Interdiffusion behavior under a temperature gradient field in a poly(ethylene-co-hexene)/poly(ethylene-co-butene) system

Abstract

We have investigated the interdiffusion of two dissimilar polymer species with different molecular masses, M_w, thus having different self-diffusion coefficients D*. A net mass flux across the interface and displacement of the original interface, Δx, between the two polymer films are observed. The displacement of the original interface moves toward the side containing the faster moving polymer species. We also examine the effect of an in-plane stationary temperature gradient on the interdiffusion of two dissimilar polymer species. As the low M_w polymer species is in the region of high temperature under the thermal gradient temperature field, the interface between the two polymer films moves faster compared with the system with the low M_w polymer species in the cold region of the temperature gradient field. We suggest that the in-plane thermal gradient accelerates polymer migration through the enhancement in polymer diffusion along the direction of the temperature gradient due to the Soret effect. We also find that the interdiffusion of polymers depends on the composition in the blend system. For a statistical copolymer system of plastic poly(ethylene-co-hexene) (PEH) and elastic poly(ethylene-co-butene) (PEB), having technologically interesting plastic and elastic properties, the diffusion of the relatively slow diffusion species (PEH) increases with the increase of PEB composition. Under the thermal gradient field the net mass flux across the interface and the movement of original interface between two polymer films can be controlled by the direction of the temperature gradient and composition of the blend system.

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Introduction

Interdiffusion of a polymer system in the melt state is a subject frequently addressed in the literature and implicated in a wide range of phenomena.^1–3 The development of microstructure in block copolymers,⁴ the self-assembling of polymeric amphiphiles,⁵ the evolution of phase-separated domains in polymer blends⁶ and thermal and mechanical properties of linear⁷ or branched polymers^8–10 are closely related to their diffusion. These diffusion phenomena are of practical importance in the control of polymer properties since their diffusion behavior affects adhesion and bonding between polymer materials and the viscoelastic and flow properties of polymer blend systems. The questions of how two dissimilar polymers interdiffuse into each other and what is the relation between thermodynamics of blend systems and their diffusion behavior have attracted great interest. The polymer diffusion phenomena in binary polymer mixtures have been investigated theoretically and experimentally.^11–14 Several theoretical approaches describing the polymer diffusion behavior in an interdiffused binary polymer system were reported. de Gennes¹⁵ was first to propose the theory of reptation to adequately describe the one-dimensional translational motion of long and entangled polymer chain in their molten state in the presence of fixed obstacles. The tube model proposed by Doi and Edwards¹⁶ considers a chain of N monomers in a virtual tube where the topological constrains are imposed by the neighboring molecules in the melt. Controlling the interdiffusion of two polymer species is often crucial in applications of these materials since the interdiffusion of polymers controls a host of physical properties.^17,18 A variety of techniques have been developed to measure the polymer–polymer interdiffusion by examining the concentration profiles across the interface between two polymer species: infrared microdensitomery,¹⁹ Rutherford backscattering spectrometry,²⁰ microanalytical electron microscopy,²¹ etching methods combined with mass spectrometry scattering,²² neutron²³ and X-ray reflectometry,²⁴ combination of scanning electron microscopy and energy-dispersive analysis of X-ray fluorescence,²⁵ and ion-beam method based on nuclear reaction analysis.^26,27 The variety of available techniques have been used to emphasize how polymers interdiffuse into each other on a scale from a few hundred to several thousand angstroms, mainly through the use of isotropic labeling or marker under a homogeneous temperature field and provide the information on very early stages of diffusion (short diffusion distance).

It is well known when multicomponent liquid mixtures are subjected to a stationary temperature gradient, diffusion processes are influenced by thermodiffusion or Soret effect.²⁸ The Soret effect is a common phenomenon observed in the mixture systems, where the dissimilar species exhibit different responses to the temperature gradient.^29,30 The Soret effect may play an important role in critical polymer blend systems. Due to the effect of Soret phenomenon, the temperature gradient can work as a thermal driving force for diffusive mass flow stimulated by the heat flow. The responses of binary mixtures to the thermal force cause all species in the system to become activated and drift along temperature gradients. The Soret coefficient is considered as a measure of the concentration variation (Δϕ) at a given temperature difference (ΔT), Δϕ/ΔT. The presence of temperature gradient would induce a substantial directional flux of heat throughout the sample. The polymer thermal diffusion behaviors in dilute binary solution have been investigated experimentally³¹ and theoretically.^32,33 In dilute solution systems the mutual diffusion coefficient strongly depends on molecular mass of polymer.³¹ In the binary polymer blend system the two components with different molecular masses might exhibit different responses to the temperature gradient due to the Soret effect. In present work, we investigate the interdiffusion behavior of binary polymer system in an in-plane temperature gradient field by directly measuring the displacement of interface between two polymer films. Unlike previous studies^20,24 that use two planar films stacked together and require some labeling or markers, in this work two polymer films are carefully aligned side by side to each other. The crystallized PEH is studied as a ‘labeled’ component that can be monitored by polarized optical microscope. As compared to other polymer system using Au layer as a marker of interface displacement,^20,24 where small, closely packed gold particles might hinder polymer interdiffusion and the possible small movements of Au markers themselves (mobile Au particles diffuse into polymer sides) increases the uncertainties of interface displacement, such a crystallized PEH component is advantageous to be used as an indicator for shifts of the interface. In this study, we are dealing with an interdiffusion behavior at a relatively large diffusion distance or very late stage of the diffusion process in the polymer system. Specifically we focus on the origin of enhanced diffusion in binary polymer systems under a temperature gradient field. We also offer a general principle for controlling the net mass flux across the interface and the movement of original interface between two polymer films by changing the direction of temperature gradient and composition of binary polymer blends. This allowed for a tuning of the mechanical property gradient in the elastic/plastic system. It seems likely that the control of the interdiffusion behavior of plastomer/elastomer should be important for applications in which mechanical property gradient is important, e.g., response of cells to polymer coatings, film friction and adhesion properties, etc.

Experimental section

Materials and sample preparation

The statistical polyethylene copolymers, plastic polyethylene-co-hexene (PEH) with M_w = 110 kg mol⁻¹ and 2 mol% hexene comonomer and elastic polyethylene-co-butene (PEB) with M_w = 70 kg mol⁻¹ and 15 mol% butene comonomer were supplied by ExxonMobil Co. Ltd. and used as received. They were both synthesized with metallocene catalysts and have relatively narrow molecular mass distributions (a polydispersity index of 2). The comonomers of PEH and PEB are uniformly distributed. PEH is the only crystallizable component in PEH/PEB system in the temperature range of our measurements. The blend of PEH and PEB was prepared by the coprecipitation method and detailed information about preparation of blend sample are given elsewhere.²⁹ The homogeneous polymer and polymer blend were hot-pressed at 130 °C on a hot plate to form films of ca. 300 μm in thickness. These films were carefully aligned side by side to ensure that there is no air gap between polymer films. To be able to remove the air at the interface, the sample is first annealed at relatively low temperature (60 °C) in the vacuum oven for 3 h. After that the sample was thermally treated under homogeneous temperature (homo-T) and temperature gradient (grad-T).

Characterization and experimental procedure

The polarized optical microscope (POM) images were obtained by using a Zeiss (Axio. imager. A2) optical microscope and a Zeiss (AxioCam HRC) CCD. Linkam LTS420 and GS350 hot stages were used to provide the homogeneous temperature control and temperature gradient, respectively. A schematic three-dimensional representation of the temperature gradient hot stage is shown in Fig. 1. The independently temperature-controlled plate I and plate II in the chamber of GS350 hot stage can establish an in-plane temperature gradient. Two heating plates of GS350 temperature gradient hot stages are perfectly aligned to ensure uniform thermal contact between the temperatures controlled plate surface and the sample substrate. The heating plates are laterally separated from each other by a 2 mm air gap. A temperature gradient is established in the sample bridging the plate I and plate II. The thermal instability of two heating plates is less than 0.1 °C. The temperature profile of the temperature gradient hot stage was obtained by directly measuring the actual temperatures on the bare substrate using a thermocouple.

Fig. 1 (a) Schematic of the thermal gradient annealing system. The temperatures of plate I and plate II are controlled independently in order to establish a temperature gradient. (b) The temperature distribution of a bare substrate sitting on the temperature gradient hot stage measured by thermocouples.

The crystallization enthalpies of the neat PEH, PEH/PEB blend and PEB were measured using differential scanning calorimetry (DSC, Mettler Toledo-822e). In a typical DSC experiment, the sample was first heated to 160 °C for 10 min in DSC sample cell to remove thermal history, and then cooled the sample at 10 °C min⁻¹.

Results and discussion

The equilibrium melting temperature, T_m, of PEH is 138 °C and the melting point of PEB is 48 °C.³⁴ The cooling DSC scans in Fig. 2 show the crystallization temperatures of neat PEH and PEB are 105 °C and 38 °C, respectively, at the cooling rate of 10 °C min⁻¹. In this study the annealing temperature is well above 48 °C and the PEH in the PEH/PEB system is the only crystallizable component at the temperature above 48 °C. For a blend system of PEH and PEB, the crystallization temperature of PEH decreases with the increase in the composition of PEB, ϕ_PEB. The large contrast between crystallized PEH and amorphous PEB in rotating the polarized light through the sample makes polarized optical microscopy an ideal technique for directly observing the interface between these two polymeric components at the temperature below the melting point of PEH. The molecular masses of PEH and PEB are 110 kg mol⁻¹ and 70 kg mol⁻¹, respectively and well above the molecular mass for entanglements (1 kg mol⁻¹).³⁵ Subjecting the polymer film to a thermal annealing at the temperature above T_m facilitates the interdiffusion of two components and we subsequently let the PEH component crystallize by quenching the polymer film to 92 °C. The maximum crystallization rate of polymers occurs at the temperature, T_max, between T_g and T_m. For the semicrystalline polymers, the value of T_max/T_m is ≈ 0.88.^36,37 In our study, subjecting the polymer film to a thermal annealing at the temperature, T_max, facilitates the formation of PEH crystals in a short time to avoid the significant interdiffusion of two polymer species during the processing of PEH crystallization. The T_max of PEH is ≈ 92 °C. The quenching is sufficiently fast (30 °C min⁻¹). After the quenching, the PEH component crystallizes at 92 °C for 5 min. Actually, due to the fast crystallization of PEH component at 92 °C, we saw no significant evolution of PEH crystallization morphology after crystallizing for 2 min. Because of the fast quenching process and relatively short crystallization time (5 min) at 92 °C we expect no significant effects on the interdiffusion of two polymer species during the quenching and PEH crystallization. Fig. 3 shows the POM images of PEH/PEB sample after annealing at 140 °C and 180 °C for different times on a homo-T hot stage. The PEH and PEB correspond to the lighter and darker regions in POM images, respectively.

Fig. 2 Cooling DSC scans at 10 °C min⁻¹ after annealing the sample at 160 °C for 10 min in DSC sample cell.

Fig. 3 The POM images of PEH/PEB sample after annealing at 140 °C and 180 °C for different times on the homo-T hot stage. The scale bar corresponds to 100 μm and also applies to all images.

The interface between crystallized PEH and amorphous PEB is clearly discerned and moves toward the amorphous PEB side with time. As mentioned before, due to the different self-diffusion coefficients the interdiffusion of two polymer species with different molecular masses leads to a net mass flux and displacement of the original interface.²⁰ According to a theoretical approach proposed by Brochard et al.,^38,39 in entangled polymer systems of two components with different mobilities (different M_w) a pressure gradient would occur and this pressure gradient can be removed by a net mass flow. The interface between the two polymers moves toward the side containing the faster moving species (low M_w component). In PEH/PEB system, the PEB is the low M_w component. It explains the moving direction of interface between PEH and PEB during the interdiffusion. The displacement of the interface with time in PEH/PEB films annealed at different temperatures in the homo-T field is shown in Fig. 4.

Fig. 4 The displacement of the interface between PEH and PEB with diffusion time annealed at different temperatures.

Theory given by Green et al.²⁰ predicts that Δx = C(D*t)^0.5, where C is a constant and depends only weakly on the ratio of molecular masses and D* is the self-diffusion coefficient of the faster diffusing species (lower M_w component). By the numerical calculation, the constant, C, was determined as a function of N_A/N_B (N_A and N_B are the degree of polymerization of species A and B, respectively). For the PEH/PEB system with a ratio of N_A/N_B of 0.64, the value of C is 0.26.²⁰ From this relation given by Green et al.,²⁰ it is evident that the interface displacement increases monotonically with t^0.5. Values of C(D*)^0.5 obtained from the slopes of Δx vs. t^0.5 plots are shown in Fig. 4. The self-diffusion coefficients of PEB, D^*_B, extracted in this way are plotted as a function of temperature (shown in Fig. 5).

Fig. 5 Self-diffusion coefficient of PEB, D^*_B, plotted against the annealing temperature.

Evidently, at the annealing temperatures below 200 °C the diffusion coefficient of PEB increases with temperature. As pointed out before by de Gennes,⁴⁰ the interdiffusion of dissimilar polymers is dominated by the excess enthalpy and entropy of segment–segment mixing. The entropy of polymer–polymer mixing is scaled as N⁻¹, where N is the degree of polymerization. For high-N polymers, the value of mixing entropy is very small as compared to that of mixing small molecules. The excess enthalpy for creating a polymer mixture with local compositions ϕ and (1 − ϕ) of two polymeric components is proportional to χϕ (1 − ϕ).¹⁷ In PEH/PEB system, this interaction parameter, χ, varies with temperature as χ(T) = −0.0011 + 1.0/T (K).³⁴ In the T range of our measurement, the value of χ is positive (0.0013 at 140 °C, 0.0012 at 160 °C, 0.0011 at 180 °C and 0.0010 at 200 °C) and the net interaction energy change (excess enthalpy) opposes mixing. Increasing the temperature leads to a decrease of interaction parameter and associated decrease in the excess enthalpy, which in turn implies an enhancement of the interdiffusion. The excess enthalpy, χϕ(1 − ϕ), is important to this diffusion process since it controls the net interaction energy change. Such enhancement is termed as segment-interaction enhancement.⁴¹ Note that a “transitional” time (t′) exist for PEH/PEB samples annealed at relatively high temperatures (200 °C). During the early stage of interdiffusion (t < t′), the PEB diffuses with relatively high rate (denoted as fast stage). In the late stage where t > t′, the interdiffusion of PEH/PEB slows down (denoted as slow stage). This two-stage diffusion process is interpreted as arising from an enhancement of the interdiffusion of PEH and PEB at the high temperature (200 °C) and associated decrease in the concentration gradient across the interface, which leads to an increase in the value of ϕ (1 − ϕ). The corresponding excess enthalpy for creating a polymer mixture, χϕ (1 − ϕ), increases. It might explain the slowing down of the interdiffusion of PEH/PEB in the late stage (slow stage) at 200 °C.

We next focus specifically on the interdiffusion behavior of PEH/PEB system in an in-plane grad-T field. The temperatures at heating plane I and plane II are 130 °C and 200 °C, respectively. The temperature at observing region is 160 °C. In Fig. 6, we observe the moving of interface between PEH and PEB toward the amorphous PEB side with time, which is natural given a net matter flux across the interface due to the different molecular masses.

Fig. 6 The POM images of PEH/PEB sample annealed at 160 °C for different times under an in-plane grad-T. The scale bar corresponds to 100 μm and also applies to all images.

Evidently, the direction of the heat flow influences the moving rate of interface (Fig. 6 and 7). When the low M_w PEB is placed at high temperature zone of grad-T hot stage (denoted as PEH/PEB_high-T), the interface between PEH and PEB moves faster as compared to a sample with the high M_w PEH placed at the high temperature zone (PEH_high-T/PEB) during the fast stage of interdiffusion (t < t′). In the slow stage of interdiffusion (t > t′), the interdiffusion of PEH/PEB_high-T slows down.

Fig. 7 The displacement of the interface between PEH and PEB with time under an in-plane grad-T field. The slopes of Δx vs. t^0.5 are indicated.

The D^*_B in PEH_high-T/PEB sample is 71.73 μm² s⁻¹, smaller compared with the corresponding value in PEH/PEB_high-T sample (139.51 μm² s⁻¹) in the fast stage. The presence of temperature gradient would induce a substantial and directional heat flux normal to the interface of two polymer films. The directionality of heat flux significantly influence the interdiffusion of two polymeric components. As the direction of diffusion of PEB component is consistent with the heat flux (PEB is placed at the warmer region) in the grad-T field, the thermal gradient leads to the enhanced interdiffusion in PEH/PEB system. As pointed out before in a polymer solution system having a positive Soret coefficient, the polymer diffuses from the warmer regions to the cooler regions of a temperature gradient field.³¹ The force of a temperature gradient acting like the pressure gradient induced by different mobilities of two components significantly influences the interdiffusion of PEH/PEB system. We suggest that thermal gradients can generically lead to an enhanced interdiffusion of two polymeric components with faster moving component placed at the warmer region of grad-T hot stage. The interdiffusion behavior is influenced by the force of a temperature gradient (Soret effect).

We also investigated the diffusion behavior of PEB diffusing into blends of PEH and PEB (denoted as PEB/blend). Fig. 8 shows that the POM images of PEB/blend samples after annealing at 160 °C for different times.

Fig. 8 The POM images of PEB/blend samples after annealing at 160 °C for different times. The composition of PEB in the blend side is 0.5 (a), 0.6 (b), 0.7 (c), 0.8 (d) and 0.9 (e). (f) The displacement of the interface between PEB and blend annealed at 160 °C for different times. The scale bar corresponds to 100 μm and also applies to all images. The slopes of Δx vs. t^0.5 are indicated.

As expected, we observe the moving of interface between PEB and blend toward the amorphous PEB side with time in the PEB/blend sample with ϕ_PEB < 0.9 (ϕ_PEB is the mass fraction of PEB component in binary blend). However, for the PEB/blend sample with ϕ_PEB = 0.9, the interface between PEB and blend surprisingly moves toward the binary blend side. It suggests that the interdiffusion of PEB/blend also depends on blend composition. For ϕ_PEB = 0.9 PEB/blend system, the high M_w component of PEH becomes the faster diffusing species and the self-diffusion coefficient of PEH, D^*_H, can be extracted. The extracted D^*_H of the faster diffusing species for ϕ_PEB = 0.9 PEB/blend sample, is 2.67 μm² s⁻¹. Fig. 9 shows that the values of D^*_B vary with the blend compositions, exhibiting a maximum at ϕ_PEB = 0.7. As pointed out before in a polystyrene (PS)/poly(2,6-dimethyl-1,4-phenyieneoxide) (PXE) system by Kramer et al.,⁴¹ the self-diffusion coefficients markedly vary with the composition of the mixture since the excess Gibbs free energy of mixing per segment strongly depends on the composition of the mixture. The self-diffusion coefficients of PS exhibit a strong maximum with ϕ_PXE. We also see that the diffusing process for ϕ_PEB = 0.7 PEH/blend system having the high interdiffusion rate is divided into two stages: fast stage and slow stage, as expected.

Fig. 9 The self-diffusion coefficients vs. PEB composition in the PEB/blend system.

In the presence of an in-plane temperature gradient the interdiffusion of PEB/blend system with PEB placed at the warmer region of grad-T hot stage is enhanced due to Soret effect (Fig. 10). However, as the diffusion direction of PEB component is opposite to the heat flux, where PEB is placed at the cooler region of grad-T hot stage, the PEB diffusing into the blend slows down. For PEB/blend_high-T samples with ϕ_PEB = 0.8 and 0.9, the low M_w PEB becomes the slower moving component. This behavior is what one expects since the pressure gradient induced by different mobilities of two species is against the heat flux (induced by the temperature gradient) and the excess Gibbs free energy for creating a polymer mixture strongly depends on the composition of the mixture. Our results suggest that the temperature gradient indeed influences the dynamical properties of long chain polymeric molecules. In the presence of the temperature gradient, the self-diffusion coefficients vary with the blend compositions, also exhibiting a maximum at ϕ_PEB = 0.7 (shown in Fig. 11).

Fig. 10 The displacement of the interface between PEB and blend vs. square root of annealing time under an in-plane grad-T field. The composition of PEB in the blend side is 0.5 (a), 0.6 (b), 0.7 (c), 0.8 (d) and 0.9 (e). The slopes of Δx vs. t^0.5 are indicated.

Fig. 11 The self-diffusion coefficients vs. PEB composition in the PEB/blend samples.

We take a closer look at the interdiffusion of PEB_high-T/blend sample with ϕ_PEB = 0.9. The interface between PEB/blend sample moves toward PEB side with two different diffusion rates. This two-step interdiffusion behavior in ϕ_PEB = 0.9 PEB_high-T/blend system might also be caused by the variation in local compositions ϕ during the diffusion process, as mentioned before. However, in the homo-T field the moving of the interface is toward the blend side with time in the ϕ_PEB = 0.9 PEB_high-T/blend sample (Fig. 8). It is a strong indication that temperature gradient greatly enhances interdiffusion of PEB/blend system as the diffusion of PEB component is consistent with the heat flux.

Controlling the interdiffusion behavior of plastomer/elastomer allows for a precise control of the mechanical property gradient, which should be a useful tool in designing polymer films with inhomogenous mechanical properties. It is also possible that the net mass flux behavior across the interface in dissimilar binary polymer system might be useful as a diagnostic for the buildup of “thermal force” during thermal processing, perhaps even providing a new method for detecting large “thermal force” in polymer system.

Conclusion

We have investigated interdiffusion process of binary polymer system by polarized optical microscope. Due to the different mass fluxes across the interface, the shift of the interface between two polymer films toward the faster moving species side is observed. The direction of the shift of interface is influenced by temperature gradient and blend composition in PEB/blend system. The temperature gradient is evidently a common situation encountered in manufacturing applications and is a closely analogous physical situation to polymer films locally heated. The in-plane thermal gradient accelerates polymer migration through the enhancement in polymer diffusion along the direction of temperature gradient due to Soret effect. If the direction of “thermal force” induced by the temperature gradient is consistent with the pressure gradient caused by the different mobilities of two components, the “thermal force” will enhance the interdiffusion of polymer system. On the contrary, the “thermal force” will slow down the polymer interdiffusion into each other. We can indeed control the net mass flux across the interface and the movement of original interface between two polymer films by changing the direction of temperature gradient and composition of binary polymer blends. It seems likely that our observations show the potential technological significance for applications in which mechanical property gradient is important, e.g., response of cells to polymer coatings. The present study also shows the self-diffusion coefficient of faster moving species does indeed vary strongly with blend composition and exhibits a maximum at ϕ_PEB = 0.7 in PEB/blend system. We believe these results should be of great interest to researchers making fundamental studies (e.g., studies of elastic modulus, film friction and adhesion properties). This report may provide the starting point for modeling the effects of the temperature gradient on polymer material properties.

Acknowledgements

The authors acknowledge financial support of National Basic Research Program of China (973 Program) (No. 2012CB821505), and National Natural Science Foundation of China (No. 21274103, 21104054 and No. 21204059).

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