Temperature Dependence of Kinetic Friction: A Handle for Plastics Sortation?

Abstract

Sortation is a crucial step in mechanical recycling of post-consumer plastics (PCR) whereby properties such as density or spectral signature are used to separate plastics. However it is difficult to sort polyolefin flakes at high throughput by these properties. We ask whether the frictional properties of plastics as a function of temperature may be used as an alternate sorting property. However, fundamental studies of friction at temperatures near their melting points are limited. Here we measure the temperature dependence of kinetic friction for three common polyolefins (high and low den- sity polyethylene and polypropylene) as well as polyethylene terephthalate (PET), focusing on the softening/melting regime. The results are augmented by differential scanning calorimetry and temperature dependence measurements of both dynamic modulus and and probe tack. For the polyolefins, we find strong increases in the coefficients of kinetic friction during temperature ramps in the melting/softening regime. For the PET, we report a notable peak in the kinetic friction which we associate with the glass transition and cold-crystallization. We discuss the enhanced friction in the context of rub- ber friction, which exhibits comparable coefficients of kinetic frictions.

1. Introduction

The international efforts to increase plastics recycling rates are driven by the needs to reduce plastic pollution, to keep valuable materials within the working economy, and to reduce greenhouse gas emissions [1, 2, 3]. The workhorse method is mechanical recycling (MR). In order to maximize performance of recyclates, the input plastics must first be sorted by type [4, 5]. For example, it is well demonstrated in polyolefins that the blending of thermodynamically immiscible polymers such as isotactic polypropylene (iPP) and high density polyethylene (HDPE) can result in materials with reduced tensile properties [6, 7]. Such mixing reduces the economic value of the recyclate and hence the recycling rates.

In MR, the quality of the recyclate is dependent on the degree to which the plastic has been sorted into its constituent types [8]. For post-consumer recycling, the plastics typically undergo a series of steps that include in- clude cleaning, sorting and grinding into flakes before they are remelted in an extruder and pelletized for subsequent use [5]. Automated sorting schemes make use of some property of the plastics that allows differentia- tion in the recycling facilities including differences in near-infrared spectra (which can detect differences between polypropylenes and polyethylenes), density, such as float-sink (which can sort PET from polyolefins) or thick- ness/flexibility (wind channels separate thin/flexible packaging from rigid plastics) shape. Research proceeds apace on development of sorting tech- nologies based on other means, such as tribo-charging [9], incorporation and sensing of tracers[10], selective grinding [11], magnetic density separation [12, 13], artificial intelligence [14] and hyperspectral imaging [15].

Despite the sorting methods, contamination of one plastic by another remains a serious problem [5, 16]. In the case of polyolefins the float-sink step separates the polyolefins from most other common plastics, such as polyethylene terephthalate (PET), but does not separate the various polyolefins from each other because they all have densities less than 1 g/cm³ and they float. Thus isotactic polypropylene (iPP), high density polyethylene (HDPE) and low-density polyethylene (LDPE) may be difficult to sort from each other.

We seek an alternate property for sortation that is based on the differences in melting points between different plastics. In particular we are interested in differences in apparent physical properties at or near the melting points. We focus on the three primary classes of polyolefins, along with polyethylene terephthalate (PET), as these together are reported to comprise 79 % by mass of plastic waste in the US [17]. As the three polyolefins listed above are well known to have melting temperatures that differ by tens of degrees Kelvin from each other, the melting point provides a natural consideration as a handle by which to sort. However, bringing the plastics to or above their melting point may be difficult as different flakes will adhere to each other on conveyor belts. Instead we consider property changes that may occur in the pre-melting region where some properties, such as crystallization and modulus, are known to exhibit decreases in value compared to room temperature. As the pre-melting, or softening, region can be many degrees C in width, it may be accessible in a reprocessing operation. In this work we explore the temperature dependence of the kinetic coefficient of friction (μ_k), also referred to here as CoF, of four common commodity polymers: HDPE, LDPE, iPP and polyethylene terephthalate (PET). If the temperature dependence of the coefficients of friction between different polymers differs sufficiently, especially near melting points, it may be a property by which one can design a sortation or purification process.

The kinetic friction between polymers and metal surfaces is a relatively old topic and generally the frictional forces are ascribed to both adhesive and visco-elastic considerations [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. While many of these studies consider temperature dependent effects, only a small number probe the temperature region in the immediate vicinity of melting points [19, 20, 21, 24, 29, 30, 31, 32] while some examine the vicinity of other thermal transitions, such as the segmental α relaxation, signifying (T_g) [25, 33, 34]. The region near the melting point was examined by Vinogradov et al. in 1967 for ball-on-disc frictional measurements of HDPE, iPP and their blends. They found strong increases in the frictional force near the melting point, and they correlated this with strong decreases in modulus. However, those measurements did not reduce this force to a coefficient of kinetic friction, perhaps due to the plowing of the ball into the polymer near the melting points[19]. Such plowing would produce a confounding effect on the frictional force, making a reduction to coefficient of friction problematic. Other works on polyolefins in the pre-melting region were conducted via plate-on-wheel geometry, to gain insights on the melting process of pellets in extrusion [24, 29, 30, 35]. These works found an increase in the kinetic coefficient of friction (CoF) near the melting point in some cases, but not others. For example, for LDPE, Chung et al. [24] reported that μ_k increases from μ_k ≈ 0.1 for T < 60 °C up to μ_k ≈ 0.3 near T ≈ 125 °C, at the onset of mechanical melting, though under other conditions, there was no reported increase in μ_k near the melting point[29]. These experiments were conducted at pressures several orders of magnitude above those in this current study, as they were simulating friction during melting of pellets in an extruder, while we are interested in weaker gravitationally induced pressures.

PET is distinct from the above polyolefins from the perspective of crystallization because its glass transition temperature is above room temperature. Thus, in typical manufacturing conditions when it is cooled rapidly below its glass transition temperature (T_g ≈ 70 °C), crystallization will cease for molecular mobility reasons before it is thermodynamically complete. When subsequently reheated above its T_g yet below its melting temperature (T_m), it will undergo significant additional crystallization, known as cold-crystallization. Temperature dependent friction studies of polyethylene terepthalate (PET) are scarce [28, 36, 37]. Using an atomic force microscope, Hammerschmidt and coworkers utilized temperature controlled force microscopy to measure friction force for several polymers including PET. They found a peak in tan(δ), the ratio of the loss to storage moduli near the bulk T_g, though no corresponding increase in the frictional force at these temperatures [37]. Interestingly, we find no reported measurements in bulk systems of the effects of cold-crystallization on kinetic friction. As we shall show, the effects are rather large.

In this work, we seek to explore the temperature dependence of friction for the four commodity polymers that comprise a majority of plastics waste. While this work is motivated by the sorting problem, we note that from the perspective of fundamental polymer physics, there is a need for the underlying data. For the polyolefins, there are no experiments that have been optimized to measure the coefficients of kinetic friction in the immediate vicinity of the melting points. For PET, there are no (or limited) macroscopic measurements probing the effects of cold crystallization on kinetic friction.

2. Post Consumer Samples

We utilized post-consumer resins that were acquired from household waste - they were initially identified by their recycling codes and confirmed by methods described below. For PET (resin code #1), we used cutouts from a clamshell food container, for HDPE (#2) we used a milk jug, for LDPE (#4) we used lids from a takeout food container, and iPP (#5) was from yogurt cups. Samples are cleaned in water and mild hand soap and rinsed with tap water. In the employed protocol, samples are not brought above room temperature before the beginning of the test, so thermally speaking, the state of the sample is set by the processing operations (e.g., injection molding) that produced the household items.

3. Sample Characterization and Experimental Protocols

Samples were characterized via attenuated total reflection Fourier-transform infrared spectroscopy (ATR-FTIR) to ensure that the resin codes properly identify the plastics, as shown in the Supplemental Information (Figure S1). The primary peaks associated with each plastic are present in the FTIR spectra for the iPP [38, 39], PE [40, 41] and PET [42, 43] confirming the resin codes are correct. For confirming the identities of the specific species of polyethylenes, the wavelength region 1300cm⁻¹ and 1400cm⁻¹ can be utilized as shown in Figure S2 [40, 41]. According to these authors, the lack of a peak at 1378 (CH₃ deformation) in the upper curve, and the presence of this peak in the lower curve confirms the former is HDPE and the latter is one of the low density polyethylenes. In order to determine whether the sample is LDPE or linear low density polyethylene (LLDPE), one can examine the relative strength of the peaks at 1378cm⁻¹ and 1367cm⁻¹. In this case, the relative strength of the former over the latter indicates it is LDPE.

Molar mass measurements of the three polyolefins were carried out via size exclusion chromatography (SEC) as described in the Supplemental Information. The results for the weight and number average are shown in Table S1. Again, these values are typical for commercial resins.

Thermal measurements to ascertain crystallinity and glass transition temperatures were carried out via differential scanning calorimetry (DSC). These measurements were conducted under a dry nitrogen purge on a TA Instruments DSC2500 equipped with an RCS120 mechanical chiller. Heat flow and temperature calibration were performed according to the manufacturer’s specifications. Temperature calibration was performed using adamantane, benzophenone, indium, tin, and lead standards. All measurements were performed at heating rates of 3 °C/min on samples of ≈ 8 mg.

The melting temperatures and the room temperature crystallinity are reported in the supplemental (Table S1). For the PET, the glass transition temperature is also reported. In all cases, these values are typical of their respective polymers, further confirming that the resin codes are correct. The experimental curves showing heat flow and crystallinity as a function of temperature will be shown and described later.

The friction experiments are conducted on a torsional rheometer (ARES- G2, TA Instruments) with a ring-on-plate tribology fixture (rotating steel- ring on stationary plastic plate). The ring-on-plate geometry reduces the plowing effect that is observed in pin-on-disc or ball-on-disc measurements when the material becomes sufficiently soft. The outer diameter of the ring is 31.70 mm and its width is 1.38 mm. The experiments were conducted at fixed sliding velocities (v_s), as specified for each experiment and always with a nominal fixed temperature ramp of 3 °C/min starting near room temperature. The temperature ramp was achieved through the rheometer’s forced convec- tion oven accessory. The temperature ramp induces a small temperature lag between the instrument’s temperature measurement point and the sample. The magnitude of this effect is found via one-time temperature measurement during a temperature ramp with a thin-wire thermocouple positioned between sample and ring in the absence of ring rotation and a correction is applied to the temperature data. This correction increases with temperature and reaches 3.1 °C at T = 160 °C.

Sections from the post-consumer resins were cut into 35 mm test samples for adhering onto the test fixtures. One side of a sample is lightly roughened with sandpaper, coated with high temperature epoxy and then adhered onto disposable bottom plates and allowed to cure overnight. Prior to measurement, the surface of the metal ring was lightly sanded with high grit paper and then rinsed with tap water, to remove possible contaminates from prior experiments. The sample was rinsed with water.

The control of axial normal force F_N (and hence P = F_N /A, where A is the area of the ring) is facilitated through an axial spring in the shaft. This allows the rheometer to set and maintain a given axial normal force (F_N) through a feedback-loop. In most experiments reported here, we utilize F_N = 1 N and we find the rheometer maintains normal force control within 10 % of a given set-point (See Fig. 1) until the sample becomes molten (discussed below). At worst, for our lowest employed value of F_N = 0.1 N, the control decreases to 25 % of the set point force(control improves for F_N > 1 N). In addition to monitoring the axial force, we also monitor the gap, and change in gap (δh).

Figure 1:

(A) The frictional force F_F, (B) change in gap height, and (C) normal force F_N during a temperature ramp for LDPE. Data is stable until approximately T = 115 °C. Conditions: v_s = 5 mm/s, P = 15 kPa

The kinetic coefficient of friction (CoF) is calculated via the relation μ_k = F_F /F_N where F_F is the kinetic friction force calculated simply from the measured torque and geometrical considerations. To compare the temperature dependencies of CoF between different plastics, measurements were conducted for each type at a constant sliding speed v_s = 5 mm/s and a constant pressure P = 15 kPa during temperature ramps. To measure the effects of P and v_s, additional experiments were conducted on HDPE - measurements were conducted at five pressures for fixed v_s, and also at four v_s for fixed P.

The effects of friction induced interfacial heating have been considered by Spalding and coworkers who employed a heat conduction model to estimate the interface temperature. [29] They reported modest temperature increase due to interfacial heating, for example, under conditions of P = 3.45 MPa and v_s = 305 mm/s and T = 100 °C they found a temperature increase of ≈ 5 °C. The interfacial heating is proportional to both P and v_s. As our nominal pressure is approximately 10³ times less than that employed by Spalding and coworkers, and our nominal v_s is ≈ 50 times less, we do not anticipate that interfacial heating will play an important role in the current experiments.

Measurements of friction near the melting point must consider the domain of experimental stability. As an example, Fig. 1 shows the torque, change in gap δh, and axial loading (F_N) during a temperature ramp at constant angular ring rotation. As seen in Fig. 1A, F_F increases steadily until a temperature of T = 115 °C where it becomes unstable. Figure 1B shows the change in δh from the start of the experiment. This quantity shows a steady increase from the start of the experiment until T = 120 °C. The increase is attributed to thermal expansion that occurs naturally in the semi- crystalline state as temperature is increased, including that attributed to the reduction in crystallinity as the melting point is approached. At the tem- perature of T = 120° C, slightly above the temperature of the F_F instability, δh decreases suddenly. This is reminiscent of the plowing effect observed by [19] Vinogradov in pin-on-disc measurements and is attributed to the normal force pressing the slider down into the increasingly soft (or molten) plastic [19]. In Fig. 1C, the rheometer is able to maintain axial normal force control until the temperatures at which δh has its precipitous drop. In practice, in the remaining CoF plots, we discard data points at temperatures beyond the onset of this instability.

As noted, the pressures utilized in the current experiments are much less than those simulating conditions in an extruder [24, 29, 30, 35]. This may be significant in the region where the plastic is softening, as the rotating ring will be less likely to cause abrasion and less likely to plow into the plastic. This will allow the experiments to proceed to higher temperatures - closer to the melting point than the extrusion simulation experiments.

Tack measures adhesive interactions between the polymer and substrate - it is known that low modulus results in increased tack [44]. In these experiments, we utilize a dynamic mechanical analyzer (TA Instruments, RSA3) with a forced convection oven, utilizing metal 8 mm parallel discs. In these experiments, cleaned samples were placed between cleaned discs, the temperature was set and equilibrated, a compressive pressure of 39 kPa was applied for 30 s (corresponding to a force equivalence of 200g) and the plates were then pulled apart at a speed of 0.1mm/s. The temperature was then increased without removal of the sample to the next measurement temperature (typically a 10 °C increment) and the process repeated. The time between experiments was set so that the overall average heating rate was 3 °C/min, to match that of the friction experiments.

Generally speaking, such tack experiments exhibit two regimes of behavior. For weak adhesive interaction relative to the cohesive energy of the sample one observes adhesive failure, characterized by complete detachment of the sample at low strain with minimal sample deformation. For larger adhesive interactions, one observes cohesive failure, characterized by large deformation of the sample including fibrillation and sample remaining on the probe. In the reported experiments, the temperatures are below the melting point of the samples and we observe no deformation (or fibrillation) of the sample, and no adhesion to the probe - the sample remains as a flat disc. For the polyolefins, sever and permanent fibrillation is observed just beyond our highest reported temperatures, but is not reported here as it is beyond the scope of the current work.

As an example, we show the temperature dependence of tack in Fig. 2 for the case of LDPE. The experiments started at T = 30 °C with increments of 10 °C, but the plot starts at T = 80 °C as their is little variation between the lower temperatures. For a given curve, the sample is in compression at early times (negative normal stress in our convention of plotting) due to the initial compressive force. At T = 80 °C we are unable to measure any attractive adhesive interaction. Adhesion is observed at higher temperatures and is indicated by positive normal stress. It clearly becomes stronger as temperature increases. Beyond our highest reported temperature of T = 110 °C, the sample cannot maintain a stable thickness during the compression step. Also, the adhesive energy becomes much higher and as noted above, fibrillation is observed. From these plots, we extract a quantity called tack, which we defined as the peak of the stress curve at a given temperature, as shown in Fig. 2.

Figure 2:

Measurements of adhesive force between plastic and stainless steel via tack protocol. Measurements shown for LDPE at four successive temperatures below the melting point. The upper three temperatures show adhesive interactions

Dynamic tensile measurements as a function of temperature were carried out on a dynamic mechanical analyzer (TA Instruments ARES G2 solids analyzer) utilizing a tensile fixture in a forced convection oven. Measurements were carried out at the same ramp rate of (3 °C/min) on strips of width 12.5 mm and length 20 mm and thickness ranging from (0.34 to 0.7) mm depending on the plastic. As the melting point is approached, the moduli decrease and the specimens eventually start to creep. For the three polyolefins, the creep remains less than 10 % strain in the presented data while for PET, it can exceed that as discussed later. Measurements were conducted at a frequency of 10 rad/s in proportional force tracking mode with the target oscillation amplitude set at 0.02 %.

4. Results

Figure 3 shows the combined results for LDPE of the four temperature ramp measurements: friction, tack, thermal and tensile. The CoF data is derived from that shown in Fig. 1(A and C) and is reported only for temperatures below the instability points, as described above. It shows a value for the CoF of μ_k ≈ 0.14 until T ≈ 40 °C and then begins trending upwards at an increasing rate with temperature. At T ≈ 105° C there is a sharper upturn in slope of μ_k vs. T. We note that reports of μ_k > 1 for such thermoplastics have not been reported to our knowledge and for this sample, that point is reached at T = 95 °C. Indeed, near the point of measurement instability, we find μ_k > 3 and has increased by a factor greater than 20 over its room temperature value.

Figure 3:

(A) Coefficient of kinetic friction, (B) Differential scanning calorimetry (DSC), and (C) tensile moduli of LDPE during a temperature ramp. Conditions: v_s = 5 mm/s,P = 15 kPa

Concomitant with the increase in μ_k, Fig. 3 shows corresponding changes in tack, crystallinity and the linear viscoelastic dynamic moduli. At the point of the instability of μ_k, the crystallinity has dropped considerably, to a value of 23 % by mass, but of importance here, it remains well above zero, indicating that for the large values of μ_k reported here, the sample is still in a semi-crystalline state (Fig. 3B). Further, the mechanical moduli also indicate that the sample can still be considered solid-like, as E^′ > E^′′. Note the precipitous drop in the tensile moduli just at the point of CoF instability. At the point of the instability, we find E^′ ≈ 15 MPa, which is approximately 50 times less than that at T = 40 °C (Fig. 3B). And finally we note that the tack temperature dependence shares some similarity to that of the CoF in terms of an overall increase, but there are notable differences Fig. 3A. Whereas the CoF starts increasing at approximately T ≈ 70° the tack does not become measurably greater than zero until T ≈ 100°.

Next we consider iPP (Fig. 4), which has the highest value of T_m amongst the polyolefins considered here. The overall trend has similarities to LDPE, however the shapes of the two CoF curves are dissimilar - whereas LDPE shows a continuous increase in μ_k over an extended temperature range, that for iPP is relatively flat, μ_k < 0.25 for T < 145 °C, which is then followed by a sharp upturn at around T = 155 °C - near the melting point. This difference in shape is reflected in the shapes of the crystallinity and moduli curves (Fig. 4B and 4C, respectively). Whereas the crystallinity for the LDPE decreases by 22% from 50 °C to 100 °C, for iPP it decreases by only 5% over the same temperature window. Similarly the modulus of iPP is greater over this temperature window and its slope with respect to temperature is less - we return to this later. For the iPP, the maximal value of the CoF is less than LDPE (and less than the other two polyolefin samples). This is likely due to a failure of the adhesive utilized to adhere the sample to the lower metal ring - this limited the maximum temperature that could be achieved before the experiment became unstable. And similar to the LDPE data, the tack curve tracks that of the CoF, but there are similar distinctions. The increase in the CoF occurs over a broader temperature range, starting at T ≈ 140° whereas the tack does not become sizable until T ≈ 150°, and the tack curve has a sharper upturn.

Figure 4:

(A) Coefficient of kinetic friction, (B) thermal data, and (C) tensile moduli of iPP during a temperature ramp. Conditions: v_s = 5 mm/s, P = 15 kPa

Figure 5 shows the case of HDPE. The overall shape of the curves mirrors that of iPP in that the CoF and crystallinity are fairly flat in the temperature region window below that where the crystallinity drops; μ_k < 0.13 for T < 120 °C. The strong upturn in CoF starts at around T = 120 °C which is about 15 °C below the melting point and reaches a peak value of μ_k = 4.1 before the instability occurs. The upturn in the tack is notably sharp. For the tack measurement, we do observe strong CoF at the point where tack is measurable, but note there is only one temperature at which a non-zero value is reported - beyond that the sample shows cohesive behavior (fibrillar deformation).

Figure 5:

(A) Coefficient of kinetic friction, (B) DSC data, and (C) tensile moduli of HDPE during a temperature ramp. Conditions: v_s = 5 mm/s, P = 15 kPa

The effects of pressure and sliding velocity on the CoF for the case of HDPE are considered. In Fig. 6A, v_s is varied at a fixed pressure (P) while Fig. 6B shows the opposite case. In both cases, the effect of sliding velocity (or pressure) is relatively weak at temperatures well below the melting point of HDPE, consistent with the findings already described in Fig. 5A for the specific case of v_s = 5 mm/s and P = 15 kPa. The results in this regime are broadly consistent with the simplest model of friction where the CoF is independent of velocity and pressure. The upturn in CoF becomes progressively stronger as v_s is increased from (5 × 10⁻³ to 5) mm/s. The upturns in CoF are not seen until temperatures exceed roughly T = 130 °C, consistent with the previous results shown for the single case of v_s = 5 mm/s. Also note that there is a strong dependence of CoF on sliding velocity. Such a trend in this dependency has been seen previously in the case of rubber on granite[45, 46]. In the Discussion section, we further compare the results here with rubber friction.

Figure 6:

Coefficient of kinetic friction for HDPE for (A) a range of sliding velocities at a constant pressure of P = 15 kPa and (B) a range of pressures at constant sliding velocity v_s = 5 mm/s. For clarity, data for T < 100 °C is not shown.

Figure 6B shows five pressures for the sliding velocity of v_s = 5 mm/s. The upturn appears to becomes progressively stronger at lower pressures. We point out that some of this effect may be due to the softening of the material at the elevated temperatures, and this effect becomes exacerbated at higher pressures. This result is consistent with friction studies mentioned previously that were conducted at higher pressures and showed smaller (or no) increase in CoF near the melting point. [29, 30] One can also consider that the point of instability is greater for the higher pressures, and thus for the lower pressures, the experiments can proceed to higher temperatures before instability. Further, one can consider that the plowing effect, or a material grinding effect may be more likely to occur at the higher pressures as the material becomes soft at these elevated temperatures. Nevertheless, if one fixes on a temperature in the upturn region, (say T = 133 °C), one can see that the CoF increases from 1.2 at the highest pressure to 3.8 at the lowest.

PET, as discussed earlier, differs from the three previously examined polyolefins in that its T_g is above room temperature and under typical industrial processing conditions, it is cooled below the glass transition temperature before crystallization completes, as mentioned above. Here, the DSC shows the crystallinity at the start of the heating ramp is 22.5 % (Fig. 7B). The glass transition can be seen at T ≈ 70 °C and that cold-crystallization commences at T = 120 °C. The cold-crystallization manifests as a near doubling of the crystallinity over the temperature range from T = (120 to 140)° C. (The transition of PET from semi-crystalline to molten state occurs at T ≈ 260 °C and is not shown here.)

Figure 7:

(A) Coefficient of kinetic friction, (B) thermal data, and (C) tensile moduli of PET during a temperature ramp. Conditions: v_s = 5 mm/s, P = 15 kPa

The effects of T_g and crystallization can also be seen in the mechanical moduli (Fig. 7C). The glass transition temperature is seen as the peak in E” that occurs at T = 76 °C. As the sample is brought further above its T_g, the moduli drop by over two orders of magnitude. When the plastic reaches a temperature of T = 120 °C and cold-crystallization commences, the moduli increase by over one order of magnitude. The mechanical measurement is challenging over this extended low moduli region because of sample creep. The dashed vertical line at T = 117 °C represents the point at which the relative change in length of the sample exceeds 10 % - values at temperatures that exceed this may be considered qualitative. We also note that the optical appearance of the sample changes during the cold crystallization process, morphing from transparent to white - consistent with increased crystallinity.

The CoF for PET shows a pronounced peak as a function of temperature, as clearly seen in Fig. 7A. Deviations from the room temperature values start at T ≈ 80 °C; this value is slightly above the T_g observed in the thermal and mechanical curves. The CoF reaches a peak at T ≈ 110 °C and then starts to decrease. Interestingly, the decrease starts at a temperature slightly lower than the start of the cold-crystallization (as seen from the DSC) and also lower than the upturn in the mechanical moduli. The CoF continues to decrease until it levels off at T ≈ 130 °C, which is near the temperature at which the cold-crystallization process has completed for this set of conditions.

The tack behavior shows interesting distinctions from what was observed in the polyolefins. Whereas the polyolefins showed an upturn in CoF before that of tack, here it is reversed. The strong upturn in tack occurs near T_g whereas that for CoF occurs approximately 20°C higher. Once the system reaches T ≈ 120°C and the crystallinity and moduli start increasing, then the tack and CoF curves become similar.

Finally, we comment briefly on surface roughness by noting that we find similar behavior in the coefficient of friction as a function of temperature regardless of the surface roughness. For example, the milk jug used here is designed to have some regions that are relatively smooth and others that are textured, but we see the same qualitative effects.

5. Discussion

The experimental results are summarized in Fig. 8 where the CoR, tensile and tack temperature ramps for the four plastics are placed together. In this figure, we plot the CoF on a logarithmic axis to better highlight the initial upturns, and we plot the tensile measurements in terms of a compliance J* = ((E^′)² + (E”)²)^−1/2 in order to provide easier comparison between CoF and mechanical properties. First, this plot shows that the temperature regions for the high friction states for the three polyolefins are well differentiated from each other, this is expected because we previously noted that the COF upturns occur near their melting points, which are well differentiated.

Figure 8:

Summary of CoF (A) and modulus (B) results for the four plastics tested.

We are also interested in determining inter-relationships between the up- turns in the CoF and associated changes in compliance, tack and crystallinity. Close examination of 8 does not indicate a simple relationship but we can glean some trends. First, we note a broad trend whereby the compliance and and tack roughly track with the CoF. For example, the PET shows a flat region, an increasing region and a decreasing region for all three properties as a function of temperature, in other words, the high friction is associated with increased compliance and tack. For example, 8A shows a horizontal dashed line at CoF = 1. If we - somewhat arbitrarily - consider this to indicate the boundary between the low and high friction states, we can use the corresponding vertical dashed lines to examine the relationship to compliance and tack. It can be seen that in the high friction states, the compliance always exceeds J* > 10⁻²MPa⁻¹. Further, the tack is always measurably greater than one. However, one also notes substantial differences between the plastics, for example the difference in the compliance at the onset of the high friction state is almost a factor of ten.

Another way to consider the inter-relationships is by examining the CoF, tack and compliance with respect to crystallinity. This is carried out in Fig 9 for the polyolefins. For the polyolefins, one can clearly discern concomitant increases in all three properties as crystallinity decreases during the course of a measurement. This indicates that crystallinity is a property that is playing a dominant role, in that it causes the decrease in modulus which then allows for the tack and CoF to become larger. Further, at low crystallinity, there are correspondingly more chain segments which are conformationally, more free to make adhesive contact with the substrate, allowing for more adhe- sion. While these three quantities all track with crystallinity, more exacting relationships are difficult to discern.

Figure 9:

Plotting as a function of crystallinity for polyolefins

For the case of PET, the plot of CoF, tack and compliance as a function of crystallinity has a distinctively different appearance (Fig. 10) compared to the polyolefins and should be plotted separately for clarity. Recall first that the temperature range used includes the cold-crystallization regime but does not extend to the crystal melting regime. Increasing crystallinity in (Fig. 10) corresponds to increasing temperature as shown by the arrow - this is opposite to the polyolefins. Note that at ≈ 22% crystallinity, we observe a large range of values of CoF, tack, and compliance. This is because in this regime, as the sample heats, it goes through its glass transition, but has not yet undergone cold-crystallization.

Figure 10:

Plotting as a function of crystallinity for polyolefins for PET

For crystallinity above 22.5%, we see that the three quantities track each other quite well. Thus we can conclude from the four polymers that far from the glass transition temperature, crystallinity is a controlling parameter for all three quantities, but when near the glass transition temperature, those effects must be considered as well.

We can gain insight to these high-friction states near the melting point by considering rubber, whose kinetic friction coefficients can exceed 1, with values up to 8 [47, 48, 49, 50]. In commercial rubbers, such as tires, the material is above T_g, has moduli in the range (10⁰to10²)MPa, has zero or low crystallinity and can contain fillers. For the plastics examined in this work, the high-friction states correspond similarly to low moduli states, crystallinity below 30 % and CoFs that exceed 1. A simple picture is that the reduced crystallinity at elevated temperatures causes reduced moduli, which then give the material a rubber-like mechanical moduli. Rubbers maintain their elasticity through chemical crosslinking. For semi-crystalline thermoplastics just below the melting point, it is the crystalline domains, linked into a network by amorphous domains that act as effective crosslinks and provide the material with rubber-like properties. We point out that high tack polymers such as adhesives must possess low moduli. There is an intricate link between high tack and the high friction states seen here.

Per Person[48], during sliding, the metal substrate has asperities, and these produces local oscillations on the rubber surface that lead to cyclic deformations and energy dissipation in the rubber, causing high levels of CoF. This could create the high friction state in the plastics as well. Rubbers are known to exhibit strong variations in their CoF as a function of sliding velocity, which is seen in the current work as well, and is attributed to dissipative mechanisms [48, 51]. This notion provides motivation for imaging studies of the interface, for example to search for Schallamach waves. [52, 53]

6. Conclusion

The fundamental properties of polymers during heating as the melting point is approached have been studied from numerous perspectives including crystallinity, modulus, vibrational modes and lamellar spacing. However considerably less effort has been expended on their frictional properties, which can be thought of as stemming from such fundamental properties. But this information is useful from both the fundamental perspective and to explore the idea of using the CoF as a means of sortation for plastics recycling. This work is a step to fill that information gap by employing a geometry and set of conditions capable of measuring the coefficient of kinetic friction near the melting point. Thus this work may be of both fundamental and practical interest.

While a detailed description of a practical sortation device is beyond the scope of this work, one can envision the general principles by which this temperature dependence of kinetic friction can be utilized to enable sortation. For example, imagine mixed plastic flakes of LDPE, HDPE and iPP are allowed to slide down a heated incline via gravity. If the temperature is set just below the melting temperature of LDPE, then a substantial variation in CoF between the three plastics will occur. According to Fig. 8, at T = 110°C, the CoF of LDPE is greater than ten times that of the other two plastics and to a first approximation, the distance travelled per unit time will be inversely related to the CoF. Thus sortation can be achieved based on how far down the incline the plastics translate. Further, the two plastics that translate fastest can then be sorted from each other in recursive fashion. In terms of the potential application in plastics sorting, we note that PET goes into a high friction state over the temperature window in which LDPE and HDPE also go into high friction states, and thus it could be difficult to use kinetic friction to separate PET from these two plastics. However, PET has a density that exceeds 1 g/cm³ and so could be separated out from the polyolefins in a separate float-sink step.

This work indicates that there is potential to utilize kinetic friction as a handle by which one can separate polyolefins from each other. Future progress towards this application would need to propose specific implementation schemes and consider aspects such as throughput, fouling, and overall energy consumption. This work is carried out at a fixed temperature ramp, and it would be interesting to learn if the plastics temperature profile is a relevant variable and how that might impact an industrial process. It would also be useful to understand what role thermally induced additive migration might play in the high friction states. At a more fundamental level, the transitions to high friction states likely occur for most other thermoplastics and a detailed understanding of the causes of this transitions would be important.

This work opens up further areas of investigation. For example, visualization of possible Schallamach waves, surface damage or fouling would be useful. Further, measurements at lower pressures, especially those commensurate with gravitationally induced pressures would inform possible sortation designs. Finally, the effects from tribo-charging and the detailed nature of the temperature dependent transition from solid friction to molten shear would be important in describing the high-friction states.

Highlights.

• Significant upturn in kinetic friction coefficient of polyolefins near melting point

• Strong peak in kinetic friction coefficient of PET above glass transition

• Correlation of upturns with thermal and mechanical properties and tack

• High friction state is analogous to rubber friction

• High friction state is possible mechanism for plastics sortation