Haifeng Shiab,
Hua Jiangab,
Guoqiang Fanc,
Zhaohui Yang*a and
Xiaohua Zhang*a
aCenter for Soft Condensed Matter Physics and Interdisciplinary Research, Soochow University, Suzhou, 215006, China. E-mail: zhangxiaohua@suda.edu.cn; yangzhaohui@suda.edu.cn
bCollege of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou 215123, China
cSINOPEC Beijing Research Institute of Chemical Industry, Beijing, 100013, China
First published on 6th July 2015
We have investigated the interdiffusion of two dissimilar polymer species with different molecular masses, Mw, 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 Mw 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 Mw 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.
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 studies20,24 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.
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.
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Fig. 2 Cooling DSC scans at 10 °C min−1 after annealing the sample at 160 °C for 10 min in DSC sample cell. |
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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 Mw) 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 Mw component). In PEH/PEB system, the PEB is the low Mw 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.
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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 Mw component). By the numerical calculation, the constant, C, was determined as a function of NA/NB (NA and NB are the degree of polymerization of species A and B, respectively). For the PEH/PEB system with a ratio of NA/NB 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 t0.5. Values of C(D*)0.5 obtained from the slopes of Δx vs. t0.5 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).
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.
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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 Mw PEB is placed at high temperature zone of grad-T hot stage (denoted as PEH/PEBhigh-T), the interface between PEH and PEB moves faster as compared to a sample with the high Mw PEH placed at the high temperature zone (PEHhigh-T/PEB) during the fast stage of interdiffusion (t < t′). In the slow stage of interdiffusion (t > t′), the interdiffusion of PEH/PEBhigh-T slows down.
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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. t0.5 are indicated. |
The D*B in PEHhigh-T/PEB sample is 71.73 μm2 s−1, smaller compared with the corresponding value in PEH/PEBhigh-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.
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 ϕPEB < 0.9 (ϕPEB is the mass fraction of PEB component in binary blend). However, for the PEB/blend sample with ϕPEB = 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 ϕPEB = 0.9 PEB/blend system, the high Mw 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 ϕPEB = 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 ϕPEB = 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 ϕPXE. We also see that the diffusing process for ϕPEB = 0.7 PEH/blend system having the high interdiffusion rate is divided into two stages: fast stage and slow stage, as expected.
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/blendhigh-T samples with ϕPEB = 0.8 and 0.9, the low Mw 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 ϕPEB = 0.7 (shown in Fig. 11).
We take a closer look at the interdiffusion of PEBhigh-T/blend sample with ϕPEB = 0.9. The interface between PEB/blend sample moves toward PEB side with two different diffusion rates. This two-step interdiffusion behavior in ϕPEB = 0.9 PEBhigh-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 ϕPEB = 0.9 PEBhigh-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.
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