by decreasing the molecular chain length of either component, the combinational entropy can become the more dominant term in the free energy [1]. Furthermore, PE-g-GMA presents the highest negative charge density centres (compared to HDPE and UHMWPE) at its glycidyl methacrylate section and therefore offers the strongest interaction with polyethylene. Also, it is noticeable that UHMWPE and PE-g-GMA with their long molecular chains and grafted glycidyl methacrylate,
4. Conclusion Polymer-polymer interaction characteristics play an important role in polymer mixture compatibility and nano-reinforcement grafting optimization in polymer nanocomposites. A comprehensive methodology was presented in this work to use AFM for polymer interaction characterization purposes. The methodology was based on previously developed stepwise discretization technique and provided interaction stress between a pair of polymers, as an example between polyethylene and three compatible polymers including HDPE, UHMWPE and PE-gGMA. The attraction forces under water were measured and it was found that the interaction stresses under vacuum or in air for all these options were lower than the strength of the corresponding polymers. It was shown that PE-g-GMA offered the strongest interaction stress with a value of 1.5 MPa (in vacuum or air), while UHMWPE and HDPE provided the weakest (i.e. 1 MPa) and shortest interaction distance (i.e. 4.3 nm at the peak stress), respectively. The smallest interaction stress 4
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in the case of UHMWPE was attributed to its high molecular weight and was according to the concept of critical molecular weight in blends miscibility studies. The lowest interaction distance in case of HDPE was perhaps due to the higher density of this polymer which resulted in a packed surface. These findings are in agreement with the polymer interaction principles demonstrated in the literature, demonstrating the validity of the proposed method and the obtained results in characterizing polymer-polymer interactions.
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