Isothermal Crystallization Kinetics of Poly(ethylene oxide)/Poly(ethylene glycol)-g-silica Nanocomposites

In this work, the crystallization kinetics of poly(ethylene oxide) (PEO) matrix included with poly(ethylene glycol) (PEG) grafted silica (PEG-g-SiO2) nanoparticles and bare SiO2 were systematically investigated by differential scanning calorimetry (DSC) and polarized light optical microscopy (PLOM) method. PEG-g-SiO2 can significantly increase the crystallinity and crystallization temperature of PEO matrix under the non-isothermal crystallization process. Pronounced effects of PEG-g-SiO2 on the crystalline morphology and crystallization rate of PEO were further characterized by employing spherulitic morphological observation and isothermal crystallization kinetics analysis. In contrast to the bare SiO2, PEG-g-SiO2 can be well dispersed in PEO matrix at low P/N (P: Molecular weight of matrix chains, N: Molecular weight of grafted chains), which is a key factor to enhance the primary nucleation rate. In particular, we found that the addition of PEG-g-SiO2 slows the spherulitic growth fronts compared to the neat PEO. It is speculated that the interfacial structure of the grafted PEG plays a key role in the formation of nuclei sites, thus ultimately determines the crystallization behavior of PEO PNCs and enhances the overall crystallization rate of the PEO nanocomposites.

In semi-crystalline nanocomposites, the presence of NPs can significantly impact the crystallinity, crystal nucleation, and growth of polymer matrix [22][23][24], which is vital to fully exploit the potentially excellent properties of PNCs. Over the past decades, there have been extensive works on the crystallization kinetics of polymer nanocomposites containing various one-dimensional and two-dimensional PGNPs, i.e., carbon nanotubes, cellulose nanocrystal, clay and graphene oxide [25][26][27][28] as well as how they were modulated by the PGNPs addition. Müller et al. [27] found that the multiwall carbon nanotubes grafted linear poly(ε-caprolactones), (PCL) (MWNT-g-PCL) can nucleate the linear PCL but cause a decrease both in spherulitic growth rate and in the overall isothermal crystallization kinetics of cyclic PCL. The results line in the contact between liner grafted chains with Polymers 2021, 13, 648 3 of 16 calculated by TGA) obtained using the "grafting to" method, which has been reported in our previous study [30,39]. For clarity, the PEG grafted SiO 2 was denoted as PEG-g-SiO 2 , where the σ in this study is 0.73 chains/nm 2 .
To prepare the PEO/PEG-g-SiO 2 nanocomposites, PEO and PEG-g-SiO 2 were individually dispersed in acetonitrile at room temperature and then mixed in the desired volume ratios to obtain the PNCs with a SiO 2 content of 24 wt%. The mixtures were sonicated for 5 min and then stirred for ≈ 6 h at room temperature before casting onto Petri dishes. The nanocomposites were dried under a fume hood for 24 h to remove the solvent.

Characterization 2.3.1. Thermogravimetric Analysis
The σ of PEO was calculated by a PerkinElmer 8000 thermogravimetric analysis apparatus [40] (TGA, PE8000, Waltham, MA, USA). Samples of 2-3 mg were heated from 50 to 100 • C at a rate of 40 • C/min and held for 2 min at 100 • C to remove physically adsorbed water, then heated from 100 to 800 • C with a rate of 20 • C/min.

Differential Scanning Calorimetry
The non-isothermal crystallization and melting behavior of PEO nanocomposites were recorded by a PerkinElmer 8500 DSC apparatus (Waltham, MA, USA). The equipment was calibrated with indium and tin standards. The samples (3-5 mg) were encapsulated in aluminium pans, and ultra-pure nitrogen was used as a purge gas. First, the samples were heated to 80 • C and held for 3 min at that temperature to erase any previous thermal history. Second, they were cooled to −60 • C, and finally, reheated to 80 • C. All tests were performed at a cooling and heating rate of 10 • C/min. The peak temperatures of the obtained crystallization (T c ) and melting (T m ) exotherms were recorded.
The isothermal crystallization of PEO nanocomposites was recorded by PerkinElmer 8500 DSC under a N 2 atmosphere. The samples were held for 3 min at 80 • C to erase thermal history, then cooled at 100 • C/min to the selected crystallization temperature and held for 20 min.
The glass temperature (T g ) of the PEO nanocomposites was recorded by PerkinElmer 8500 DSC under a He atmosphere. The samples were cooled to −150 • C after holding 3 min at 80 • C under a ballistic cooling procedure, approximately with a rate of 280 • C/min. Then heated to 0 • C at 500 • C/min, and the T g was recorded during subsequent heating scans.

Polarized Light Optical Microscope
A polarized light optical microscope (PLOM, Olympus BX51, Tokyo, Japan) equipped with a Linkam THMS600 temperature controller was used to observe the crystalline morphology of PNCs. The samples were sandwiched between two cover glasses and heated to 80 • C for 5 min. Then, the samples were cooled at 60 • C/min to desired T c , and the number of spherulites and their sizes were monitored as a function of time. The nucleation density (N*) was calculated from the numbers by determining the volume (cm 3 ) from the measured sample thickness and the area of the field of view of the microscope.

Nucleation Kinetics of PEO Nanocomposites Studied by PLOM: Primary Nucleation
Before exploring the isothermal crystallization kinetics in PEO nanocomposites, we first focus on the non-isothermal crystallization behavior of the samples. Figure 1a,b illustrates the DSC melting and cooling curves of neat PEO, PEO/SiO 2 and PEO/PEG-g-SiO 2 with a matrix molecular weight (M n ) of 1700 g/mol and the SiO 2 content of 24 wt% (The DSC curves of PEO nanocomposites with matrix M n = 7800 g/mol are shown in Figure A1 of Appendix A). Figure 1c presents the crystallization (T c ) and melting (T m ) temperatures of all PEO nanocomposites employed here. The appearance of the increased T c in PEO/PEG-g-SiO 2 suggests that the PGNPs exhibit a significant nucleation effect on the crystallization process of PEO. Based on our recent work [30], it is probably more relevant to the better dispersion state (the dispersion state of PEO nanocomposites was studied using SAXS scattering combined with TEM, not shown here) of the PGNPs under a higher grafting density (σ = 0.73 chains/nm 2 ) and lower P/N value (the P/N studied here is 0.425 and 1.95) compared to the bare SiO 2 . The well dispersed sample, 1700PEO/PEG-g-SiO 2 (where 1700 represents the matrix M n = 1700 g/mol), showed a more excellent increase in T c (neat 1700PEO undergoes crystallization at 28.5 • C and 1700PEO/PEG-g-SiO 2 at 35.2 • C) as well as an increase in the PEO crystallinity ( Table 1 summarizes the relative parameters obtained in the crystallization process). The data in Figure 1c show there are minor differences in the melting point with the changing of P/N. illustrates the DSC melting and cooling curves of neat PEO, PEO/SiO2 and PEO/PEG-g-SiO2 with a matrix molecular weight (Mn) of 1700 g/mol and the SiO2 content of 24 wt% (The DSC curves of PEO nanocomposites with matrix Mn = 7800 g/mol are shown in Figure A1 of Appendix A). Figure 1c presents the crystallization (Tc) and melting (Tm) temperatures of all PEO nanocomposites employed here. The appearance of the increased Tc in PEO/PEG-g-SiO2 suggests that the PGNPs exhibit a significant nucleation effect on the crystallization process of PEO. Based on our recent work [30], it is probably more relevant to the better dispersion state (the dispersion state of PEO nanocomposites was studied using SAXS scattering combined with TEM, not shown here) of the PGNPs under a higher grafting density (σ = 0.73 chains/nm 2 ) and lower P/N value (the P/N studied here is 0.425 and 1.95) compared to the bare SiO2. The well dispersed sample, 1700PEO/PEG-g-SiO2 (where 1700 represents the matrix Mn = 1700 g/mol), showed a more excellent increase in Tc (neat 1700PEO undergoes crystallization at 28.5 °C and 1700PEO/PEG-g-SiO2 at 35.2 °C) as well as an increase in the PEO crystallinity ( Table 1 summarizes the relative parameters obtained in the crystallization process). The data in Figure 1c show there are minor differences in the melting point with the changing of P/N. The changes in the Tc and Tm for the two different nanocomposites with matrix molecular weights of 1700 g/mol and 7800 g/mol, and the silica content is 24 wt% in the nanocomposites studied here.
In this part of the study, the main point is to defer a detailed exploration of the crystal nucleation and growth kinetics in PEO nanocomposites. Therefore, we employed PLOM measurements to monitor the spherulitic growth for different nanocomposites at different crystallization temperatures, Tc. Figure 2 summarizes the primary nucleation kinetics studied by PLOM. The direct information on the nucleation ability of PEO nanocomposites can be obtained by counting the number of spherulites with time changing, as shown in Figure 2a-c. PEO and PEO/SiO2 exhibit similar nucleation kinetics with respect to the measured nucleation density, N* (as shown in Figure 2d). In the case of PEO/PEG-g-SiO2, PEG-g-SiO2 behaves more effectively as the nucleating agent and presents a much higher nucleation density in the Tc range, i.e., 38-41 °C for 1700PEO/PEG-g-SiO2 (with P/N = 0.425) and 44-48 °C for 7800PEO/PEG-g-SiO2 (with P/N = 1.95) (details on the N* changing at matrix Mn = 7800 g/mol are shown in Figure A2, Appendix B). It can be seen the nucleation densities of 1700PEO/PEG-g-SiO2 are almost two orders of magnitude higher than that of neat PEO, which shows a constant nucleation density in the Tc range (as shown in Figure 2d). A similar changing tendency with higher nucleation densities can also be observed in 7800PEO/PEG-g-SiO2. This leads us to speculate that the grafted PEG chains may serve as a template providing an increase of the nucleation sites to enhance the N* of PEO The changes in the T c and T m for the two different nanocomposites with matrix molecular weights of 1700 g/mol and 7800 g/mol, and the silica content is 24 wt% in the nanocomposites studied here.
In this part of the study, the main point is to defer a detailed exploration of the crystal nucleation and growth kinetics in PEO nanocomposites. Therefore, we employed PLOM measurements to monitor the spherulitic growth for different nanocomposites at different crystallization temperatures, T c . Figure 2 summarizes the primary nucleation kinetics studied by PLOM. The direct information on the nucleation ability of PEO nanocomposites can be obtained by counting the number of spherulites with time changing, as shown in Figure 2a-c. PEO and PEO/SiO 2 exhibit similar nucleation kinetics with respect to the measured nucleation density, N* (as shown in Figure 2d). In the case of PEO/PEG-g-SiO 2 , PEG-g-SiO 2 behaves more effectively as the nucleating agent and presents a much higher nucleation density in the T c range, i.e., 38-41 • C for 1700PEO/PEG-g-SiO 2 (with P/N = 0.425) and 44-48 • C for 7800PEO/PEG-g-SiO 2 (with P/N = 1.95) (details on the N* changing at matrix M n = 7800 g/mol are shown in Figure A2, Appendix B). It can be seen the nucleation densities of 1700PEO/PEG-g-SiO 2 are almost two orders of magnitude higher than that of neat PEO, which shows a constant nucleation density in the T c range (as shown in Figure 2d). A similar changing tendency with higher nucleation densities can also be observed in 7800PEO/PEG-g-SiO 2 . This leads us to speculate that the grafted PEG chains may serve as a template providing an increase of the nucleation sites to enhance the N* of PEO nanocomposites. Regardless, the changing tendency of increasing nucleation density with a decrease of P/N is consistent with our recent study [30], the more stretched grafted PEG chains at high grafting density (0.73 chains/nm 2 ) and lower P/N can enhance the interaction with matrix PEO, thus improving the nucleation density. nanocomposites. Regardless, the changing tendency of increasing nucleation density with a decrease of P/N is consistent with our recent study [30], the more stretched grafted PEG chains at high grafting density (0.73 chains/nm 2 ) and lower P/N can enhance the interaction with matrix PEO, thus improving the nucleation density. The primary nucleation rate I was obtained by counting the number of spherulites in a specific area at different crystallization times [41] (i.e., = * ). Turnbull-Fisher model [42,43] is adopted here to better understand the effects of NPs on the primary nucleation: where I0 is related to the segments' diffusion from the melt state to the nucleation site. ΔF* represents a parameter proportional to the free energy of primary nucleation. k is 1.381 × The primary nucleation rate I was obtained by counting the number of spherulites in a specific area at different crystallization times [41] (i.e., I = dN * dt ). Turnbull-Fisher model [42,43] is adopted here to better understand the effects of NPs on the primary nucleation: where I 0 is related to the segments' diffusion from the melt state to the nucleation site. ∆F* represents a parameter proportional to the free energy of primary nucleation. k is 1.381 × 10 −23 J·K −1 . ∆H v is the volumetric melting enthalpy (J/cm 3 ), and ∆H v can be calculated as ∆H v = ∆H m 0 ·ρ (∆H m 0 is the melting enthalpy of 100% crystalline PEO [44] with a value of 205 J·g −1 and ρ is the monomer density of PEO with a value of 1.064 g·cm −3 ). ∆T is the supercooling calculated by ∆T = T m 0 − T c , and T m 0 is the equilibrium melting point. The T m 0 of PEO nanocomposites studied here were determined by DSC 8500, as shown in Figure A3 of Appendix C. In PEO nanocomposites with matrix M n = 1700 g/mol and 7800 g/mol, it is observed that either isothermal thickening to the integral-folding chain (IF) (n = 0) crystal or thinning to the IF (n = l) crystal occurs depending upon the thermodynamic stability of the nonintegral-folding chain (NIF) crystal. Both thickening and thinning processes are observed at intermediate crystallization temperatures. An almost constant melting temperature may basically be attributed to the competition between overall crystallization and the isothermal thinning process (Appendix C) [45]. σ and σ e are the free energies of the lateral and fold surface of PEO, respectively. ∆σ is a parameter related to nucleation efficiency [43]. σσ e (∆σ) = 140 erg 3 /cm 6 for 1700PEO/PEG-g-SiO 2 and σσ e (∆σ) = 134 erg 3 /cm 6 for 7800PEO/PEG-g-SiO 2 were obtained from the slope of the straight line given by logI vs. 1/(T∆T) 2 [43].
Two basic conclusions can be obtained from Figure 2e: (1) The significant change of primary nucleation rate I is closely related to the addition of PGNPs, (2) nucleation rate decreases with the increase of P/N value in the measured temperature range. This result implies that the good compatibility between PEG-g-SiO 2 and the PEO matrix at low P/N can enhance the interactions between matrix chains and PGNPs. Compared to the bare SiO 2 , the improvement of dispersion state of PEG-g-SiO 2 appears to be the key factor for the enhancement of N* observed in Figure 2. Similar trends of increasing nucleation density have been observed in PLLA nanocomposites containing PEG grafted graphene oxide [46] and linear PCL system containing MWNT-g-PCL (linear PCL chains grafted multiwall carbon nanotubes) [27].

Growth Kinetics of PEO Nanocomposites Studied by PLOM: Secondary Nucleation
Following the discussions above, to further separate out the effects of PEG-g-SiO 2 on the spherulitic growth kinetics (i.e., secondary nucleation), the growth process of each sample at different times is measured by PLOM. Figure 3a-c shows the micrographs of 1700PEO/PEG-g-SiO 2 spherulites isothermally crystallized at 39 • C at different times. The results clearly show that the number of spherulites in 1700PEO/PEG-g-SiO 2 increases with the increase of time, while neat PEO and PEO/SiO 2 exhibit only one nucleus during the growth process, as shown in Figure A4 of Appendix D.
The linear dependence of the spherulitic radius on the measured time was shown in Figure 3d, which indicates there is no disturbance by the diffusion during growth. Lauritzen and Hoffman model (LH theory) is used here to ascertain the spherulitic growth rate (G) according to the following form [47][48][49]: where U * is the activation energy for transporting segments to the crystallization front (a universal value is taken as 1500 cal·mol −1 ), R is the gas constant with a value of 8.314 J·mol −1 ·K −1 and G 0 is a constant. T c is the crystallization temperature. T m 0 is the equilibrium melting point and the T m 0 value was shown in Table 1 that summarizes the parameters related to the crystallization and melting behavior of the studied PEO PNCs. f is the temperature correction factor defined as f = 2T c / T 0 m + T c . T ∞ is the temperature associated with chain dynamics cease and usually taken as T ∞ = T g − 30K (T ∞ value was shown in Table 1). Fitting the data (converted to the liner formula as lnG + U * /(R(T c -T ∝ )) vs. 1/T c T 0 m − T c f , as shown in Figure A5 of Appendix E) by the LH theory in Figure 3e allows the prediction of the secondary nucleation energy barrier K G g , as shown in Table 1. Obvious retardation in the growth rate (G) was obtained in Figure 3e with the presence of NPs. Bare SiO 2 tends to form aggregations at a higher content as 24 wt% (results were confirmed by TEM and SAXS measurement [30]), which may cause the polymer chains to be confined in the restricted space [50]. It is considered that the reduction in the G is mainly linked with the geometric constraints within NPs [51] at a considerably high content. In the case of PEO/PEG-g-SiO 2 with a low P/N = 0.425, PEO nanocomposites exhibit the lowest G within the measured T c range. The results may partially relate to an increase of the interfacial interaction under a good dispersion state. Kumar et al. [31] studied the effects of unimodal and bimodal grafted SiO 2 with various dispersion states on the PEO spherulitic growth and they found the decrease of the growth rate was mainly caused by the increase in the nanocomposite viscosity, which finally hindered the transport of crystallizable segments to the crystalline growth front [34,[51][52][53]. The linear dependence of the spherulitic radius on the measured time was shown in Figure 3d, which indicates there is no disturbance by the diffusion during growth. Lauritzen and Hoffman model (LH theory) is used here to ascertain the spherulitic growth rate (G) according to the following form [47][48][49]: where * is the activation energy for transporting segments to the crystallization front (a universal value is taken as 1500 cal·mol −1 ), R is the gas constant with a value of 8.314 J·mol −1 ·K −1 and G0 is a constant. Tc is the crystallization temperature. Tm 0 is the equilibrium melting point and the Tm 0 value was shown in Table 1 that summarizes the parameters related to the crystallization and melting behavior of the studied PEO PNCs. f is the temperature correction factor defined as = 2 /( 0 + ). ∞ is the temperature associated with chain dynamics cease and usually taken as ∞ = − 30 ( ∞ value was shown in Table  1). Fitting the data (converted to the liner formula as lnG + * /(R(Tc -T∝)) vs. 1/ ( 0 − ) , as shown in Figure A5 of Appendix E) by the LH theory in Figure 3e allows the prediction of the secondary nucleation energy barrier , as shown in Table 1. Obvious retardation in the growth rate (G) was obtained in Figure 3e with the presence of NPs. Bare SiO2 tends to form aggregations at a higher content as 24 wt% (results were confirmed by TEM and SAXS measurement [30]), which may cause the polymer chains to be confined in the restricted space [50]. It is considered that the reduction in the G is mainly linked with the geometric constraints within NPs [51] at a considerably high content. In the case of PEO/PEG-g-SiO2 with a low P/N = 0.425, PEO nanocomposites exhibit the lowest G  Figure 4 shows the secondary nucleation energy barrier of the PEO nanocomposites, K G g normalized by the neat PEO, K G g PEO. It is clearly implied that the addition of PEG-g-SiO 2 obviously decreases the energy barrier in spherulitic growth. In the case of 1700PEO/SiO 2 , K G g exhibits larger value than that of neat PEO. It means that more energetic requirements are needed for secondary nucleation. Table 2 summarizes the K G g studied in different systems, a decrease of K G g values can be observed with the addition of bare nanoparticles and polymer grafted nanoparticles in PCL nanocomposites [27,54]. The phenomenon that the addition of nanofillers can lower the energetic requirement in the secondary nucleation was also reported in PEO nanocomposites combined with unmodified SiO 2 NPs (NPs radius = 7 nm) [50], as shown in Table 2. One special case was reported by Kumar et al. [31,55], who shows a relatively minimal change in K G g value with different NPs and loadings, as shown in Table 2. Moreover, they found that the spatial dispersion of the unimodal or bimodal amorphous polymer chains grafted NPs mainly impacts the chain diffusion [31]. Table 1. Parameters related to the crystallization and melting behavior of the studied PEO nanocomposites.   11.2 10.4 8.7 a VPEO/SANP represents the ratio of PEO volume (VPEO) to NPs surface area (SANP). b PCL-CNW represents PCL with surface modified sisal nanowhiskers (CNW) and c PCL-MFC represents PCL with microfibrillated cellulose (MFC). d L-PCL represents linear poly(ε-caprolactones). e L-PCL/SWNT-ODA represents PCL with octadecylamine functionalized single wall CNTs. f L-PCL/MWNT-g-PCL represents PCL with linear PCL grafted multiwall carbon nanotubes.

Overall Isothermal Crystallization Behavior
The overall isothermal crystallization behavior was probed by the DSC measurements in which both primary nucleation and crystal growth are considered [56,57]. Avrami equation was employed to understand the primary crystallization process. It provides an efficient analytical method to describe the spherulitic nucleation and growth at the early stages of the impingement [27,58-60]: where t is the crystallization time, t0 is the induction time, and n is the Avrami index. K is

Overall Isothermal Crystallization Behavior
The overall isothermal crystallization behavior was probed by the DSC measurements in which both primary nucleation and crystal growth are considered [56,57]. Avrami Polymers 2021, 13, 648 9 of 16 equation was employed to understand the primary crystallization process. It provides an efficient analytical method to describe the spherulitic nucleation and growth at the early stages of the impingement [27,[58][59][60]: where t is the crystallization time, t 0 is the induction time, and n is the Avrami index. K is overall crystallization constant. X c (t) is the relative crystallinity at time t. Figure 5 shows the relative crystallinity of the neat PEO changing with the crystallization time at T c = 35 • C. The Avrami fittings correspond to the primary crystallization process covering 3%-20%. Figure 6a shows the inverse of half-crystallization, 1/τ 50% (which represents the overall crystallization rate containing both nucleation rate and growth rate) as a function of the isothermal crystallization temperature, T c . The overall crystallization rate constant K, obtained from the Avrami equation with a unit of min −n , is directly related to the Avrami index, n. To make a direct comparison of K in the same units, K was normalized by elevating to the power 1/n. Figure 6b shows the K 1/n (with a unit of min −1 , which also implies the overall crystallization rate) vs. T c . It was found that the values of K 1/n predict the trend of experimental data points (1/τ 50% vs. T c ) in Figure 6a, which indicates the Avrami theory can adequately fit the data. Figure 6c shows the Avrami indexes, n as a function of crystallization temperature. The Avrami index values are very similar for neat PEO and PEO nanocomposites, which are around 2.5 in the tested T c range, indicating that the PNCs formed spherulites instantaneous [61]. The obtained n values reflect the superstructures formed are slightly influenced by the incorporation of SiO 2 .
Polymers 2021, 13, x FOR PEER REVIEW 10 of 17 units, K was normalized by elevating to the power 1/n. Figure 6b shows the K 1/n (with a unit of min −1 , which also implies the overall crystallization rate) vs. Tc. It was found that the values of K 1/n predict the trend of experimental data points (1/τ50% vs. Tc) in Figure 6a, which indicates the Avrami theory can adequately fit the data. Figure 6c shows the Avrami indexes, n as a function of crystallization temperature. The Avrami index values are very similar for neat PEO and PEO nanocomposites, which are around 2.5 in the tested Tc range, indicating that the PNCs formed spherulites instantaneous [61]. The obtained n values reflect the superstructures formed are slightly influenced by the incorporation of SiO2.  It is clear that the presence of PEG-g-SiO 2 can obviously accelerate the overall crystallization rate both in the case of P/N = 0.425(with matrix M n = 1700 g/mol) and P/N = 1.95 (with matrix M n = 7800 g/mol). The overall crystallization rate follows the order as: PEO/PEG-g-SiO 2 > neat PEO > PEO/SiO 2 . Previous studies have shown the high enhancement of the crystallization rate in nanocomposites with the addition of PGNPs [25,34,46], and one possible rationale for these results is attributed to more nucleation sites under the good dispersion of the PGNPs. In our work, as described above, the T m (as shown in Table 1) of the PEO matrix are almost unaltered by the presence of any SiO 2 nanoparticle, while the PGNPs endow a high nucleation ability to SiO 2 nanoparticles, resulting in a marked enhancement of T c . The surface decoration of the PEG chains remarkably improves the interactions between PGNPs and PEO matrix. Better compatibility of the PEG-g-SiO 2 with PEO matrix compared to the bare SiO 2 generates notable nucleation sites. Thus, we speculate that the strongly stretched grafted crystallizable chains coupling to a wetting brush interface allows the matrix chains to be templated by the surface chains [39]. In the case of PLOM results, the addition of PEG-g-SiO 2 notably hindered the spherulitic growth rate. Therefore, the significant increase of the overall crystallization rate should be dominated by the increase of nucleation density. It is clear that the presence of PEG-g-SiO2 can obviously accelerate the overall crystallization rate both in the case of P/N = 0.425(with matrix Mn = 1700 g/mol) and P/N = 1.95 (with matrix Mn = 7800 g/mol). The overall crystallization rate follows the order as: PEO/PEG-g-SiO2 > neat PEO > PEO/SiO2. Previous studies have shown the high enhance-

Conclusions
We have investigated the isothermal crystallization kinetics of PEO nanocomposites (PEO/SiO 2 and PEO/PEG-g-SiO 2 ) using DSC and PLOM techniques. The key conclusion of our study is that the addition of PEG-g-SiO 2 in PEO matrix can alter the primary nucleation and the spherulitic growth rate. Compared to the unmodified SiO 2 , the better dispersion of PEG-g-SiO 2 at lower P/N shows a stronger nucleation effect and elevates the nucleation density, thus resulting in a marked enhancement in the crystallization rate. On the other hand, the spherulitic growth rate of PEO nanocomposites was significantly retarded.
The results are quite different from the bare silica NPs or NPs grafted with amorphous brushes, in which the addition of NPs does not affect the secondary nucleation energy barrier. Thus, we believe that the nature of the graft chains also plays a crucial role in the crystallization behavior of semi-crystalline polymer nanocomposites.