SAN

Article Cite This: Langmuir 2018, 34, 14358−14367

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Segmental Dynamics and Cooperativity Length of PMMA/SAN Miscible Blend Intercalated in Organically Modified Nanoclay Ehsan Chehrazi*,†,‡ and Nader Taheri-Qazvini*,§,⊥

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†

Department of Polymer Reactions Engineering, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, P.O. Box 14155-143, Iran ‡ Department of Polymer Engineering, Amirkabir University of Technology, Mahshahr Branch, Mahshahr, P.O. Box 6351713178, Iran § Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29208, United States ⊥ Biomedical Engineering Program, University of South Carolina, Columbia, South Carolina 29208, United States S Supporting Information *

ABSTRACT: The effect of nanoconfinement on the segmental dynamics of a poly(methyl methacrylate) (PMMA)/poly(styrene-ranacrylonitrile) (SAN) miscible blend, intercalated into the interlayer spacing of the organically modified nanoclay (OMNC), was investigated using dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC) methods. We reported an unusual phenomenon in which the weak interfacial interactions between the polymer chains and OMNCs was responsible for increase in segmental mobility at the glasstransition temperature (Tg). Remarkably, we found a positive correlation between dynamic fragility and thermodynamic fragility, in which both fragilities decreased under nanoconfinement. The cooperative length of segmental motions, or length of cooperatively rearranging regions, ξCRR, decreased from 2.64 nm for the PMMA/SAN blend to 1.86 nm for the PMMA/SAN/OMNC nanocomposite. The segmental mobility of the PMMA/SAN/OMNC model was also studied using the molecular dynamics simulations. The simulation results showed the increased segmental mobility of the PMMA/SAN chains in the presence of OMNCs, which is in agreement with the DMA and DSC results.

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nearly the same mobility at Tg of the blend.10 Specifically, the PMMA/SAN blend system with a lower critical solution temperature at around 160 °C is homogeneous at Tgs of both components11 and therefore the PMMA and SAN chains are mixed in a molecular scale. The effects of confinement on the segmental dynamics of polymer chains can be investigated in three different types of nanometric confined spaces. The first type includes a thin film of the polymer, confined on a nonpolymeric substrate. To date, a huge number of experimental studies show that the Tg of a polymer thin film under confinement deviates relative to the bulk behavior.7,8,12−17 It is established that not only Tg but also other Tg characteristics of polymer thin films, for example, the fragility index and segmental dynamics, vary under this type of confinement. Fakhraai et al.16 and Lan et al.17 found that confinement of the polymer thin film without strong attractive interactions with a substrate resulted in a reduced Tg,

INTRODUCTION The cooperative motions of chain segments in the glasstransition region govern the segmental dynamics of polymers.1,2 The insertion of polymer chains into the confined media raises the question of how the confinement affects the segmental relaxation behavior of polymers at Tg. If the polymer chains are confined to the scale of several nanometers, segmental dynamics show deviations from the bulk.3,4 In this circumstance, Tg and other Tg properties of confined polymers decrease, increase, or remain the same. These observations may be due to the change in chain conformation,5 change in chain entanglement,6 access to a larger free volume in direct contact with the free surface,7 etc. The effect of confinement on the relaxation behavior of polymers becomes more complicated when it comes to the investigation of polymer blends.8 In a miscible polymer blend, the segmental relaxation depends on the cooperative segmental motions of the individual components at their Tgs.9 When Tgs of components in a thermodynamically miscible polymer blend are close, for example, in poly(methyl methacrylate) (PMMA)/poly(styrene-ran-acrylonitrile) (SAN) blend system, both components are expected to exhibit © 2018 American Chemical Society

Received: September 16, 2018 Revised: October 25, 2018 Published: October 31, 2018 14358

DOI: 10.1021/acs.langmuir.8b03160 Langmuir 2018, 34, 14358−14367

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mers,32,33 to the best of our knowledge, this is the first example of investigating how the intercalated organically modified nanoclay (OMNC) alters the segmental dynamics and cooperativity length in miscible polymer blends. This is important because, in many applications including thin films and nanocomposites where nanoconfinement plays a role, multicomponent polymer systems are involved. In this work, the combined use of differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) is systematically performed to investigate the nanoconfinement effects on the segmental dynamics in the PMMA/SAN/ OMNC nanocomposite at Tg. Furthermore, the principal objective of this study is to understand the effects of the nanoconfinement on the length of CRR in the PMMA/SAN/ OMNC nanocomposite. Moreover, a comparison between thermodynamic fragility and dynamic fragility as the measures of cooperative segmental relaxation is presented. In addition, a comprehensive investigation on the glasstransition behavior and the miscibility of the PMMA/SAN blend, by calculating the Flory−Huggins (FH) interaction parameter, χ, is conducted using the molecular dynamics (MD) simulations. Also, MD simulations are performed to study the effects of the nanoconfinement on the segmental mobility after the intercalation of PMMA/SAN chains into the OMNC platelets.

accompanied by a decrease in fragility and length scale of cooperativity. In the second type, the polymer chains are confined in the vicinity of nanoparticles (e.g., spherical and tubular nanoparticles).18−22 In this regard, the nanoparticles can perturb the segmental dynamics of polymer chains and therefore change the glass-transition behavior of nanocomposites. The polymer segments confined at the interface with nanoparticles experience the effects similar to those that occur in the polymer thin films. However, when the nanoparticles are added to the polymer, two different behaviors are observed in the case of segmental relaxation and cooperative motions at the glass-transition temperature. Sharma et al.18 found that due to the restricted segmental motions of chains bonded to the carbon nanotubes (CNTs), poly(vinylidene fluoride) (PVDF)/PMMA/CNTs nanocomposite showed slower segmental dynamics in the glass-transition region. On the other hand, their group observed that the segmental dynamics of PVDF/PMMA blend increased under confinement, upon addition of the aminated multiwalled nanotubes.19 The third type consists of polymer chains confined between two surfaces such as polymer intercalation into the galleries of layered nanoparticles (e.g., clay or graphite oxide).23−36 Depending on the strength of interfacial interactions between the polymer matrix and layered nanoparticles, the nanometric confinement strongly influences the structural relaxation and segmental dynamics of polymer chains. Lorthioir et al.25 reported a reduced segmental mobility in a poly(ethylene oxide)/clay nanocomposite because the exfoliated clay nanoparticles create hindrance to the segmental dynamics. In contrast, Fotiadou et al.26 investigated the effect of confinement on the segmental dynamics in poly(hexa(ethylene glycol)methacrylate)/clay nanocomposite and observed an enhanced segmental mobility in confined spaces compared to the pure polymer in the glass-transition region. Moreover, it has been well established in the literature that the confinement affects the cooperative length scale, the so-called “cooperatively rearranging region (CRR)”, for chain segments in the glasstransition region.32,33 The dispersion degree of nanoparticles is a crucial factor governing the segmental cooperativity of polymeric nanocomposites in the glass-transition region. As higher interfaces are formed between the polymer and nanoparticles, as a result of strong interfacial interactions, the more restricted structure is anticipated and thus the length of cooperativity increases. On the other hand, weak polymer−nanoparticles interactions result in the decrease of segmental relaxation time and the length of CRR in a polymer nanocomposite.37 Chen et al.32 investigated the segmental dynamics of two structurally different polystyrene (PS)/clay nanocomposites, including the intercalated and exfoliated clay nanoparticles. They observed that the length of CRR in the exfoliated PS/clay nanocomposite was significantly larger than that of the pure PS. However, their similar analysis for the intercalated PS/clay nanocomposite did not show any significant increase in the length of CRR compared to the pure PS. In this regard, Tran et al.33 studied the length scale of cooperativity of an intercalated nanocomposite at Tg, by confining the PMMA chains between the layered silicates. They showed that the segmental cooperativity and the length of CRR decrease upon the incorporation of clay nanoparticles. While most of the studies concerning the effect of nanoconfinement on segmental dynamics have been conducted using model homopoly-

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EXPERIMENTAL SECTION

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METHODS

Materials. Poly(methyl methacrylate) (PMMA) and poly(styreneco-acrylonitrile) (SAN) were obtained from Atofina (France) and Samsung (South Korea), respectively. Organically modified nanoclay (Cloisite 30B) with a cation-exchange capacity of 90 mequiv/100 g was supplied by Southern Clay Products and used without further purification. According to the supplier, the organoclay contains methyl-tallow-bis(2-hydroxyethyl) (MT2EtOH) quaternary ammonium as an organic compatibilizer. Sample Preparation. The PMMA/SAN (50/50 wt %) blend and its corresponding nanocomposite containing 3 wt % of Cloisite 30B were prepared by the melt blending method in a Brabender internal mixer (Germany) at 443 K and 60 rpm. The mixing continued until a constant torque was reached.

Gel Permeation Chromatography. Gel permeation chromatography (GPC) was used to evaluate the molecular weight of PMMA and SAN. The GPC measurements were performed in tetrahydrofuran using a Waters model Alliance GPC 2000 with a refractive index detector. Monodisperse polystyrene standards covering a wide range of molecular weight were used to calibrate the columns. The weight average molecular weight (Mw), number-average molecular weight (Mn), and polydispersity index of PMAA and SAN determined by GPC analysis are collected in Table S1. Elemental Analysis. The nitrogen content of the SAN copolymer was measured by elemental analysis (PerkinElmer 2400 series II CHNS/O Analyzer). The acrylonitrile composition in styrene-coacrylonitrile was calculated by A=

M1

(

N D

)

− |(M 2 − M1) × 0.01|

(1)

where N, D, M1, and M2 are the mass number of nitrogen, nitrogen percent (%), molecular weight of acrylonitrile (53.06 g/mol), and molecular weight of styrene (104.15 g/mol), respectively. The nitrogen content and, therefore, the acrylonitrile content in SAN copolymer were calculated to be 6.14 and 29%, respectively. X-ray Diffraction (XRD). The change in the layer distance of the modified clay before and after melt mixing was studied using X-ray 14359


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Langmuir diffraction (XRD) measurements. XRD patterns were recorded on an X’Pert (Philips, the Netherlands) diffractometer using Cu Kα radiation (λ = 1.54 Å) operated at 40 kV and 100 mA. Experiments were performed in the scanning range (2θ) of 1−10°, at a scanning rate of 1°/s. Differential Scanning Calorimetry (DSC). The glass-transition temperature of all samples was measured using a differential scanning calorimeter (PerkinElmer Thermal Analysis, Diamond DSC) at the inflection point of the endothermic heat flow associated with the glass transition. Samples, approximately 10 mg in weight, were sealed in aluminum pans with the weight identically matching the reference pan. The data of heat capacity (Cp) were evaluated concerning sapphire as a heat capacity standard. Each measurement of the heat capacity (Cp) included three runs: first, the empty pans for baseline determination; second, the sapphire for Cp calibration; and third, the sample run. The samples were held for 10 min at Tg + 60 K to erase thermal history, cooled to 298 K, and finally heated to Tg + 60 K at a heating rate of 10 K/min. All measurements were performed under nitrogen gas atmosphere. Dynamic Mechanical Analysis (DMA). Dynamic mechanical experiments were conducted with a dynamic mechanical analyzer (Diamond DMA, PerkinElmer) in a single cantilever bending mode. Samples with an approximate length of 50 mm and a thickness of 1.5 mm were used. Thermal scans were made from 313 to 423 K at a heating rate of 3 K/min and in the frequency range of 0.1−100 Hz. Simulations Methodology. The molecular dynamics (MD) simulations were performed using the “Amorphous Cell”, “Discover”, and “Forcite” modules of Materials Studio 6.0 simulation software package, a powerful workstation developed by Accelrys Software Inc.38 Details of the MD simulations are described in the Supporting Information. In MD simulations of polymer models, the minimum chain length is one of the most important factors that control the different properties of polymers. The solubility parameter (δ) was used to determine the minimum length of polymer chains. Where the solubility parameter against chain length reaches a nearly flat plateau, the chain length can be assumed as the real polymer chain.39 Therefore, polymer chains of PMMA and SAN with different lengths were put in the simulation cells and the solubility parameters were calculated from the cohesive energy density (eq S1). Figure S1 shows the δ values of PMMA and SAN as a function of the number of repeat units. At 10 repeat units of the PMMA and SAN, the solubility parameter becomes nearly independent of the chain length and thus, only 10 repeat units for both PMMA (Mw = 1002 g/mol) and SAN (Mw = 1163 g/mol) are necessary to simulate a real polymer chain. On the basis of obtained minimum chain length, the threedimensional unit cells of the studied systems under periodic boundary conditions were constructed (Figure S2), with the chemical compositions presented in Table S2. The resultant constructed atomistic structures were subsequently geometrically optimized and energetically minimized by the procedure described in the Supporting Information.

structure suggests that there are no strong interfacial interactions between the PMMA/SAN blend and layered silicate (in comparison to the exfoliated structures) and, therefore, not much interfaces are formed. Interfacial Interactions in the PMMA/SAN/OMNC by MD Simulations. The polymer/filler interfacial interactions govern the degree of intercalation and exfoliation and, consequently, dispersion of fillers within the nanocomposite, that is dependent on the type of filler and its surface modification. Therefore, the strength of polymer/filler interfacial interactions is too crucial to affect the segmental dynamics and cooperativity at Tg. The interfacial interactions between the PMMA/SAN blend and OMNCs were fundamentally investigated on the basis of the interaction energies by MD simulations to obtain more comprehensive information about the nanoconfinement effects on the segmental dynamics. After constructing the model structure of the PMMA/SAN/OMNC nanocomposite, the equilibration procedure was performed as described in the Supporting Information. The interfacial interaction energy between the polymer and fillers can be calculated as41 Eint = Et − (E P + E F)

(2)

where Et is the total potential energy of the nanocomposite model, EP and EF are the potential energy of the polymer and filler, respectively. Table S3 presents the calculated interfacial interaction energies of the PMMA/SAN/OMNC model and its components. The PMMA/SAN/OMNC model has a relatively low interfacial interaction energy (Eint), indicating that interfacial interactions are not high enough to allow the exfoliation of OMNCs and, therefore, intercalation state occurred. Glass-Transition Behavior. Figure 1 shows the typical thermograms of the PMMA, SAN, PMMA/SAN blend, and

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RESULTS AND DISCUSSION OMNC Characterization. Figure S3 shows the XRD patterns of OMNC nanosheets and PMMA/SAN/OMNC nanocomposite. The interlayer distance of nanosheets (d001) was obtained utilizing the Bragg equation.40 The OMNC exhibits an intense peak at 2θ = 4.85° (d001 = 1.8 nm). In addition, the diffraction peaks at 2θ values of 2.69° (d001 = 3.2 nm) and 5.33° (related to 002 planes) are observed in the pattern of nanocomposite. The intensity of the peaks in the nanocomposite was decreased and the main peak was shifted to lower degrees. Therefore, the interlayer distance of OMNC platelets was increased from 1.8 to 3.2 nm in the PMMA/ SAN/OMNC nanocomposite. The slight increase in the interlayer distance demonstrates that PMMA/SAN chains were intercalated into the OMNC interlayers. The intercalated

Figure 1. Typical DSC thermograms of PMMA, SAN, PMMA/SAN, and PMMA/SAN/OMNC.

PMMA/SAN/OMNC nanocomposite, measured by the DSC method. The PMMA/SAN blend exhibits a single glass transition located between Tg’s of the PMMA and SAN copolymer (Figure 1 and Table 1), which suggests that the PMMA and SAN are miscible. 14360


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Langmuir Table 1. Values of Different Parameters Obtained from DSC Analysis for All Systems Tg (K) systems PMMA SAN PMMA/SAN PMMA/SAN/OMNC

ΔCp (J/(g K)) 0.1661 0.2379 0.2506 0.2359

± ± ± ±

0.0003 0.0004 0.0008 0.0006

Cp (J/(g K)) 4.01 2.50 2.76 2.74

± ± ± ±

0.03 0.02 0.01 0.01

δT (K) 3.95 2.83 2.85 2.76

± ± ± ±

sim.

0.04 0.01 0.01 0.02

384.3 375.2 378.8 377.1

The MD simulations were also performed to predict the thermal behavior of neat and OMNC-containing systems. To calculate the Tg’s of the PMMA, SAN, PMMA/SAN, and PMMA/SAN/OMNC models, the energetically minimized and geometrically optimized models were heated from 293 to 493 K and then cooled down to 293 K by 20 K steps. The models were kept at each step for 20 ps under the NPT ensemble. The densities were recorded at each temperature step and plotted against temperature in Figure S4. The density versus temperature data in low- and high-temperature regions were separately fitted to the linear curves (R2 > 0.99). As presented in Figure S4, the density decreases linearly with the temperature and shows a slope change in the temperature range of 374−385 K for all models. When both linear curves with different slopes were extrapolated, they interacted at a temperature which was considered as the glass-transition temperature, Tg. The Tg’s estimated from the intersection of the high-temperature (rubbery) and low-temperature (glassy) regions are 383.1, 374.2, 379.4, and 376.8 K for PMMA, SAN, PMMA/SAN blend, and PMMA/SAN/OMNC nanocomposite, respectively. The predicted Tg’s are in good agreement with the experimental results (Table 1) and demonstrate that MD simulations can be used as a reliable method to predict the miscibility of the polymer blends.42 Miscibility of PMMA/SAN Blend by MD Simulations. The PMMA/SAN blends with different compositions of the PMMA and SAN were generated by “Amorphous Cell” module. Then, the PMMA/SAN models were optimized and equilibrated in the NVT and NPT ensemble simulations at 300 K as described in the Supporting Information. In this work, the Flory−Huggins theory was combined with the MD simulations technique to investigate the compatibility of the PMMA and SAN copolymer. The energy of mixing, ΔEmix, and the Flory−Huggins interaction parameter, χ, of different blends were calculated using eqs S3 and S4, respectively, and are presented in Table S4. The polymerization degrees of the PMMA and SAN were considered as 10 and, thus, χcritical of the PMMA/SAN blend was calculated as 0.2 (eq S5). The calculated χ values are lower than χcritical (Figure 2), indicating that PMMA/SAN blends are miscible in the whole range of compositions, which is in agreement with experimental data reported in the literature.43 Moreover, the χ value of the PMMA/SAN/OMNC nanocomposite is much lower than those of PMMA/SAN blends, suggesting that the presence of OMNC nanoparticles improves the miscibility of the PMMA and SAN copolymer. The improved miscibility of polymer blends induced by nanoparticles was also reported by other researchers.44 From the microstructure point of view, there are the repulsive forces between the styrene and acrylonitrile groups of SAN copolymer.45 Therefore, it is hypothesized that the miscibility of the PMMA and SAN copolymer is affected by the mentioned repulsive forces as well as the interactions between the PMMA and SAN copolymer.

± ± ± ±

VCRR (nm3)

exp. 1.1 0.6 0.4 0.5

383.1 374.2 379.4 376.8

± ± ± ±

0.6 0.3 0.4 0.4

2.36 11.61 7.91 5.57

± ± ± ±

0.4 0.7 0.5 0.6

ξCRR (nm) 0.79 3.87 2.64 1.86

± ± ± ±

0.03 0.07 0.04 0.05

NCRR 16.6 47.6 41.3 29.1

± ± ± ±

1.1 2.1 1.3 0.8

Figure 2. Flory−Huggins interaction parameters of PMMA/SAN blends vs weight fraction of the PMMA.

Specific Interactions in PMMA/SAN. To investigate the specific interactions between different atoms in the PMMA/ SAN model, radial distribution function (RDF) was calculated by MD simulations. The RDF gives the probability of finding an atom with a distance r from another atom compared to the ideal gas distribution,46 that is, completely random distribution. This function gives a way to explore the interactions between atoms or groups in the polymer systems. It is defined as K

gAB

N

∑t = 1 ∑ j =AB1 ΔNAB(r →r + δr ) 1 (r ) = NAB × K ρAB 4πr 2

(3)

where NAB is the total number of atoms of A and B in the simulated system, K is the number of time steps, δr is the distance interval, ΔNAB is the number of B (or A) atoms between r and r + δr around an A (or B) atom, and ρAB is the bulk density. It should be noted that A and B can be the same type of atoms. There is no clear peak in g(r) function of the carbonyl group pairs in the PMMA, indicating the random distribution of carbonyl groups in the PMMA bulk (Figure 3a). The several minor peaks observed in the spectra may be attributed to the nonideal distribution arising from the limited size of the model. Similarly, no clear peak is seen in the spectra of the ether group pairs in the PMMA, due to the random distribution of ether groups in the PMMA bulk (Figure 3b). Figure 3c illustrates the hydrogen−carbonyl group interactions in the PMMA/SAN blend. The RDF of the PMMA/SAN blend shows a sharp peak at about 1.8 Å, indicating that the hydrogen−carbonyl interactions in the blend model play a crucial role in the PMMA/SAN miscibility (Figure 3c). The RDF corresponding 14361


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Figure 3. RDFs for (a) carbonyl group pairs in the PMMA, (b) ether group pairs in the PMMA, (c) hydrogen−carbonyl group in the PMMA/ SAN, and (d) nitrogen−carbonyl group in the PMMA/SAN.

at Tg govern the length of cooperativity in the polymer blends.48 To further understand the nature of nanoconfinement effects on the segmental dynamics in glass-transition region, the heat capacity changes of the PMMA, SAN, PMMA/SAN blend, and PMMA/SAN/OMNC nanocomposite were investigated by the DSC method. The length scale of cooperative segmental motions in the glass-transition region reveals valuable information about the structural properties of polymers. The length scale of segmental motions or, equally, the length of the cooperatively rearranging regions (CRR) returns a measure of the segmental dynamics. The CRR concept introduced by Adam and Gibbs is a subsystem consisting of a series of repeat units of a polymer chain that can independently rearrange to another configuration.49 Based on the thermal fluctuation theory, Donth proposed an expression for the length scale of cooperativity at Tg in homogenous systems as follows50,51

to the nitrogen atoms in the SAN and oxygen atoms of carbonyl groups in the PMMA (Figure 3d) shows two main peaks at 3.8 and 5.2 Å along with indefinite peaks at large distances. The presence of these peaks indicates the appropriate interactions between nitrogen and carbonyl groups, which help to improve the miscibility of the PMMA/SAN blend. Nanoconfinement Effects on Cooperativity at Tg. As shown in Figures 1 and S4, the Tg of the PMMA/SAN blend was decreased by intercalating the PMMA/SAN chains into the galleries of OMNC nanoparticles. The interactions between OMNCs and the near-neighbor environment govern the glass-transition temperature of the PMMA/SAN/OMNC nanocomposite. Therefore, the decrease in Tg of the PMMA/ SAN blend with the addition of OMNCs is mainly related to the confinement of the PMMA/SAN chains into the OMNC layers, while weak interactions exist between the OMNCs and the intercalated PMMA/SAN chains. As the temperature increases to Tg, the chain segments start their cooperative motions.47 The length of cooperativity in the glass-transition region is a major factor that provides useful information about segmental relaxation. The molecular structure of components, miscibility, and segmental mobility

ij 1 yz 3 VCRR = ξCRR = kBTg2Δjjj zzz/ρ(δT )2 j Cv z k {

(4)

where VCRR is the volume of a CRR, ξCRR is the characteristic length of cooperativity at Tg, kB is the Boltzmann constant, ρ is the polymer density, and Cv is the specific heat capacity at the 14362


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Langmuir constant volume. The step change in 1/Cv at Tg, Δ(Cv−1), is determined as51 Δ(Cv−1) = Cv−g1 − Cv−l 1

(5)

where Cvg and Cvl are the glassy and rubbery heat capacity tangents at Tg, respectively. The heat capacity gradient at constant volume can be related to that at constant pressure by the following correction51 Δ(Cv−1) = (0.74 ± 0.22)Δ(C p−1)

(6)

The mean temperature fluctuation of one CRR, δT, for the heating measurement of the glass transition can be estimated as51 δT =

ΔT 2.5

(7)

where ΔT is the temperature width, where Cp varies between 16 and 84% of the total ΔCp step in the glass-transition region. In addition, the number of repeat units present in one CRR is calculated using the following equation51 NCRR = (ρVCRR NA )/M m

(8)

where NA is Avogadro’s number and Mm is the molar mass of a repeat unit. Figure 4 presents the heat capacity versus temperature plot for the PMMA/SAN blend and the PMMA/SAN/OMNC nanocomposite. By applying the Donth equation to the heat capacity data, the volumes of cooperatively rearranging regions (VCRR) were estimated as 2.36 and 11.61 nm3 for the PMMA and SAN copolymer, respectively (Table 1). The VCRR value for the PMMA/SAN blend, 7.91 nm3, is intermediate between those of the pure components. The PMMA/SAN/OMNC nanocomposite shows the smaller volume of cooperatively rearranging regions (5.57 nm3) than the PMMA/SAN blend at the glass-transition temperature. The smaller VCRR value of the PMMA/SAN/OMNC nanocomposite compared to that of the PMMA/SAN blend is associated with the fact that the polymer chains were confined to the nanometric spaces (≈3.2 nm, from XRD results) of the OMNC platelets in the nanocomposite. Since the typical size of a polymer chain estimated by the radius of gyration, around 5−20 nm,52 is higher than the distance between the OMNC platelets, the chains rearrange into the gallery spaces with changing their conformation. Therefore, the dependence of polymer segments on the neighbors in gallery spaces decreased compared to the bulk. In addition, the weak polymer−OMNC interactions lead to dynamic heterogeneities and increased concentration fluctuation inside the CRR domains as well as decrease the coupling of polymer segments into the OMNC platelets. The decrease in the cooperativity length of polymer segments in the OMNC galleries reduces the activation energy barrier for segmental motions, which is manifested in a lower Tg, as reported in our previous work.30 Fragility under Nanoconfinement. Since nanoconfinement affects the segmental dynamics of polymer chains, investigation of the temperature sensitivity of segmental relaxation time, dynamic fragility, helps to better understand the degree of segmental cooperativity at Tg.53,54 The fragility concept is defined as a measure of the deviation of the temperature dependence of relaxation time from simple Arrhenius behavior. The polymers that display highly non-

Figure 4. Specific heat capacities at constant pressure vs temperature for (a) PMMA/SAN and (b) PMMA/SAN/OMNC nanocomposites.

Arrhenius temperature dependence of relaxation time with steep variations close to Tg are called “fragile”, and the polymers with nearly Arrhenius dependence of relaxation time are called “strong”. In fact, fragility is a criterion of the possibility of conformational change for polymer chains in the glass-transition region.55 The degree of departure of segmental relaxation time from the Arrhenius behavior, dynamic fragility index, can be calculated by the steepness of a semilogarithmic plot of relaxation time (obtained by the inverse of applied test frequencies from the DMA analysis) versus normalized temperature scale (Tref/T) at Tref. Here, Tref is defined as the temperature at which the segmental relaxation time is assumed to be 1 s.56,57 This type of plot is often called a “fragility plot”, and for polymers, the term “cooperativity plot” is more accurate.56 The dynamic fragility index, m, was determined by calculating the steepness of fragility plot at Tref m=

dlog τ d(Tref /T )

T = Tref

(9)

where τ is the relaxation time (s) and T is the temperature (K). Figure 5 exhibits the cooperativity plot of the PMMA, SAN, PMMA/SAN, and PMMA/SAN/OMNC systems. The solid lines in Figure 5 represent the fit on the basis of the Vogel− 14363


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blend (0.088) is between those of the PMMA and SAN copolymer, and decreases to 0.072 for the PMMA/SAN/ OMNC nanocomposite. It should be noted that the thermodynamic fragility is an entropy-based property, which is attributed to the degree of freedom of segmental mobility of polymers at Tg. After polymer intercalation in the lack of strong polymer−OMNC interactions, the degree of freedom increases and leads to decrease in required activation entropy of the system. Therefore, the lower thermodynamic fragility of the PMMA/ SAN/OMNC nanocomposite is interpreted regarding the nanoconfined structure. Figure 6 compares the thermodynamic fragility and the dynamic fragility of the PMMA, SAN, PMMA/SAN blend, and

Figure 5. Dynamic fragility for PMMA, SAN, PMMA/SAN blend, and PMMA/SAN/OMNC nanocomposite (the solid lines represent the VFT equation fit).

Fulcher−Tammann (VFT) equation.31 In addition, Table 2 lists the dynamic fragility values of the above-mentioned systems. The dynamic fragility values of the PMMA and SAN copolymers are 140 and 94, respectively, which indicate that cooperative motions of the PMMA segments containing large side groups are more constrained than those of the SAN copolymer in the glass-transition region. Moreover, Table 2 demonstrates an explicit decrease in the dynamic fragility of the PMMA/SAN blend from 115 to 105 for the PMMA/SAN/OMNC nanocomposite. These results show that the nanoconfinement decreases the apparent activation energy of the PMMA/SAN blend for cooperative motions at Tg. Such a reduction in the dynamic fragility is based on the fact that the penetration of polymer chains into the galleries of layered silicates decreases the dependence of polymer segments on their neighboring segments and thus facilitates the chain conformational rearrangements. Accordingly, inside the silicate layers, the cooperative length of local segmental motions is reduced in comparison to the bulk of the polymer. Moreover, the segmental motions in confined spaces become faster than those in bulk and, consequently, the cooperative segmental motions are decreased.58,59 Furthermore, the dimensionless ratio of the change in heat capacity, ΔCp/Cp,l, has been defined as the thermodynamic fragility.60 The change in heat capacity ratio at the glasstransition temperature is dependent on the strong/fragile properties of polymeric materials. Strong materials display a small value of ΔCp/Cp,l ratio, while fragile materials show a high ΔCp/Cp,l ratio. The thermodynamic fragility, ΔCp/Cp,l value, for the SAN copolymer (0.093) is greater than that for PMMA (0.058), which indicates that SAN is more thermodynamically fragile than PMMA (Table 2). The salient point is that the thermodynamic fragility of the PMMA/SAN

Figure 6. Correlation between dynamic fragility and thermodynamic fragility for the investigated systems.

PMMA/SAN/OMNC nanocomposite. The dynamic fragility of the PMMA is higher than that of the SAN, whereas the thermodynamic fragility of the SAN is higher than that of the PMMA. It is believed that the large side groups in PMMA chains are responsible for the higher dynamic fragility of the PMMA, whereas the higher concentration fluctuation of the SAN copolymer at Tg governs the higher thermodynamic fragility. However, as shown in Figure 6, both dynamic and thermodynamic fragilities decrease with the addition of OMNC nanoparticles. Therefore, a positive correlation was found between dynamic fragility and thermodynamic fragility when OMNC nanoparticles were added to the PMMA/SAN blend. Also, the decrease of dynamic and thermodynamic fragilities is in direct correlation with the decrease of the VCRR value by addition of OMNCs to the PMMA/SAN blend. Therefore, the lower segmental coupling of the PMMA/SAN/OMNC nanocomposite than that of the PMMA/SAN blend suggests that the dynamic heterogeneity is increased by intercalation of polymer chains into the layered silicate galleries. Polymer Segmental Mobility by MD Simulations. The segmental dynamics and cooperatively rearranging regions (CRR), as well as the thermodynamic and dynamic fragilities, are correlated with the segmental mobility of the polymer

Table 2. Dynamic and Thermodynamic Fragilities of Studied Systems fragility index

PMMA

SAN

PMMA/SAN

PMMA/SAN/OMNC

thermodynamic fragility (ΔCp/Cp,l) dynamic fragility (m)

0.058 ± 0.004 140 ± 11

0.093 ± 0.003 94 ± 2

0.088 ± 0.002 115 ± 5

0.072 ± 0.005 105 ± 3

14364


Article

Langmuir

in the glass-transition region, in agreement with experimental results.

chains at the glass-transition temperature. To theoretically confirm the increased segmental mobility of the PMMA/SAN/ OMNC nanocomposite, the mean square displacements (MSDs) of the studied systems were calculated at corresponding Tg’s, by MD simulations. Figure 7 shows that the slope of

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.8b03160.

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Molecular weight of polymers; theory of polymer− polymer miscibility; number of repeat units; details of the MD simulations; XRD pattern of OMNC and nanocomposite; interaction energies between components of nanocomposite; simulated glass-transition temperature; and Flory−Huggins (FH) interaction parameter PMMA/SAN blend (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (E.C.). *E-mail: [email protected] (N.T.Q.). ORCID

Ehsan Chehrazi: 0000-0001-7008-1799 Notes

Figure 7. Mean square displacements of the PMMA/SAN blend and the PMMA/SAN/OMNC nanocomposite at glass-transition temperature.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the Iranian Nanotechnology Initiative for partial financial support. They thank Dr. Mohammad Alimardani for valuable discussion in experiments.

the MSD plot of the PMMA/SAN/OMNC nanocomposite is steeper than that of the PMMA/SAN blend. This indicates that the segmental mobility in the PMMA/SAN/OMNC nanocomposite is higher than that in the PMMA/SAN blend, which is in agreement with the effects of nanoconfinement on the fragility and Tg discussed above.

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REFERENCES

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CONCLUSIONS The PMMA/SAN blend showed a single Tg between the Tg’s of the PMMA and SAN in both experimental and MD simulations results, indicating that the PMMA and SAN are miscible. In addition, by considering the Flory−Huggins (FH) interaction parameter, the MD simulations confirmed that the PMMA and SAN are miscible in all compositions. We also studied the effects of nanoconfinement on the cooperative segmental motions of the PMMA/SAN/OMNC nanocomposite at Tg. The PMMA/SAN/OMNC nanocomposite demonstrated lower Tg than the PMMA/SAN blend, from the DSC method and the MD simulations. Furthermore, by applying the Donth equation to the calorimetry data, the length of the cooperatively rearranging regions (CRR) was calculated for the PMMA, SAN, PMMA/ SAN blend, and PMMA/SAN/OMNC nanocomposite. The length of the CRR decreased after intercalation of the PMMA/ SAN chains into the galleries of OMNCs, due to the decrease in the segmental cooperativity at Tg in confined spaces. Moreover, the dynamic fragility was determined by calculating the steepness of a semilogarithmic plot of log τ versus Tref/T at Tref and compared to the ΔCp/Cp,l ratio as a measure of thermodynamic fragility. The comparison indicated that both fragilities were decreased by intercalation of polymer chains into the OMNC galleries. The MD simulations successfully predicted increased segmental mobility in the PMMA/SAN/ OMNC model by calculating the mean square displacements 14365


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Langmuir

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