Diffusion Mechanism for - American Chemical Society

Mar 10, 2014 - Department of Polymer Science and Engineering, School of ... Center, School of Chemical Biology & Biotechnology, Peking University Shen...
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Diffusion Behavior of Polystyrene/Poly(2,6-dimethyl-1,4-phenylene oxide) (PS/PPO) Nanoparticles Mixture: Diffusion Mechanism for Liquid PS and Glassy PPO Linling Li,† Xiaoliang Wang,† Dongshan Zhou,† Chao Teng,‡ Qing Sun,§ and Gi Xue*,† †

Department of Polymer Science and Engineering, School of Chemistry and Chemical Engineering, Key Laboratory of High Performance Polymer Materials and Technology (Nanjing University), Ministry of Education, State Key Laboratory of Co-ordination Chemistry, Nanjing National Laboratory of Microstructures, Nanjing University, Nanjing 210093, P. R. China ‡ Nano-Micro Materials Research Center, School of Chemical Biology & Biotechnology, Peking University Shenzhen Graduate School, Shenzhen 518055, China § Department of Pharmacology of SUNY, Upstate Medical University, Syracuse, New York 13210, United States S Supporting Information *

ABSTRACT: We investigated the diffusion behavior of polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide) (PS/ PPO) nanoparticles mixture prepared by the nanoprecipitation method. The diffusion experiments of liquid PS into the glassy PPO matrix (l-PS/g-PPO) were conducted by annealing the PS/PPO mixture at temperatures between the glass transition temperatures (Tgs) of the PS and PPO components. By tracing the Tg evolution of the PS-rich domain behind the diffusion front, we obtained the master curve of PS volume fraction during diffusion by time−temperature superposition (TTS) and studied the diffusion mechanism of the l-PS/g-PPO system based on the core−shell model. As there is ongoing debate on the diffusion mechanism for the liquid/glassy polymers interdiffusion, herein we confirm that the diffusion behavior of PS/PPO nanoparticles mixture follows the characteristics of the Fickean mechanism rather than the case II mechanism. Both of the shift factors (aT) and the diffusion coefficients in the initial (Dinitial) obey the Arrhenius equation, which yield almost the same apparent activation energy (Edf) (about 153.6 kJ/mol). As the PS/PPO nanoparticles mixture is a limited liquid supply system, both of the calorimetric and rheological measurements reveal the departure in the time scaling laws, which corresponds to the change of PS chain dynamics from the reptation type to the Rouse type during the diffusion process.

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INTRODUCTION Polymer diffusion plays an important role in various fields of polymer applications, such as adhesion, mixing, phase separation, packing, and coating. Investigation of the diffusion behavior at polymer interfaces is practically important, as it controls the kinetics of polymer blending and welding process that influences the performance of the final products.1 In the past decades, the diffusion behaviors of organic penetrants in glassy polymer matrix have attracted a lot of attention. It seems that the size of the penetrant molecules can significantly influence the diffusion behavior. The penetration of small molecules into glassy polymers has been widely studied and understood, where the case II mechanism is applied in most conditions.2−5 However, the penetration of large molecules in glassy polymer matrix is much less investigated, and some controversial results have been reported.6−13 The approaches to model the diffusion process are generally based on a dimensionless group called the diffusional Deborah number (De), which is defined by Vrentas14 as the ratio of the © 2014 American Chemical Society

characteristic relaxation time of polymer chains (τm) to the characteristic diffusion time (τd). It reveals that the transport behavior of polymers is determined by the diffusion mobility relative to the relaxation rate of polymeric segments:15 for the diffusion cases that the diffusion rate is much quicker than the segmental relaxation, such as the penetration of small molecules into glassy polymers, the diffusion behaviors follow the case II diffusion characteristic, while for the diffusion cases that the diffusion rate is much slower than the segmental relaxation, such as that of rubbery−rubbery polymers interdiffusion, the diffusion behaviors obey the classic Fick’s laws. However, for the diffusion cases that the diffusion rate is comparable to the segmental relaxation, such as the diffusion of liquid polymer into a glassy polymer matrix, the diffusion mechanism becomes complicated. Composto and Kramer6 first studied the diffusion Received: October 24, 2013 Revised: February 13, 2014 Published: March 10, 2014 2131

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during diffusion, which is very sensitive to the features that control the diffusion process. As the diffusion mechanism for the liquid/glassy polymers is a controversy topic, here we also paid a lot attention to the diffusion mechanism of the PS/PPO nanoparticles mixture. Besides, we also investigated the polymer dynamics during diffusion by dynamic mechanical analysis (DMA) based on the reptation theory.

behavior of liquid polystyrene into glassy poly(phenylene oxide) matrix (l-PS/g-PPO) using Rutherford backscattering spectrometry (RBS). They found that the movement of the liquid−glassy interface toward the glassy side scaled at the square root with diffusion time, which was consistent with the characteristic of Fickean diffusion. Later, Sauer and Walsh7,8 showed the conflict results for the diffusion of liquid poly(vinyl methyl ether) into glassy polystyrene (l-PVME/g-PS) by neutron reflection (NR) and spectroscopic ellipsometry (SE). The linear dependence of the front propagation with time indicated that the case II diffusion process prevailed in the liquid−glassy interface. Lin et al.9 investigated the chain diffusion behavior at the rubbery/glassy polymer interface using the depth-resolved technique of secondary ion mass spectroscopy (SIMS), and they found the polymer chains diffused across the interface showing both the Fickean and the case II characteristics simultaneously. Recently, Tomba et al.10−13,16,17 employed the confocal Raman microspectroscopy in the depth-profiling mode to study the diffusion behavior at the liquid−glassy polymer interface and concluded that case II diffusion mechanism must not be expected for the diffusion of liquid polymers into glassy matrix due to the negligible osmotic pressure. It seems that the diffusion mechanism for the liquid− glassy polymer system is hard to reach a consensus. In our previous works, we investigated the polymer compatibility and interdiffusion behavior of deuterated polystyrene (PS-D) and hydrogenated poly(2,6-dimethyl-1,4phenylene oxide) (PPO) at the molecular level by dipolar filter 1 H solid-state NMR under fast magic angle spinning (MAS).18,19 It was observed that the evolution of chain interpenetration between the PS-D and PPO was composed of two stages: the wetting stage and the diffusion stage. Besides the spectroscopic techniques mentioned above, the thermal and rheological analyses can also be used to probe the interdiffusion behavior at polymer/polymer interface. Dlubek et al.20−22 studied the interdiffusion in a particle/matrix system of poly(vinyl chloride) and poly(n-butyl methacrylate) (burying the PVC nanoparticles into the PnBMA matrix) using differential scanning calorimetry (DSC). Because of the large surface−volume ratio of diffusion system, the variation of the glass transition temperature (Tg) becomes quite sensitive to the feature of the diffusion process. The complex dynamic behavior of polymer in the melt state can be described by the tube model,23−25 in which the chain moves along a virtual tube defined by the surrounding chains. By tracing the time evolution of dynamic complex shear modulus (G*(t)), Bousmina et al.26,27 have successfully utilized the rheological method to study the diffusion at the polymer/polymer interface. As the polystyrene (PS)/poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) polymer pair has attracted considerable attention due to its excellent performance and good compatibility in all blending proportions and over a considerable range of molecular weights, herein we choose this polymer pair for our diffusion experiment. In this article, we prepared the polystyrene/poly(2,6-dimethyl-1,4-phenylene oxide) (PS/ PPO) nanoparticles mixture by the nanoprecipitation method developed by Fessi and co-workers28,29 and then investigated the diffusion behavior of the PS/PPO mixture at several temperatures below the glass transition temperature (Tg) of the PPO matrix using differential scanning calorimetry (DSC). By tracing the Tg evolution of the PS-rich domain behind the diffusion front, we studied the evolution of PS volume fraction

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EXPERIMENTAL SECTION

Materials. The monodisperse polystyrene sample (Mn = 100 kg/ mol, Mw/Mn = 1.06, labeled as PS100K) was purchased from Polymer Source Inc. (Dorval, Canada), and the poly(2,6-dimethyl-1,4-phenylene oxide) sample (Mn = 20.8 kg/mol, Mw/Mn = 1.97, labeled as PPO20K) was purchased from Sigma-Aldrich Co. The molecular weight of the polymer was characterized by gel permeation chromatography (GPC). The antioxidant (Santonox) was purchased from J&K CHEMICA Co. (Beijing, China) and used as received. Sample Preparation. The demixed PS/PPO mixture for diffusion experiment was prepared by physical mixing the PS100K and PPO20K latex prepared by the nanoprecipitation method. First, the polymer/ toluene solutions with 1 wt % concentration were prepared and stirred overnight to ensure homogeneity. Then, the solutions were dropped into a large amount of ethanol slowly with vigorous stirring (800 rpm), separately. The resulting polymer latex samples were then repeatedly washed by ethanol to ensure no residual solvent remaining in the polymer matrix. The PS100K/PPO20K nanoparticles mixture was prepared by mixing PS100K and PPO20K latex samples (contain the equal amount of polymer mass, PS100K/PPO20K = 50/50) together and ultrasonicating for 10 min. In addition, antioxidant (Santonox, 200 ppm) was added to the mixture to prevent the oxidation during annealing at high temperatures. Finally, the PS/PPO nanoparticles mixture was dried under vacuum at room temperature until reaching a constant weight. To obtain the standard curve of PS/PPO blends (the glass transition temperature, Tg vs the PS mass fraction, wPS), a series of PS100K/PPO20K blends with different PS weight fractions were prepared. The PS and PPO samples with different ratios were dissolved in chloroform and then solution-casted onto the thin cover glasses. After drying the films in ambient environment for several days, they were dried under vacuum for 12 h at temperature about 20 K above each Tg (here the Tg value was estimated by the Fox equation). Transmission Electron Microscopy (TEM) and Scanning Electron Microscopy (SEM). TEM was conducted on a JEM-1011 instrument (JEOL Co.) at 80 kV. One drop of PPO latex was placed on the sample grid, and then the solvent was evaporated. The morphologies of PS100K/PPO20K nanoparticles mixture before and after annealing were characterized by SEM, which was performed using a Hitachi S-4800 instrument at an accelerated voltage of 20 kV and different magnification. For the samples after annealing, the morphology of cross section part was investigated. Differential Scanning Calorimetry (DSC). The DSC measurements were performed on a PerkinElmer DSC-Pyris1 system. The temperature was calibrated with indium standard. All the measurements were carried out under an argon atmosphere (20 mL/min). The sample mass varied from 5 to 10 mg. The glass transition temperatures (Tgs) of pure polymers and well-mixed PS/PPO blends with different ratios were investigated in the temperature range from 50 to 250 °C at the heating and cooling rates of 20 K/min. To trace the diffusion process of PS100K/PPO20K nanoparticles mixture at different annealing temperatures (Tas), a thermal procedure with two processes (the annealing process and Tg measurement process) as shown in Figure S1a of the Supporting Information was designed and described as below: in the annealing process, the demixed PS/PPO nanoparticles mixture was first heated from 50 °C to the annealing temperature (Ta) at a quick heating rate (40 K/min, to minimize the polymer diffusion may take place during the DSC runs), and then after holding at Ta for certain annealing time (ta), it was cooled back to 50 °C with the same cooling rate (40 K/min); in the Tg measurement process, a reheating scan from 50 to 250 °C at 20 K/min was carried out to determine the 2132

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glass transition temperature of the sample after annealing. Besides, in Figure S1b,c, we also investigated the influence of heating and cooling rates on the final results; for details please see the discussions in the Supporting Information. In this article, the middle point of the glass transition region is taken as the glass transition temperature. Dynamic Mechanical Analysis (DMA). To investigate the dynamic behavior of polymer chains during the diffusion process, we performed the rheological experiment on the DMA/SDTA861e instruments (Mettler Toledo Inc.). The samples for rheological measurement were prepared by compression molding the powdery PS/PPO nanoparticles mixture at room temperature into a disk form with 13 mm in diameter and 0.7 mm in thickness using a pressure of 500 MPa. The DMA measurement was carried out in the oscillatory shear mode under the N2 atmosphere. As shown in Figure S2, two identical samples were clamped symmetrically into the shear fixture with the sandwich structure. During the measurement, the molds on two sides were stationary, and the one in the middle was movable. An oscillatory stress was applied to the sample, the shear strain was 10 μm, and the frequency range was from 1 to 10 Hz. The sample was first heated from 25 to 190 °C at 3 K/min and then held at 190 °C for 600 min; the evolution of complex shear modulus (G*) during the diffusion process was monitored.

estimated. The morphological evolution of PS/PPO nanoparticles mixture during annealing was investigated by SEM. SEM micrographs of the PS/PPO mixture before and after annealing at 180 °C (for 2 and 120 min) are shown in Figure 1b−d. As shown in Figure 1b, the PS and PPO nanoparticles present the separated state before annealing. The diffusion couple PS/PPO has a large difference in Tg (Tg of PPO is 110 K higher). When annealing at temperatures between the Tgs of PS and PPO, the molten PS should first wet the glassy PPO nanoparticles before the interdiffusion process. In this process, liquid PS infiltrates into the gaps among PPO nanoparticles and forms a nanostructure of molten PS-capped glassy PPO nanoparticles. In our experiment, the PS/PPO nanoparticles mixture contains the equal amounts of PS and PPO. If ignoring the difference in density of PS and PPO, the thickness of the molten PS layer capping the PPO nanoparticles is about 26 nm. Previous studies reveal that the PS/PPO couple usually forms a sharp glassy−rubbery interface with a thickness around 25 nm before interdiffusion, which can be considered as an “intermixing layer”, a region where the mass transport steps.9,10 The PS/PPO pair has known to be miscible at any concentration due to the quite negative Flory−Huggins interaction parameter, χ.30 In our system, when the liquid PS contacts with the glassy PPO particle surface, the liquid PS molecules would quickly plasticize the glassy PPO molecules and form an intermixing layer. Once the PPO molecules are sufficiently plasticized, the individual PPO chains are then able to undergo higher order chain motions to diffuse in the liquid state. At the early stage of diffusion process, due to the formation of PS-capped PPO nanostructure, the PS nanoparticles flow away from their original places, which would generate some cavities inside the sample as shown in Figure 1c. As the diffusion process continues, the liquid PS chains continually plasticize the glassy PPO chains at the PS−PPO interface, and the glassy−rubbery interface gradually moves toward the PPO domain. Meanwhile, the plasticized PPO chains disperse into the liquid PS phase quickly, which results in a homogeneous PS-rich domain behind the advancing diffusion front.18 At the later stage of diffusion process, the PPO domain almost disappears, and the system becomes a nearly homogeneous mixed PS/PPO blend (seen in Figure 1d). Figure 1e illustrates the schematic pictures of the morphological evolutions for PS/PPO nanoparticles mixture before and during diffusion. Differential scanning calorimetry (DSC) is a classical and convenient method to diagnose the degree of compatibility in polymer blends. Herein we used the DSC method to monitor the interdiffusion process of PS/PPO nanoparticles mixture by measuring the change in Tg value. First, we investigated the influence of annealing temperature (Ta) on the diffusion behavior. Figure 2a shows the DSC heating traces of PS/PPO nanoparticles mixture after annealing at different annealing temperatures for 0.5 min. The PS/PPO nanoparticles mixture displays two distinct Tgs when annealing at low Tas. The lower Tg corresponds to the PS-rich domain, and the higher one corresponds to the PPO domain as illustrated in Figure 1e. However, the intermixing layer is absent. This absence can possibly ascribe to the relatively thin thickness of the PS-rich domain which induces a very fast mass transport between the intermixing layer and PS-rich domain. At the subsequent heating, it is difficult to distinguish them. When annealing at very low Tas (such as 150 and 160 °C), the Tg of PS-rich domain is close to the value of pure PS. With the increase of Ta,

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RESULTS AND DISCUSSION Figure 1a shows the TEM micrograph of the PPO latex prepared by the nanoprecipitation method. The size distribution of the PPO nanoparticles ranges from about 50 to 400 nm, and the number-average nanoparticle diameter of ca. 200 nm is

Figure 1. Morphology of PPO latex and the morphological evolutions of the PS/PPO nanoparticles mixture during diffusion characterized by TEM and SEM: (a) shows the TEM micrograph of PPO latex; the inset is the photo of PPO latex. (b), (c), and (d) are the SEM micrographs of PS/PPO nanoparticles mixture before diffusion (b) and after annealing at 180 °C for 2 min (c) and 120 min (d). (e) represents the schematic pictures of the morphological evolutions for the PS/PPO nanoparticles mixture before and during diffusion; the red color represents the PS or PS-rich component, and the blue color represents the PPO component. 2133

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Figure 2. Influence of annealing temperature (Ta) on the diffusion behavior of PS/PPO nanoparticles mixture characterized by DSC: (a) the DSC heating traces (20 K/min) of the PS/PPO nanoparticles mixture after annealing at different diffusion temperatures for 0.5 min, the arrows point out the Tgs of PS-rich domain and PPO domain; (b) the relationship of the Tg of the PS-rich domain and the annealing temperature. The solid line is the fitting curve by Boltzmann function. The red and blue star symbols represent for the Tgs of pure PS and the well-mixed PS/PPO (50/50) blend, respectively.

Figure 3. Diffusion process of the PS/PPO nanoparticles mixture at different diffusion temperatures (Ta) traced by DSC. (a) DSC heating traces (20 K/min) of PS/PPO nanoparticles mixture after annealing at 180 °C for different diffusion times (ta); the red and blue dashed lines represent the variations of the Tgs of PS-rich domain and PPO domain, respectively. (b) Relationship between the Tg of PS-rich domain and the elapsed diffusion time at different Tas; the solid lines are guides to the eye.

Figure 4. (a) DSC thermograms of pure PS, PPO, and the PS100K/PPO20K blends with different ratios; the arrow line points out the variation trend of Tgs. (b) Standard curve for PS100K/PPO20K blends (the glass transition temperature, Tg, vs the PS mass fraction, wPS). The solid and dashed lines are calculated by the Fox (black), Gordon−Taylor (red), and Couchman (blue) equations.

the Tg of PS-rich domain would gradually increase and approach to a fixed value (close to the Tg of well-mixed PS/ PPO (50/50) blend) when Ta is close or higher than the Tg of PPO (Tg,PPO = 213 °C). Meanwhile, the Tg of PPO domain almost stays the same and disappears at high Tas. The exothermic peak before the Tg of PPO domain is due to the

collapse of the cavities inside the sample (seen in Figure 1c) during the reheating process. In a certain period of time, more PPO chains disperse into the PS-rich domain the higher Tg can be measured. Herein, the rate of diffusion process can be qualitatively judged by the value of the Tg of PS-rich domain. As shown in Figure 2b, we can see that the diffusion process is 2134

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Figure 5. (a) Chemical composition of the PS-rich domain as a function of the elapsed diffusion time for the PS/PPO nanoparticles mixture at different annealing temperatures. (b) Temperature dependence of the half diffusion time (t1/2). (c) Master curve of the PS volume fraction vs the elapsed diffusion time at the reference temperature 180 °C using the time−temperature superposition (TTS) principle; the solid line is the curve fitted by the Boltzmann equation. (d) Arrhenius relationship of the shift factor, aT, with the temperature, 1000/T.

very slow at low Tas due to the low mobility of PS chains, and it accelerates quickly with increasing Ta. The diffusion process is extremely fast as Ta is close to or higher than the Tg of PPO, and the diffusion time 0.5 min is enough to form a well-mixed PS/PPO blend. In addition to the high mobility of PS chains and the revival of PPO domain, such fast mixing is partly due to the unique PS/PPO nanostructures in our system. Second, we investigated the diffusion behavior of PS/PPO nanoparticles mixture with various annealing times at different Tas. Based on the results of Figure 2, the diffusion temperature range in our experiment is chosen to be 170−190 °C, at which the diffusion process is neither too fast nor too slow. Figure 3a shows the DSC heating traces of PS/PPO nanoparticles mixture after undergoing the diffusion with various annealing times at 180 °C. As time goes on, the Tg of PS-rich domain gradually increases, while the Tg of PPO domain stays the same, which is similar to the behavior observed in Figure 2. Figure 3b shows the relationships between the Tgs of PS-rich domain and the elapsed diffusion times (ta) for PS/PPO nanoparticles mixture annealing at different Tas. For all Tas, the increase of the Tg of PS-rich domain is very rapid at the beginning of the diffusion process and gradually slows down in the later time. In Figure S3, the normalized temperature derivative of the heating curves in Figure 3a is presented: the Tg value of the PS-rich domain gradually increases, but the distribution of Tg almost stays the same during diffusion, which indicates an equilibrium composition in the PS-rich domain. To calculate the chemical composition of the PS-rich domain, a series of mixed PS100K/PPO20K blends were prepared by the solution-cast method, and the standard curve of PS/PPO blends was plotted. Figure 4a shows the DSC thermograms of

pure PS100K, PPO20K, and mixed PS100K/PPO20K blends with different ratios. Figure 4b compares the experimental data and the theoretical curves fitted by the Fox equation, the Gordon− Taylor equation, and the Couchman equation (eqs 1−3).31,32 1

Fox equation:

Tg,blend

=

wPS 1 − wPS + Tg,PS Tg,PPO

(1)

Gordon−Taylor equation: Tg,blend =

Tg,PPO + (kTg,PS − Tg,PPO)wPS 1 + (k − 1)wPS

(2)

Couchman equation: ln Tg,blend =

(1 − wPS) ln Tg,PPO + kwPS ln Tg,PS 1 + (k − 1)wPS

(3)

Tg,PS, Tg,PPO, and Tg,blend are the glass transition temperatures of the pure PS100K, PPO20K, and the PS100K/PPO20K blend, respectively. wPS is the weight fraction of PS in the PS/PPO blend, and k is the parameter of the equations. It reveals that the experimental data are best fitted by the Gordon−Taylor equation with the parameter k = 1.47. Previously, we investigated the miscibility of PS/PPO blend confined in thin films by alternating current (ac) calorimetry.32 Only one glass transition was observed even for the thinnest film (6 nm, corresponding to about half of PPO’s radius of gyration, Rg). The well miscibility of PS/PPO blend can be ascribed to the strong interaction between the phenyl ring of PS and phenylene ring of PPO.19 Besides, in the thin films, the composition 2135

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Figure 6. (a) Schematic graph of the morphological evolution and chemical composition development of the PS/PPO nanoparticles mixture for the l-PS/g-PPO diffusion process. (b, c) Kinetics of the advancing diffusion front for annealing experiments performed at different temperatures: (b) the advance of the diffusion front (rdf) as a function of the elapsed diffusion time (t) and (c) rdf as a function of the square root of the elapsed diffusion time (t1/2).

could also be fitted by the Boltzmann equation. As shown in Figure 5d, the shift factors (aT) obey the Arrhenius relationship, which yields an apparent activation energy (Edf) of about 158.7 ± 8 kJ/mol. Previous studies about the diffusion behavior of polymer− polymer couples are mainly based on the planar two-layer model. A different core−shell model is proposed due to the spherical geometry of our system. The sketch of the morphological evolution and chemical composition development of the PS/PPO nanoparticles mixture is shown in Figure 6a. Based on the mass conservation principle, the depth of the glassy−rubbery interface moving toward the PPO domain (rdf) can be calculated by eqs 4 and 5. In eq 4, the left and right parts are the total mass of the PPO components before and after the diffusion process, respectively, and mPPO and mPS represent the mass of PPO and PS components before diffusion (t = 0), respectively. The right part is divided into two terms: one is the PPO component in the PS-rich domain, and the other is the glassy PPO remained in the core volume.

dependence of Tg can also be well described by the Fox, Couchman, or Gordon−Taylor mixing law that are used for the miscible bulk blends. So we believe that the standard curve shown in Figure 4b should be applicable to the PS-rich domain. The PS-rich domain behind the advancing diffusion front corresponds to the highest polymer mobility in the system, and its time evolution is very sensitive to the features that control the diffusion process. As the glassy−rubbery interface gradually moves toward the PPO domain leaving behind a PS-rich domain with the equilibrium composition at each transient time, we can convert the Tgs of PS-rich domain in Figure 3b to the chemical composition using the Gordon−Taylor equation in eq 2. Figure 5a shows the relationships between PS volume fraction (ΦPS) of the PS-rich domain (here we ignore the difference in density between the PS and PPO components) and the elapsed diffusion time (ta) for the PS/PPO nanoparticles mixture annealing at different temperatures (Tas). As increasing Ta, the diffusion rate of the PS/PPO nanoparticles mixture increases, so the PS volume fraction decreases faster for higher Tas. The data of PS volume fraction vs the logarithmic elapsed diffusion time for different Tas can all be fitted by the Boltzmann equation. At the very beginning of the diffusion process, the PS volume fraction (ΦPS) equals 1. As the diffusion process continues, the ΦPS gradually approaches to 0.5 (where the elapsed diffusion time ta tends to infinity). If taken the diffusion time where ΦPS = 0.75 as the half time of diffusion process (t1/2), the temperature dependence of t1/2 is shown in Figure 5b. As Ta increases, t1/2 decreases rapidly, and its logarithmic value reveals a linear relationship with Ta. The time−temperature superposition (TTS) principle is a concept widely used in polymer physics to predict the long-term viscoelastic behavior.33 As the curves in Figure 5a do not change shape as the temperature is changed, herein we use the TTS principle to create the master curve of the PS volume fraction vs the elapsed diffusion time at the reference temperature 180 °C (seen in Figure 5c). The shifted data

3 ⎛r ⎛ 1 − ΦPS ⎞ − rdf ⎞ mPPO = ⎜ PPO ⎟ mPPO + ⎜ ⎟mPS ⎝ rPPO ⎠ ⎝ ΦPS ⎠

(4)

As the mass of PS and PPO before diffusion are equal (mPPO = mPS) in our system, so eq 4 can be simplified as 1/3⎤ ⎡ ⎛ 1 − ΦPS ⎞ ⎥ rdf = ⎢1 − ⎜1 − ⎟ rPPO ⎢⎣ ΦPS ⎠ ⎥⎦ ⎝

(5)

where rPPO is the radius of PPO nanoparticle (about 100 nm) and ΦPS is the volume fraction of PS in the PS-rich domain. We note that there have been some studies on the liquid− liquid diffusion behaviors of the same polymer nanoparticles.34−36 Winnik et al. reported energy transfer experiments on poly(butyl methacrylate) (PBMA) latex films prepared from a 1:1 mixture of donor and acceptor labeled 2136

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latex particles.35 According to their researches, for PBMA with high molecular weight, the extent of mixing f m (the values of f m are only indirectly related to the fraction of mass that has diffused across the interface) increased with time as t1/2 at early times, which is consistent with diffusion that follows Fick’s law. At later times, there is a change in sharp crossover to a t1/4 scaling relationship. Similar to Winnik’s method, we define (1 − ΦPS)/ΦPS as the extent of interdiffusion for the l-PS/g-PPO system, which indicates the fraction of PPO component that has diffused across the glassy−rubbery interface. As shown in Figure 7a, we plot the experimental data in Figure 5c

Fickean mechanisms have been proposed. Our results on the PS/PPO nanoparticles mixture support the idea that the Fickean mechanism rather than the case II mechanism is applicable to the diffusion of l-PS/g-PPO system. For the Fickean diffusion mechanism, the characteristic diffusion distance should follow the equation r ∼ 2(D*t)1/2, where D is the diffusion coefficient. From slopes of the data at the beginning in Figure 6c, we calculate the initial diffusion coefficient (Dinitial) of the PS/PPO nanoparticles mixture at different annealing temperatures. Figure 8 shows the relation-

Figure 8. Arrhenius plot of the initial diffusion coefficient (Dinitial) against the annealing temperature (1000/T) of the PS/PPO nanoparticles mixture over the temperature range from 170 to 190 °C. Figure 7. Log−log plots of (a) (1 − ΦPS)/ΦPS and (b) rdf/rPPO vs aTt ((1 − ΦPS)/ΦPS represents the extent of interdiffusion, rdf is the advance of the diffusion front, rPPO is the radius of PPO nanoparticles, and aTt is the annealing time after shifting the experimental data by time−temperature superposition, Tref =180 °C) for the PS/PPO nanoparticles mixture. The black and red lines indicate the slopes of the fitted straight lines.

ship of Dinitial with the reciprocal of the annealing temperature (1000/Ta). The initial diffusion coefficient of the l-PS/g-PPO system obeys the Arrhenius equation, which yields an apparent activation energy (Edf) of 153.6 ± 7.4 kJ/mol. It is almost the same as the value calculated from the plot of aT ∼1000/T in Figure 5d. On the other hand, it verifies the reliability of the core−shell model we proposed. The value of Edf for our l-PS/gPPO system is a little larger than that reported by Tomba,13,16 which is possibly due to the larger molecular weight of PS we used. In both Figure 6c and Figure 7, the departure of original linearity is observed. Although the similar departures in time scaling laws have been reported by other researchers, very different explanations are proposed.11,13,16,27,34,35,37 Winnik et al. speculated the sharp change in time scaling relationships of poly(butyl methacrylate) (PBMA) latex films to the broad dispersity in polymer molecular weight, where the lower molecular weight components scaled at t1/2 and the larger ones scaled at t1/4.35 Bousmina et al. interpreted the two scaling law regimes for polystyrene (PS)/polystyrene welding in terms of reptation theory and attributed the transition between the two regimes to the transition from the Rouse mode to the reptation mode, which strongly depended on the chain-ends distribution at the interface.27 In our system, the penetrant PS molecules are nearly monodisperse, so the effect of polydispersity in molecular weight can be excluded. Besides, the annealing temperature is far above the Tg of PS component, and the influence of chain-ends distribution at the interface could be neglected. As suggested by Tomba et al.,11,13,16 in the limited liquid supply system, the transport of PPO chains toward the liquid PS-rich domain would increase the local Tg along the PS diffusion path, which reduces the gap between the diffusion

logarithmically (in the form of log((1 − ΦPS)/ ΦPS) vs log aTt). At the early times, (1 − ΦPS)/ΦPS appears to increase in proportion to t1/2, crossing over at later times to a t1/4 dependence. As the time evolution of the front positions during diffusion process is a direct way of revealing the type of scaling for the diffusion controlling step,10 we also plot the relationship between the normalized depth of diffusion front rdf/rPPO and the annealing time aTt. As shown in Figure 7b, similar time scaling laws are observed. Our results are consistent with that of Winnik reported for PBMA nanoparticles, which reveal that the diffusion at the early times follows the Fickean mechanism. In Figure 6b,c, we show the calculated advance diffusion fronts, rdf, as a function of the elapsed diffusion time (t) and the square root of elapsed diffusion time (t1/2) at different diffusion temperatures. The diffusion front advances of liquid PS into the glassy PPO matrix are markedly nonlinear with time as shown in Figure 6b, which is definitively not consistent with the case II diffusion mechanism. On the contrary, the data in Figure 6c pass well through the origin and show an excellent agreement with the t1/2 scaling law at the beginning of the diffusion process, which is a characteristic of the Fickean diffusion mechanism and consistent with the results in Figure 7. There is ongoing debate on the diffusion mechanism for the liquid/glassy polymers interdiffusion; both the case II and 2137

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temperature and the local Tg and thus slows down the transport rate of the liquid component. Here, we agree with Tomba’s ideas that the departure from linearity observed in the t1/2 plot should be related to the limited supply of the liquid PS in our system. Different from the calorimetric method to trace the local chemical composition variations in the PS-rich domain, we also employ the rheological method to in situ detect the changes in viscoelastic properties of the l-PS/g-PPO system during the diffusion process. The viscoelastic measurements were carried out in the oscillatory shear mode on Mettler Toledo’s DMA instrument, and the time evolution of the complex shear modulus (G*) was monitored. Figure 9 shows the variation of

dynamics of a polymer chain far above the glass transition temperature is complex and falls into different regimes (the Doi−Edwards regimes 0−IV) with different scaling laws depending on the length and time scales.24,27,38 For the highly entangled polymer chains, the mean-square segment displacement, g(t), is predicted to undergo the time-dependent power law changes from g(t) ∼ t1/2 in the reptation regime (regime III) to ∼ t1/4 in the constrained Rouse regime (regime II).38,39 The experimental window of our rheological measurement is between 1 and 10 Hz. At early times, the mobility of PS chains is very high, and the experimental window locates in the dynamic regime III of polymer chains, which obeys the reptation-type dynamics and scales at t1/2. As the limited liquid supply system we studied, the local Tg in the PS-rich domain gradually increases, which would slow down the dynamics of PS chains. The PS chains begin to feel the topological constraints imposed by the surrounding chains (both of the PS and PPO chains), and the experimental window locates in the dynamic regime II of polymer chains, which obeys the Rouse-type dynamics and scales at t1/4. The rheological results indicate that the change in time scaling laws should correspond to the change of PS chain dynamics during the diffusion process as the limited liquid supply system we studied. What should be mentioned is that the critical time (tc) for the variation of chain dynamics in Figure 9 is much larger than that for the departure of the linearity in Figures 6c and 7. This is possibly due to the difference in the free volume of PPO domains before and after compression. Because of the steric hindrance effect, the free volume of the glassy PPO domain plays an important role in the diffusion behavior. The decrease in free volume would increase the steric hindrance for the diffusion of liquid PS. Positron annihilation lifetime spectroscopy (PALS) has proved to be a unique experimental technique for determining the size and concentration of free volume in polymers.40,41 Figure S4 compares the free volume sizes of PPO nanoparticles samples under different compressions (the sample suffered very small pressure is considered to be the same state as the powdery sample) and PPO bulk sample using the PALS method. The PPO chains in the nanoparticles prepared by the nanoprecipitation method have the reduced chain packing density and larger free volume than the bulk sample, while the average free volume size recovers back to the bulk characteristic after applying the high compression. So the whole diffusion rate of PS/PPO nanoparticles mixture slows down after compression.

Figure 9. Polymer dynamics of the compressed PS/PPO nanoparticles mixture during annealing at 190 °C under the frequency range of 1− 10 Hz: black (1 Hz), red (2 Hz), blue (5 Hz), and green (10 Hz). The dashed line points out the critical point (tc) where the polymer dynamics changes, and the solid lines are the linear fitting curves of the data before and after tc.

G* as a function of annealing time at 190 °C over the frequency range of 1−10 Hz. As discussed above, the microstructures of PS-rich liquid-capped glassy PPO nanoparticles are formed during the diffusion process. Both of the liquid PS-rich domain and glassy PPO domain should contribute to the value of G*, in which the part of glassy PPO plays a dominant role. As the diffusion process continues, the PPO molecules in the PPO domain with high G* gradually blend into the PS-rich domain with much lower G*. So, in contrast with Bousmina’s results,27 the G* in our experiments is found to decrease with increasing the diffusion time. As shown in Figure 9, G*(t) decreases linearly with time (in logarithmic scale) in two time regions and then tends toward a plateau for long diffusion times. G*(t) first decreases with a slope of about −0.5, and then a transition occurs at approximately tc = 85 min, and the slope of G*(t) reduction becomes about −0.25. The decrease in G* is also a signature of diffusion processes across the interface, which should be related to the amount of PPO molecules that depleted in the glassy PPO domain. Clearly, the amount of PPO molecules depleted in the glassy PPO domain should be equal to that blend into the PS-rich domain. This is maybe the reason that the time scaling laws obtained by rheological method echo the results of calorimetry shown in Figure 7a. Essentially, the decrease of G* should connect with the dynamics of PS chains in the PS-rich domain, as the PPO chains should first be plasticized by PS chains before blending into the PS-rich domain. According to the tube model, the

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CONCLUSIONS In this article, we prepared the PS100K/PPO20K nanoparticles mixture by the nanoprecipitation method and investigated the diffusion behavior of liquid PS and glassy PPO by annealing the PS/PPO mixture at several temperatures below the Tg of the PPO matrix. By tracing the Tgs of the PS-rich domain behind the diffusion front advance, the time evolutions of the PS volume fraction (ΦPS) and the diffusion front position (rdf) were investigated. First, the ΦPS data at different diffusion temperatures can be converted to a master curve and the shift factors (aT) obey the Arrhenius equation. Second, we confirm that the diffusion mechanism for the l-PS/g-PPO system should be the Fickean law rather than the case II mechanism as the rdf shows an excellent agreement with the t1/2 scaling law at early times. The diffusion coefficients in the initial of the diffusion process (Dinitial) also obey the Arrhenius equation, and both of the two Arrhenius equations yield the apparent activation 2138

dx.doi.org/10.1021/ma402200d | Macromolecules 2014, 47, 2131−2139

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energy (Edf) of about 153.6 kJ/mol. Besides, the departure in time scaling laws is observed for the diffusion of PS/PPO nanoparticles mixture which can be ascribed to the limited liquid supply system we studied. At last, we investigated the polymer dynamics during the diffusion process by rheological method. On the basis of the reptation theory, we believe that the diffusion of the PS/PPO nanoparticles mixture could be divided into two regimes: one follows the reptation model, and the other obeys the constrained Rouse model.

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ASSOCIATED CONTENT

S Supporting Information *

Thermal procedure used in this study, DSC heating curves at different heating and cooling rates, the sample geometry for viscoelastic measurement, the temperature derivative of the heat flow curves shown in Figure 3a, and the free volume sizes of PPO nanoparticles samples under different compression pressures and PPO bulk sample characterized by positron annihilation lifetime spectroscopy (PALS). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (G.X.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author appreciates the financial support of National Basic Research Program of China (973 program, 2012CB821503) and Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT). This work was also supported by the NSF of China (51133002, 21174062, 21274060, and 21304003).

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REFERENCES

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dx.doi.org/10.1021/ma402200d | Macromolecules 2014, 47, 2131−2139