Article pubs.acs.org/Macromolecules
Effects of Molecular Weight below the Entanglement Threshold on Interfacial Nanoparticles/Polymer Dynamics Panagiotis Klonos,*,† Kostiantyn Kulyk,‡ Mykola V. Borysenko,§ Vladimir M. Gun’ko,§ Apostolos Kyritsis,† and Polycarpos Pissis† †
Department of Physics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden § Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, 17 General Naumov Street, Kiev 03164, Ukraine ‡
S Supporting Information *
ABSTRACT: This work deals with effects of polymer molecular weight, Wm, below the entanglement threshold, Wm,e, on molecular dynamics of polydimethylsiloxane (PDMS) adsorbed onto silica particles, employing differential scanning calorimetry (DSC) and two dielectric techniques: broadband dielectric spectroscopy (BDS) and thermally stimulated depolarization currents (TSDC). The rigid amorphous polymer fraction at interfaces, RAFint, was found suppressed for larger Wm by all techniques in qualitative agreement with each other. Results on RAFint were supported by evaluating, for the first time, the coverage of hydroxyls at the surfaces of nanoparticles by polymer chains (S relaxation). The mobility of interfacial polymer (αint relaxation) was followed by BDS and TSDC, showing suppression of dynamics and cooperativity with decreasing Wm. We suggest that interfacial polymer fraction and dynamics are dominated by the concentration of polymer− particle contact points, the latter increasing for smaller Wm due to more free chain ends, as expected below Wm,e. Furthermore, adopting models that describe multiple conformations for polymers adsorbed on solid surfaces, we explain our results in terms of promotion of tail/loop-like conformations in the particle−polymer interfacial layer for shorter/longer polymer chains, respectively. The model was further checked by employing surface modification of initial silica, which resulted in smoothening of nanoparticle surface and led to further suppression of RAFint and interfacial polymer dynamics.
1. INTRODUCTION Polymer nanocomposites (PNCs) have attracted much attention the past two decades, since they are characterized by improved physical properties as compared to neat polymer and conventional composites.1 A widely adopted concept for rationalizing improvements of PNCs properties involves the existence of a fraction of polymer at interfaces between particles and polymer, which demonstrates modified structure,2−4 dynamics,5−11 and properties1,10,12,13 as compared to the bulk. Because of the large surface to volume ratio of nanoparticles (NPs), a large fraction of polymers are located at the interface with the nanofillers, so that the modified properties of the interfacial polymer fraction may dominate in the nanocomposite. Other scenarios have also been discussed, especially for explaining mechanical reinforcement in PNCs, for example percolation of NPs with a “bound” glassy layer around them and/or formation of a flexible network of NPs with the polymer playing the role of bridging between the NPs (refs 14 and 15 and references therein). Methodologies involving computer simulations,2−4,11,16,17 structural characterization (e.g., FTIR7,18), calorimetry,19−22 and dielectric spectroscopy5,7,18,23−25 have been developed for the study of interfacial polymer characteristics and showed that © 2016 American Chemical Society
modified polymer properties are observed in an interfacial zone of 1−10 nm in thickness.5−8,11,12,20,26 Kumar and co-workers have demonstrated that the interfacial layer (shell) thickness depends on the size,24 curvature,12 and shape27 of the filler, while Pissis and co-workers showed more recently a respective dependence on surface roughness25 and suggested an interfacial chain packing−polymer dynamics relationship.9,28−31 Polymer dynamics at the interfaces is under intensive investigation, several questions being still open.32,33 Interfacial polymer is considered completely immobile (rigid) according to calorimetry,20,21 as it is thought responsible for the observed suppression in heat capacity step at glass transition in PNCs as compared to the unfilled polymer matrix. However, several results published during the past decade show that interfacial polymer may not be completely immobile, exhibiting retarded dynamics accompanied by suppressed cooperativity, as compared to polymer in bulk.5−9,18,34 Results suggest that this retarded dynamics is more clearly observed in PNCs based on rubber and rubber-like polymers,5,23,34 probably in relation Received: September 1, 2016 Revised: December 7, 2016 Published: December 14, 2016 9457
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Macromolecules to lower polymer chain rigidity.9,32,35 For a more in-depth interpretation of results, models involving multimodal chain conformations,36,37 developed mainly for thin supported polymeric films,37−40 have been adopted.3,9,10,41,42 Recently, we reported9,28,29 that polydimethylsiloxane (PDMS), the polymer of interest in the present study, adsorbed on fumed silica (SiO2, aerosil) NPs exhibits similarities with polymers adsorbed on flat solid surfaces:10,41 the directly adsorbed chains adopt in both cases multimodal conformations, with their concentration and interfacial polymer density depending on the adsorption conditions and the subsequent thermal treatment.29,31 In addition, results showed a systematic increase of the interfacial polymer fraction, as potential contact points at the surfaces of particles (surface hydroxyls, their number increasing with nanometric surface roughness) approach each other, this effect being accompanied by enhanced dynamics and cooperativity of the corresponding segmental relaxation.25 More recently, we reported30 effects of surface characteristics and polymer chain length (molecular weight, Wm) on the fraction and dynamics of polymer in the interfacial layer in systems based on adsorbed PDMS and titania (titanium dioxide, TiO2) NPs of very low surface roughness. For low Wm, where entanglement effects are not significant,43−47 our results revealed that the increased concentration of free chain ends in the case of short polymer chains promotes stronger polymer adsorption, while interfacial polymer dynamics becomes slower and exhibits lower cooperativity as compared to longer polymer chains.30 Sokolov and co-workers32 studied by similar methodology PNCs for high Wm, namely in the range where entanglement effects dominate, and discussed variation in the fraction and density of interfacial polymer in terms of an interplay between formation of (a) looplike conformations of the polymer at interfaces and (b) of chain (loops) bridges between neighboring nanoparticles. They suggested that cases a and b are promoted for lower and higher Wm, respectively.32 Regarding the type of nanoinclusions, previous work on PDMS/silica5 and PDMS/ titania48 PNCs, where NPs were in situ generated and dispersed employing sol−gel technique in the cross-linked polymer matrix, indicated stronger interfacial effects in the titania PNCs, assigned to stronger hydrogen bonds between titania and PDMS, as compared to silica−PDMS.6 Thus, in order to further study the effects described above,30 we focus here on PNCs based on silica of significantly high specific surface area (∼320 m2/g, i.e., quite rough surfaces). In order to follow effects imposed by polymer chain length on polymer adsorption, we employ three types of linear PDMS with different molecular weight (Wm ∼ 1700, 4170, and 7960, i.e., below entanglement threshold for PDMS43,44). Finally, we manipulate the surface characteristics (roughness−porosity) of initial silica by grafting small cerium dioxide nanoparticles (CeO2, ceria, ∼3 nm in size) on the initial silica particles, before adsorption of the polymer. With respect to similar studies in PNCs, we would like to note that less attention has been paid to effects imposed by different W m , especially below entanglement,30,32,49 while such effects have been more extensively reported for thin films.38−40,44,50,51 In this study we employ differential scanning calorimetry (DSC) for thermal transitions (focusing on glass transition) and two dielectric techniques, broadband dielectric spectroscopy (BDS) and thermally stimulated depolarization currents (TSDC), for segmental dynamics.
2. EXPERIMENTAL SECTION 2.1. Materials. Preparation and morphological characterization of the initial oxides have been described previously;52−54 therefore, we briefly summarize here the preparation procedure. Initial silica A-300 (pilot plant of Chuiko Institute of Surface Chemistry, Kalush, Ukraine) consists of aggregates formed by primary nanoparticles of ∼8 nm in diameter. The aggregates are characterized by high specific surface area, SAr = 319 m2/g, according to the results of low-temperature argon adsorption/desorption measurements.54 Silica A-300 was used as substrate for the formation of CeO2 (ceria) nanoparticles at two amounts by one and four reiterations of the ceria reaction, resulting in ∼7 and 23 wt % CeO2 and SAr = 265 and 189 m2/g, respectively.54,55 According to X-ray diffraction (XRD) studies, CeO2 forms crystalline nanoparticles of ∼2.4 and ∼3.4 nm in size for one and four reiterations of the reaction, respectively.53 Commercial linear polydimethylsiloxane (PDMS) (Kremniypolimer, Zaporozhye, Ukraine, linear, −CH3 terminated, polydispersity index PDI ≤ 1.1) of three molecular weights (code names: PDMS-20, PDMS-200, and PDMS-1000 for PDMS with molecular weight, Wm, 1700, 4170, and 7960 g/mol, degree of polymerization dp 22, 55, and 105, and viscosity at 20 °C 18−22, 190−210, and 950−1050 mm2/s, respectively) was adsorbed onto dried silica and silica−CeO2 in the amount of 40 wt %. For the adsorption, proper amounts of hexane solution of PDMS at a constant concentration (1 wt % PDMS) and of dry oxide powder were mixed together. This choice of polymer loading was based on the results of previous studies on similar systems,9,13,25,30 suggesting that 40 wt % PDMS is sufficient for full coverage of the oxide surface. Interaction of PDMS and oxide particles occurs mainly via hydrogen bonding between the oxygens (−O−) in the backbone of PDMS and the surface hydroxyls (−OH) of the particles.56 Nanocomposites are in the form of powder, similar to the initial oxide powder, while neat PDMS samples are in liquid form. Throughout the article, we use specific code names for describing composition of the samples. For instance, (i) A300/PDMS-20 corresponds to the sample where PDMS-20 (at 40 wt %) is adsorbed onto initial A-300 and (ii) A300C4/PDMS-1000 corresponds to the sample where PDMS-1000 (at 40 wt %) is adsorbed onto A-300 that previously suffered four cycles of CeO2 reaction (23.3 wt % CeO2). 2.2. Differential Scanning Calorimetry (DSC). Thermal properties of the materials were investigated in helium atmosphere in the temperature range from −170 to 20 °C using a TA Q200 series DSC instrument, calibrated with indium (for temperature and enthalpy) and sapphires (for heat capacity). Samples of ∼8 mg in mass were closed in standard Tzero aluminum pans (for powders) or Tzero hermetic aluminum pans (for liquids). Samples were equilibrated in ambient conditions before measurement. Typical cooling and heating rates were 10 K/min, deviations from that being mentioned explicitly. PDMS crystals are melted at room temperature, so that a first heating scan to erase thermal history was not necessary here. Regarding the evaluation of DSC results, first, using the enthalpy of crystallization, normalized to the polymer content (wPDMS), ΔHc,n (eq 1)
ΔHc,n = ΔHc,DSC/wPDMS
(1)
the degree of crystallinity (crystalline fraction), CF, was calculated by eq 2
CF = ΔHc,n/ΔH100%
(2)
where ΔH100% is the enthalpy of fully crystallized PDMS, taken as 37.4 J/g (ref 39 in ref 6). As far as glass transition is concerned, the characteristic temperature Tg was determined as the midpoint of the heat capacity step during the transition. Following previous work,6,21,29 results for the heat capacity step at glass transition, ΔCp, were normalized to the same fraction of amorphous polymer according to eq 3
ΔCp ,n = 9458
ΔCpDSC wPDMS(1 − CF)
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Figure 1. Comparative DSC thermograms in the glass transition region during heating at 10 K/min of (a) neat amorphous PDMS (see caption to Table 1 for conditions of measurements) and (b) PDMS-20 adsorbed on initial and surface modified silica A-300, samples being indicated on the plots. The heat flow curves have been normalized to the mass of the amorphous polymer and to heating rate (specific heat capacity, Cp). The added dash-dotted lines represent the baselines of the thermograms before and after glass transition.
Table 1. Quantities of Interest from DSC Measurementsa sample PDMS-20 neat A300 + 40% PDMS-20 A300C1 + 40% PDMS-20 A300C4 + 40% PDMS-20 PDMS-200* neat amorph PDMS−200 neat A300 + 40% PDMS-200 A300C1 + 40% PDMS-200 A300C4 + 40% PDMS-200 PDMS-1000* neat amorph PDMS-1000 neat A300 + 40% PDMS-1000 A300C1 + 40% PDMS-1000 A300C4 + 40% PDMS-1000
Tg (°C) (±0.5)
ΔTg (K) (±0.5)
ΔCp,n (J/(g K)) (±0.02)
MAF (wt %) (±10%)
RAF (wt %) (±10%)
CF (wt %) (±5%)
RAFcryst (wt %) (±10%)
RAFint (wt %) (±10%)
−134 −132
2 7
0.56 0.02
1.00 0.04
0.00 0.96
0.00 0.00
0.00 0.00
−132
5
0.11
0.20
0.80
0.00
−133
3
0.16
0.29
0.71
−130
2
0.48
1.00
−130 −129
2 6
0.42 0.03
−129
5
−130
Tc (°C)
Tm1 (°C)
Tm2 (°C)
0.00 0.96
−66
−58
0.00
0.80
−63
0.00
0.00
0.71
−65
0.00
0.00
0.00
0.00
−51
−40
0.84 0.06
0.12 0.93
0.04 0.01
0.12 0.03
0.00 0.90
−98 −102
−53 −50
−40
0.04
0.08
0.85
0.07
0.21
0.64
−104
−52
−46
4
0.05
0.09
0.82
0.09
0.27
0.55
−105
−54
−45
−129
3
0.33
1.00
0.00
0.00
0.00
0.00
−52
−40
−127 −129
12 9
0.22 0.03
0.23 0.09
0.12 0.91
0.65 0.00
0.12 0.00
0.00 0.91
−82
−49 −48
−39
−128
7
0.04
0.11
0.72
0.17
0.03
0.69
−99
−49
−129
4
0.06
0.13
0.61
0.26
0.05
0.56
−94
−50
−44
Glass transition temperature, Tg, difference between the onset and end temperatures of glass transition, ΔTg = Tend − Tonset, normalized heat capacity step at the glass transition, ΔCp,n, mobile amorphous polymer fraction, MAF, total rigid amorphous fraction, RAF, rigid amorphous fraction at interfaces, RAFint, and around crystals, RAFcryst, crystalline fraction, CF, crystallization and melting temperatures, Tc and Tm1,2, respectively. Details of calculations are being given in the text. *Note: PDMS-200 and PDMS-1000 were partially crystallized during cooling at 10 K/min, while for the same cooling condition PDMS-20 remains amorphous. Thus, in order to have a better comparison between neat amorphous polymers, we eliminated crystallization during cooling for neat PDMS-200 and PDMS-1000 by faster cooling (∼70 K/min, quenching); the respective results (∗) being included in the table. Values of main interest are marked in bold. a
where ΔCpDSC is the measured heat capacity step, taken as the distance between the baselines before and after glass transition. 2.3. Thermally Stimulated Depolarization Currents (TSDC). Thermally stimulated depolarization currents (TSDC) is a special dielectric technique in the temperature domain, characterized by high sensitivity and high resolving power, the latter arising from its low equivalent frequency (10−4−10−2 Hz).57 TSDC measurements were carried out on samples of ∼1 mm thickness for powders (compressed pellets, using a PerkinElmer manual hydraulic press operating at ∼10 tons) and ∼50 μm thickness for liquids (employing thin silica spacers, to keep distance between the brass electrodes constant and ensure good electrical contacts). The sample was inserted between the brass plates of a capacitor, placed in a Novocontrol TSDC sample cell and polarized by an electrostatic field Ep (∼300 V/mm) at polarization
temperature Tp = 20 °C for time tp = 5 min. With the field still applied, the sample was cooled down to −150 °C (cooling rate 10 K/min, under nitrogen flow), sufficiently low to prevent depolarization by thermal energy, then short-circuited, and reheated up to 60 °C at a constant heating rate, b = 3 K/min. Temperature control was achieved by means of a Novocontrol Quatro cryosystem. A discharge current was generated during heating and measured as a function of temperature with a sensitive programmable Keithley 617 electrometer. TSDC results were evaluated in terms of temperature maxima of the TSDC peaks being related to segmental mobility (glass transition) and of the area of these peaks, the latter representing the dielectric strength, Δε,58 of the relaxations and being correlated to the population of the relaxing molecular units. 9459
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Figure 2. Comparative diagrams of (a) rigid amorphous polymer fraction at interfaces (RAFint) vs specific surface area (roughness) for all PNCs studied. In the model in the inset to (a) CF is the crystalline fraction and MAF is the mobile amorphous fraction, while RAFint and RAFcryst are the rigid amorphous fractions in the interfacial particle/polymer layer and in close proximity to crystals, respectively. (b) Difference between the onset and end temperatures of glass transition, ΔTg = Tend − Tonset, against MAF for all PNCs (same symbols as in (a), lines connect PNCs of the same Wm) and the respective neat polymers studied here, along with results taken for comparison from the literature (namely, cross-linked −OHterminated PDMS of higher Wm (magenta crossed stars) suffering various thermal treatments (1−3)6 and crystallization annealed PDMS-1000 (blue crossed triangle, 129). 2.4. Broadband Dielectric Spectroscopy (BDS). Broadband dielectric spectroscopy (BDS)58 measurements were carried out on samples same as those used for TSDC. Each sample was inserted between the finely polished brass plates of a capacitor. This sandwichlike capacitor was inserted between the parallel electrodes of a Novocontrol BDS-1200 sample cell. Then, an alternate voltage was applied to the capacitor in the sample cell. The complex dielectric permittivity ε* = ε′ − iε″ was recorded isothermally as a function of frequency in the broad range from 10−1 to 106 Hz, at temperatures from −150 to 30 °C on heating (in nitrogen atmosphere) in steps of 2.5, 5, and 10 K (depending on the process under investigation) using a Novocontrol Alpha analyzer. The temperature was controlled to better than 0.5 K with a Novocontrol Quatro cryosystem. BDS results were analyzed by fitting model functions59 to the experimental data in order to evaluate the time scale (temperature dependence of the frequency maxima of dielectric loss), the dielectric strength, and the shape parameters of the recorded relaxations.58 To that aim, we employed the Havriliak−Negami (HN) equation59
ε*(f ) = ε∞ +
Δε [1 + (if /f0 )αHN ]βHN
These steps resulted in a significant reduction of the number of free parameters in the final fitting, which was then performed.
3. RESULTS AND DISCUSSION 3.1. Glass Transition and Evaluation of Rigid Amorphous Fraction (DSC). Figure 1 shows DSC thermograms for neat PDMS (Figure 1a) and the PNCs of PDMS-20 (Figure 1b) in the glass transition region during heating at 10 K/min. The overshoots observed for neat PDMS are related with structural relaxation.60−62 We follow in Figure 1a that the area (enthalpy) of structural relaxation diminishes with increasing of Wm, which can be understood in terms of suppression of freedom of movement in the glassy state for the longer chains.63 Structural relaxation disappears in the PNCs in Figure 1b, which is interesting with respect to reports on effects of nanoparticles on physical aging in PNCs.64,65 Values for glass transition temperature, Tg, and heat capacity change at glass transition, ΔCp, can be found in Table 1. Because of the semicrystalline character of PDMS (overall DSC thermograms in Supporting Information Figure SM.1, Table 1), effects on glass transition imposed by Wm and the presence of nanoparticles should be correlated also with respective effects on crystallinity.6,29,60 Values for the degree of crystallinity, CF, can be found in Table 1 (details in section 2.2). The presence of nanoparticles in PNCs result in suppression of CF and of crystallization temperature, Tc (Table 1), suggesting that the nanoparticles do not act as crystallization nuclei66,67 and polymer crystals are formed away from the surfaces of nanooxides.6,9,30 In Figure 1 and Table 1, Tg of PDMS increases with Wm and, at the same time, ΔCp,n decreases, as expected for linear polymers of low Wm.60 The recorded Tgs are in agreement with findings for PDMS in the literature,43 this point being further discussed later in comparison with results by BDS. According to the literature for PDMS, Wm values studied here are in the range just below the entanglement threshold, W m,e (∼10 000).43,44 Above Wm,e, Tg values stabilize at about −129 °C.43,44 Regarding effects imposed by the presence of NPs, one may easily observe in Figure 1b and Table 1 that Tg of PDMS increases by 1−2 K in PNCs, while at the same time, the glass transition step becomes more wide (increasing of ΔTg). Surface
(4)
In eq 4, ε∞ describes the value of the real part of dielectric permittivity, ε′, for f ≫ f 0, Δε is the dielectric strength, f 0 is a characteristic frequency related to the frequency of maximum dielectric loss (ε″), and αHN and βHN are the shape parameters of the relaxation.59 A sum of HN terms of the type (4), one for each of the relaxations (namely β, S, α, αc, and αint, later in the text) present in the frequency window at the temperature of measurement, was critically fitted to the experimental data, and the fitting parameters were determined.5,28,30 A comment on the number of the fitting parameters needed and the term “critical fit” mentioned above is here in order. The maximum number of relaxations contributing to a spectrum and, thus, the number of HN terms used for the fitting was three, as αint and α/αc do not overlap with each other (results later in section 3.3). By the term “critical fit” we mean that after many reiterations of the initial fitting process in the whole temperature range, we could lock one or two shape parameters of HN.9,28,29 For example, α is the only relaxation which shows nonasymmetric shape (βHN < 1) already in the raw data (examples are shown later in the text, section 3.3), while all other relaxations are characterized by symmetric HN (βHN = 1). S and β relaxations, in particular, being local processes, are expected to be symmetric.58 S relaxation in neat silica in section C of the Supporting Information shows a symmetric shape already in the raw data. In addition, depending on the temperature evolution of αHN, Δε, and log f max, we could lock or confine αHN within a specific range, in order that all fitting parameters exhibit reasonable evolution with temperature. 9460
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Figure 3. Comparative TSDC spectra for the three neat polymers (a) in the region of glass transition, cold crystallization and melting and (b) overall behavior. In (b), results for A300/PDMS-20 have been included for comparison. Indicated on the plots are the main thermal events along with conductivity related phenomena at higher temperatures in (b).
ΔCPDMS p,amorphous in eq 5 is the heat capacity change at glass transition for fully amorphous neat PDMS, found equal to 0.56, 0.48, and 0.33 J/(g K) for PDMS-20, PDMS-200 and PDMS1000, respectively (Table 1 and Figure 1a). Calculated values are listed in Table 1. Please note that according to the above equations, both mass fractions refer to the mass of the whole polymer in the composite [factor (1 − CF) in eq 5]. Also, since the RAF to MAF ratio may change with temperature,21,69 we refer to the calculated values as representative for temperatures around Tg. In previous work on semicrystalline PNCs6,30,69 RAFint and RAFcryst have been disentangled under the assumption that the RAFcryst to CF ratio, Rc, determined for the unfilled polymer matrix, remains the same in the PNCs. We will perform similar calculations here, bearing in mind, however, that semicrystalline morphology may differ significantly for different samples, as samples had been crystallized nonisothermally. We estimate RAFcryst by the term Rc·CF in eq 7, where Rc has been determined to 3.00 and 0.18 for PDMS-200 and PDMS-1000, respectively.
modification of silica in PNCs leads to suppressed interaction with the polymer (in the sense of less contact points25,28,29), as compared to the unmodified PNCs, and therefore to an increase in fraction of bulk polymer (MAF, Table 1). The latter is probably responsible for the recorded decreasing in ΔTg. For the low Wm samples (no crystallinity, Table 1) these effects originate merely from the presence of filler, while for the higher Wm samples (semicrystalline, Table 1) additional effects of crystallinity interfere. The latter is supported by the recorded differences in ΔTg for neat polymers between measurements at slow (10 K/min) and fast cooling (quenching). For neat PDMS-200 no significant increase in CF was observed after cooling at 10 K/min, this being accompanied by unchanged ΔTg (∼2, Table 1), while for PDMS-1000 the recorded increase in CF from 0 to 0.65 wt % led to a significant increase in ΔTg from 3 to 12 K, respectively. These results are in agreement with findings for other PDMS/metal oxide systems6,13,30 and suggest a broad distribution of segmental relaxation times and glass transition temperatures in PNCs (a gradient of mobility of polymer segments from the filler surface to the bulk matrix).15,19 Values related to crystallization and melting have been included in Table 1 for the sake of completeness. They will not be, however, discussed here; we refer to previous work6,29 and references therein for further information. The most striking effect of the nanoparticles is the significant reduction of ΔCp,n in PNCs, interpreted in terms of a fraction of polymer being immobilized at the interface with the filler, RAFint, in agreement with results obtained previously.5,20,21 Because of the semicrystalline nature of PDMS, an additional RAF should exist in close proximity to PDMS crystals,68 RAFcryst (inset to Figure 2a). RAF is thought to be completely immobile in DSC, making no contribution to the glass transition.20,21 According to Schick and co-workers,21,68 a “3phase model” (inset to Figure 2a) can be applied for the quantitative estimation of the various polymer fractions from DSC results in semicrystalline PNCs [i.e., crystalline fraction (CF), rigid amorphous (RAF), and mobile amorphous (MAF)]. Thus, we may calculate MAF and total RAF using eqs 5 and 6, respectively. MAF =
ΔCp ,n ΔCpPDMS ,amorphous
RAFint = RAF − RAFcryst = RAF − R c· CF
Figure 2a shows RAFint comparatively for all studied PNCs (Table 1). Surface modification of silica with CeO2 results in reduction of SAr, and we follow in Figure 2a that RAFint reduces as well. Regarding the Wm dependence, RAFint is larger for the lower Wm, whereas for the two higher Wms the RAFint(SAr) dependences are rather similar. The same is true for the ΔTg(MAF) dependences in Figure 2b. These results suggest significant changes in polymer mobility with Wm approaching Wm,e or, in other words, while approaching saturation of Tg to a maximum value.44,45 On the other hand, the ΔTg(MAF) dependences for neat polymers in Figure 2b do not follow the same trends as in the respective PNCs, neither for the amorphous (ΔTg ∼ 2 K for MAF = 1.00 in all polymers, Table 1) nor for the semicrystalline materials (ΔTg ∼ 2 and 12 K, for MAF = 0.84 (PDMS-200) and 0.23 (PDMS-1000), respectively, Table 1). The overall results in Figure 2b, compared also with results from the literature,6,29 indicate significant effects imposed on polymer mobility by both strong polymer−particle interactions15 and the presence of crystals. A final comment in this section refers to the large difference in Rc (RAFcryst to CF ratio) between PDMS-200 (Rc ∼ 3.0) and PDMS-1000 (Rc ∼ 0.2), surprising at first glance. This result could be, however, rationalized in terms of serious differences
(1 − CF)
RAF = 1 − CF − MAF
(7)
(5) (6) 9461
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Figure 4. (a−c) Comparative TSDC spectra in the region of segmental relaxation (glass transition) for the various PNCs showing effects imposed on polymer dynamics by surface modification of silica A-300. Results are shown separately for PDMS-20 (a), PDMS-200 (b), and PDMS-1000 (c). The arrows mark the peak temperatures (depolarization current maxima) of the recorded segmental relaxations (α and αint). The horizontal lines added mark the TSDC substrate. (d) Effects on interfacial polymer fraction, RAFint, imposed by both molecular weight and surface modification (specific surface area, SAr), as obtained by TSDC (details of calculation in the text) and, comparatively, by DSC (taken from Figure 2a).
in semicrystalline morphology. Crystallization temperatures, Tc, in Table 1 are systematically lower for the PDMS-200 based samples than those based on PDMS-1000. Thus, we may expect a large number of small crystallites in PDMS-200 due to stronger supercooling66 against a few larger crystallites in PDMS-1000, which would result in different numbers for Rc. PNCs based on PDMS-200 and modified silica show a quite weak increase in CF (0.07 and 0.09 wt % in Table 1) as compared to that in neat polymer (0.04 wt %). However, Tc decreases systematically also in these PNCs (Table 1), suggesting that filler NPs do not act as crystallization sites and they are not embedded into the crystals.67,70 The large difference in Rc between PDMS-200 and PDMS-1000 discussed above points to the limitations of the route used for separating RAF into RAFcryst and RAFint. A second route available for that is based on DSC measurements in both amorphous and crystallization annealed samples (our ref) and a strong assumption is necessary also for that namely no changes in the topology of filler dispersion caused by crystallization. Reported results in the literature show that in some cases the first route (e.g., PDMS/titania30) and in other cases the second route works better (e.g., polymer nanocomposites based on polylactide71). Obviously, more work is needed to get a deeper insight into these issues. 3.2. Thermally Stimulated Depolarization Currents (TSDC). TSDC thermograms in the temperature range from −150 to −50 °C are presented in Figures 3 for neat PDMS and
in Figures 4a−c for PNCs. The depolarization current density has been normalized with the applied electric field,57 so that results for different samples can be compared to each other, not only with respect to the temperature position of a peak (time scale of the corresponding relaxation) but also with respect to the magnitude of a peak (dielectric strength of the corresponding relaxation, Δε). In the temperature range from −145 to −70 °C, i.e., in the range of the calorimetric glass transition (Figure 1 and Table 1), single peaks appear in the neat PDMS thermograms (α relaxation in Figure 3), while multiple peaks (α and αint relaxations in Figures 4) appear for all PNCs. We know that the equivalent frequencies of TSDC and DSC measurements57 are of similar range, so the recorded relaxation peaks are related with cooperative PDMS chain motions in the glass transition region.5 Taken together, the DSC results in the previous section and the TSDC results here suggest that the interfacial polymer appears immobile by DSC,6,20,21 whereas it shows retarded segmental dynamics by dielectric techniques.5−8 This discrepancy between DSC and dielectric techniques (TSDC, BDS) has been discussed in terms of different probes measured by the two methods (DSC being sensitive to enthalpy or entropy fluctuations, against dipoles fluctuations for BDS)69 and of cooperativity of the relaxing units in relation to the small thickness of the interfacial layer31,71 The latter is sufficient for cooperative motions to be detected by dielectric techniques (as an additional loss peak, next to that for the bulk segmental 9462
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Figure 5. Imaginary part of dielectric permittivity (dielectric loss), ε″, against frequency at selected temperatures, experimental data (points) and analysis into individual Havriliak−Negami (eq 4) components (lines) for each of the recorded relaxations α, αc, αint, β, and S, in (a) neat polymers, (b) the PNC A300/PDMS-200, and (c) comparatively for A300/PDMS-20, A300/PDMS-200, and A300/PDMS-1000. (d) Comparative isochronal plots of ε″ at 1 kHz (and 1 Hz in the inset) replotted from BDS isothermal measurements for the samples indicated on the plot. Results for initial silica A300 have been included in (d) for comparison.
recorded at around −40 °C in Figure 3b due to the interfaces between polymer and filler.6 For PNCs, the temperature position and dielectric strength of MWS (not shown) do not change systematically, neither with Wm of PDMS nor with silica modification. In a previous work on cross-linked PDMS filled with in situ generated silica and titania nanoparticles via the sol−gel technique,6 the strength of polymer/filler interfacial MWS relaxation was found to increase with filler content, almost linearly, while its temperature position remained unchanged. The area under a TSDC peak is a measure of the dielectric strength, Δε, of the corresponding relaxation, that may be considered as representative for the population of the relaxing units (molecular groups).5,57 Thus, by comparing the area of αint peak (Δεαint) with that of the total dielectric signal (Δεtotal = Δεα + Δεαc + Δεαint), we may estimate directly the interfacial polymer fraction, RAFint (in consistency with the literature,20,21,30 we use the term RAF, although interfacial polymer is not completely rigid in TSDC), according to eq 8.
relaxation), 5 however not by DSC (as an additional contribution to glass transition or even an additional separated step at higher temperatures).72,73 We observe in Figure 3 that next to α, a quite weak αc relaxation, by ∼10 K higher than α, contributes to the TSDC response in neat PDMS-200 and PDMS-1000. We have documented in previous studies6,9,29 that αc arises from polymer chains restricted between condensed crystalline regions.9,28,29 The temperature position of the TSDC peak of α relaxation, Tmax,α, increases with increasing Wm (Figure 3), as expected.43,44 Tmax,α does not change significantly in the PNCs of PDMS-20 and PDMS-200 (Figures 4a,b), while it varies for PDMS-1000 (Figures 4c), as a result of changes in CF (Tmax,α increases with increasing of CF, Table 1). As far as αint relaxation is concerned, it is interesting in Figures 4a−c that the relaxation peak immigrates toward higher temperatures for higher Wm and, further, with smoothening of silica surfaces (lower SAr). These results suggest significant changes of the time scale of the relaxation in PNCs, both in the bulk and at interfaces, as compared to neat polymer, in agreement with to DSC findings, which will be discussed later in relation to results by BDS. The strong peaks recorded at higher temperatures (>−60 °C) in Figure 3b are due to conductivity related effects. In neat polymers, they originate from electrode polarization,74 probably combined with interfacial Maxwell−Wagner−Sillars (MWS) relaxation.74 MWS arises from the trapping and the subsequent release of charges at the interfaces between amorphous and crystalline polymer.58,74 In the case of PNCs, MWS relaxation is
RAFint =
Δεα int Δεα int (1 − CF) = Δεtotal Δεα + ΔεαC + Δεα int
(8)
Equation 8 implies, implicitly, that RAF around crystals, RAFcryst, does not contribute to the TSDC response (as well as to the BDS response, next section). This is supported by the present and previous data from the literature, for both unfilled semicrystalline polymer and their PNCs (refs 5, 30, 68, 69, and 75 and references therein). We refer to Supporting Information (Figure SM.2) for the analysis employed for the evaluation of 9463
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Figure 6. (a) Arrhenius plot and (b) dielectric strength vs reciprocal temperature of the local relaxations (S, β) and the segmental relaxations arising from bulk polymer (α) and polymer constrained between condensed crystal regions (αc) [insets to (b)], for the three neat PDMS samples, initial silica A-300 and neat silica modified by four cycles of CeO2 reaction. The symbols used for each type of relaxation are described in (a). The lines in (a) are fittings of the VTFH (eq 9) and the Arrhenius equations (details in the text). The arrows in (a) mark changes in α and β imposed by increasing of molecular weight. The insets to (b) aim at explaining the rising of αc at the expenses of α (and unaffected MAF) with temperature increasing, in terms of the simultaneous increase of CF (via cold crystallization) at the expenses of MAF.
Figure 7. (a) Arrhenius plot and (b) dielectric strength vs reciprocal temperature of the local relaxations (S, β) and the segmental relaxations arising from bulk polymer (α), polymer constrained between crystal regions (αc), and interfacial polymer (αint) for the two PNCs based on unmodified A300 and two types of PDMS, PDMS-20 (open black symbols) and PDMS-1000 (open blue symbols). Results for neat PDMS-20 (solid black symbols), initial silica A-300 (S relaxation, orange stars in (a)), and αint relaxation for A300/PDMS-200 (open red circles) have been included for comparison. Error bars for S relaxation in PNCs are shown representatively for A300/PDMS-1000, while uncertainty is represented by symbol size for all other relaxations. The lines in (a) are fittings of the VTFH (eq 9) and the Arrhenius equations (details in the text). The arrows mark changes in αint, α, and S imposed by increasing of molecular weight.
TSDC peaks in terms of dielectric strength. The factor (1 − CF) was inserted in eq 8 in order that RAFint refers to the whole polymer fraction and may be directly compared with RAFint obtained by DSC. At this point, we would like to draw attention to the different type of eq 8 and eqs 5−7 for determining RAFint from dielectric (TSDC and, later, BDS) and DSC data, respectively. That is so because interfacial polymer is considered to be mobile by dielectric techniques, giving rise to the segmental α int relaxation, 5,7,8,18,28 and immobile by DSC, making no contribution to the glass transition.5,21 It is interesting to note that an equation similar to eq 5 used for the evaluation of DSC data has been employed also for the evaluation of dielectric data for nanocomposites based on different (more rigid) polymers, where interfacial polymer was found to make no contribution to segmental mobility.24,67,71 It becomes clear already from the raw data of Figures 4a−c that αint in the PNCs is stronger for the lower Wm (Figure 4a) and for the unmodified silica. Increase of Wm and surface modification of silica (surface smoothening) both result in suppression of αint as compared to α. These effects are quantitatively demonstrated in Figure 4d, which shows the SAr
and, simultaneously, the Wm dependence of RAFint in the PNCs. Results for RAFint(SAr) are qualitatively similar to those obtained by DSC (Figure 2a); however, the TSDC results exhibit an almost linear RAFint(SAr) dependence and the suppression of RAFint with increasing of Wm, at least for Wm below entanglement threshold studied here, becomes more clear. We come back to further discussion and interpretation of these results in combination with respective results obtained by BDS in the next section. 3.3. Molecular Dynamics (BDS). We now focus on BDS results for the local and, mainly, the segmental dynamics related to glass transition. Results are presented here in the form of frequency dependence of the imaginary part of dielectric permittivity (dielectric loss) ε″ (isothermal plots of Figures 5a,b).58 Next to the neat polymers and the PNCs, also the neat oxides A300, A300C1, and A300C4 were studied by BDS (raw data in Supporting Information, SM.3a,b). Representative results are shown also in the form of temperature dependence of ε″ replotted from the isothermal data at selected temperatures (isochronal plots of Figure 5d). The isochronal BDS plots of Figure 5d facilitate easier comparison with the DSC (Figure 1) and TSDC (Figures 3 and 4) thermograms in 9464
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Figure 8. (a) Arrhenius plot and (b) dielectric strength vs reciprocal temperature of the local S relaxations (stars) and the segmental relaxations arising from bulk polymer (α, squares), polymer constrained between crystal regions (αc, up triangles) and interfacial polymer (αint, circles), for the four PNCs indicated on (a). The lines in (a) are fittings of the VTFH (eq 9) and the Arrhenius equations (details in the text). Open symbols are used for PNCs with unmodified silica A-300, while solid symbols are used for PNCs with modified A-300_C4. The arrows mark changes in αint and S relaxations imposed by surface modification of A-300 (smoothening of silica surfaces).
the temperature range from −150 to 60 °C. Results obtained by analysis of the data (described previously in section 2.4) are comparatively presented in Figures 6−8 in terms of time scale (Arrhenius plots with added TSDC and DSC data at the equivalent frequencies of 0.0016 and 0.02 Hz, respectively5,57) and dielectric strength of all the relaxations recorded. In the inset to Figure 5d, we follow for the neat polymers a steep increase in ε″ at higher temperatures, as a result of increasing in conductivity, while for the PNCs the interfacial MWS relaxation is recorded. We refer to section 3.2 for the origin of MWS. No systematic effects of filler on MWS were observed, so MWS and conductivity were not further studied in this work. It should be stressed, however, that MWS and conductivity related phenomena are recorded well separated from polymer dynamics, and thus, they do not affect analysis of the data.8,76 In fact, the main relaxation peaks (α, αc, αint) are clearly distinguished already in the raw data (Figure 5). The main interest here is on segmental dynamics, namely the relaxations α, αc, and αint (see section 3.2 for the origin of the relaxations). The high resolving power of BDS and the employed analysis (section 2.4) enabled, however, to identify also dielectric relaxations related to local (noncooperative) mobility of both the polymer (β relaxation) and the nanoparticles (S relaxation). A faster than α but relatively weak relaxation can be followed in the raw data of Figure 5b, located at around 100 Hz at −135 °C, and, after analysis, in the dielectric map of Figure 6. This is the secondary (local) β relaxation of PDMS.29,44 β is characterized by shape parameters αHN ∼ 0.2 and βHN ∼ 1 (eq 4), mean values over the temperature range of the relaxation. β was recorded in all neat polymer samples (Figure 6) and, clearly, only in two nanocomposites (A300/PDMS-20 and A300/PDMS-200 in Figure 7). Effects of Wm and filler on β are not clear at this stage, and further investigation of the relaxation is out of the scope of this work. 3.3.1. Local Relaxation of the Surface Silica Hydroxyls (S Relaxation). S relaxation in Figures 6 and 7 is the local dielectric relaxation of surface hydroxyl groups of silica (silanols, Si−OH), probably with attached water molecules (via hydrogen bonding).77,78 S relaxation dominates the response of initial nanooxides (raw data and evaluation in terms of Δε in Supporting Information, Figures SM.3a,b, time scale in Figure 6a). As expected, the relaxation is significantly
enhanced by the presence of interfacial water molecules (compare Figures SM.3a,c in Supporting Information) for dried and ambient neat silica A-300 samples. The S relaxation has been recorded previously also in other neat silica samples,9,77,78 in different neat metal oxides, such as titania (TiO2),30,79 and in PNCs.5,9,30 S, characterized by shape parameters αHN ∼ 0.4 and βHN = 1 (eq 4, average values), was recorded in neat oxides (Figure 6) and in all PNCs (Figures 7 and 8). Regarding its strength, S is dramatically suppressed in the PNCs by a factor of ∼20 (please compare Figures 6b and 7b, where Δε drops from 1.5 in neat oxides to 0.02−0.10 in PNCs) as a result of the disturbance in mobility of surface silanols due to their engagement by PDMS chains. Moreover, the dielectric strength of S, ΔεS , in PNCs decreases systematically with lowering of Wm (arrow on S in Figure 7b). In addition, we follow in Figure 8b that ΔεS in PNCs increases with surface modification of A-300 with CeO2 (i.e., with lowering of SAr). We will come back to this point later in section 3.3.3. Surface hydration (hydration level, structure of adsorbed water, type of water−silanols interaction, etc.) has a strong impact on the S relaxation Further analysis and comments on S can be found in the Supporting Information, section C),77,78 whereas work along these lines is in progress in order to better understand the changes recorded in time scale and Δε(T) dependence in Figures 7 and 8. 3.3.2. Bulklike Segmental Dynamics (α and αc Relaxations). The α relaxation at around 104−106 Hz at −115 °C in Figure 5a is associated with the glass transition of the amorphous unaffected (bulk) polymer fraction,6,23,29 observed in all PDMS based samples. Next to α, at around 100−103 Hz at −115 °C, αc relaxation is affiliated to polymer chains restricted either between condensed crystal regions6,23,28,29 (i.e., case of neat PDMS, Figure 5a) or in the voids between nanoparticles in their aggregates (i.e., case of PNCs at low polymer loading, Figure 5b).9,29 For neat PDMS-200 and PDMS-1000 time scales of αc in Figure 6a are almost identical, whereas both α and αc are faster for PDMS-20. Nevertheless, at higher temperatures time scales of αc of PDMS-200 and PDMS1000 meet that of PDMS-20 (initially more amorphous, Table 1). This is most probably due to cold crystallization and the resulting increase of CF (inset schemes to Figure 6b), since isothermal BDS frequency scans (section 2.4) can be 9465
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Figure 9. (a) Interfacial polymer fraction calculated from the additive contribution of αint relaxation to the total dielectric relaxation strength of segmental mobility, Δε, in BDS (eq 8, inset scheme) against specific surface area (nanometric roughness) of the hosting particles for the samples described on the plot. Data taken from the recent literature in similar systems (open symbols blue triangles25 and open black square30) have been included on the plot. (b) The apparent coverage of surface hydroxyls, CSH (eq 10, inset scheme, details in text), for the same samples. Arrows mark the effects imposed by increasing of Wm in PNCs.
D.82 We calculated fragility (cooperativity) index, m, values for αint, results being shown in Figures 7a and 8a. From a first glance at the Arrhenius plots (Figures 6a−8a), the time scale of αint relaxations seems to tend to more linearlike (Arrhenius, constant Eact) behavior as compared to α and αc. The average value of the fragility index, m, is ∼105 and ∼90 for α and αc, respectively.29,30 With increasing Wm in PNCs, αint becomes faster and more cooperative (Figure 7a), but, simultaneously, weaker (Figure 7b). Please note that at the same time the S relaxation (due to nonengaged surface silanols) is enhanced (Δε increases in Figure 7b). As far as effects of CeO2 modification is concerned, it becomes clear in Figure 8 that with increasing of CeO2 grafting (smoothening of silica surfaces) the faster αint of A300/PDMS1000 becomes slower (Figure 8a), and its cooperativity and Δε are reduced in A300C4/PDMS-1000 (Figure 8b). On the other hand, the already slow and noncooperative αint of A300/ PDMS-20 does not change in time scale and cooperativity with CeO2 modification in A300C4/PDMS-20 (Figure 8a); however, its strength is dramatically suppressed (Figure 8b). Again, any suppression of Δε of αint is accompanied by enhancement of S in Figure 8b. The temperature dependence of Δε of αint (nonmonotonic) in Figures 7a and 8a will be discussed later in section 3.4. We may now proceed with the calculation of interfacial polymer fraction, RAFint, adopting the model described previously for TSDC (eq 8). Results for RAFint in Figure 9a show clearly, in qualitative agreement with DSC (Figure 2a) and TSDC (Figure 4d), that RAFint is reduced with increasing of Wm and with smoothening of the hosting particles surfaces. Results agree with previous findings for PDMS-20 adsorbed at 40 wt % onto titania particles30 and for PDMS-1000 adsorbed on silica and titania particles, covering together a wide range of specific surface area.25 As discussed above, changes in Δε of αint in Figures 7b and 8b seem to correlate with respective changes of S in the opposite direction. In the belief that during the first stage of polymer adsorption on silica the initial contact points to PDMS chains are the surface silanols, we will compare RAFint with the fraction of silanols that indeed have interacted (are disturbed) with PDMS. Thus, by comparing the average Δε of S (representative of the nondisturbed silanols) of the PNC, oxide ΔεPNC , we S , with that of the respective neat oxide, ΔεS estimate the coverage of surface hydroxyls, CSH, by the equation
considered as multitemperature crystallization annealing. These results suggest that the constraints imposed by the PDMS-20 crystals are more loose than those imposed by the crystals of PDMS-200 and PDMS-1000, probably in relation to smaller size and/or worse quality of PDMS-20 crystals, manifested by lower melting points in DSC (Table 1, Tm1,2), as compared to PDMS-1000. The time scale of α and αc is practically independent of Wm for the PNCs (Figures 7a and 8a), while this is not the case for the neat PDMS samples in Figure 6a, as both α and αc become slower with increasing Wm. This is in agreement with the previous findings by DSC (Figure 1a and Table 1) and TSDC (Figure 3), suggesting effects by changes in the CF. Previous work has demonstrated direct and indirect effects of crystallinity on the bulklike relaxations of PDMS, imposed by the different measurement conditions,6 the polymer structure (linear9 against cross-linked6,48), and the nanocomposite compositions.6,9 Looking back at Figures 6−8b, one can observe that for both neat polymers and PNCs Δε of α decreases as temperature increases, as expected for bulk-unconstrained segmental dynamics,58,80 while Δε of αc relaxation increases, as the constraints imposed by the crystals are gradually loosened.6,29,60 As illustrated in the insets to Figure 6b, with increasing of temperature, formation of CF (via cold crystallization) and, subsequently, development of αc occur, most probably at the expenses of the gradually vanishing α.29 3.3.3. Interfacial Polymer Dynamics (αint Relaxation). The αint relaxation in Figures 5b,c, located for example in the broad range from 101 to 106 Hz at −65 °C, represents the dynamics of polymer chains in the interfacial layer, with strongly reduced mobility due to interactions with the surface hydroxyls of silica.5,6,9,25,28−30 The temperature dependence of segmental dynamics is typically described by the Vogel−Tammann− Fulcher−Hesse (VTFH) equation81,82
⎛ DT0 ⎞ f = f0 exp⎜ − ⎟ ⎝ T − T0 ⎠
(9)
where f 0 is a frequency constant, D is the strength parameter, and T0 is the Vogel temperature. After fitting eq 9 to our experimental data (Figures 6a−8a) and fixing the f 0 parameter to the phonon value 1013 Hz,5 we obtained values for T0 and D. D is related to the steepness or fragility index m = 16 + 590/ 9466
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CSH = 1 −
interesting to note, in this connection, that Füllbrandt et al.7 and, more recently, Lin et al.18 studied silica/poly(vinyl acetate) (PVAc) PNCs and measured the degree of silica−polymer interaction, on the one hand, by BDS similarly to the present work, and, on the other hand, by Fourier transform infrared spectroscopy (FTIR). 3.4. Interpretation in Terms of Models. The various effects on interfacial polymer fraction (RAFint) and dynamics (αint) described above look very complex at first glance. However, employing models proposed previously, which involve multimodal conformations36,37,83 of a polymer interacting with a solid attractive surface,2,3,10,35,41 proved very helpful in our recent work on similar systems.9,25,28,29 Results in previous work on fumed silica/PDMS-1000 core− shell systems9 suggest that the adsorption of PDMS in the first layer(s) onto the surfaces of the oxide particles proceeds via two, at least, chain segment conformations (Scheme 2), which
ΔεSPNC ΔεSoxide
(10)
Absolute CSH values should be “apparent”, as complete coverage of free surface silanols by the polymer is practically impossible. 83 Results of C SH presented in Figure 9b demonstrate quantitatively similar trends with those of RAFint in Figure 9a, providing additional support for the origin of αint and, at the same time, another indirect measure for the degree of particle−polymer interaction. Regarding effects of specific surface area, SAr, we have recently shown28,30 that for fumed silicas in the form of aggregates SAr measures the concentration of surface pores (Scheme 1). SAr increases with decreasing size of the initial Scheme 1. Simplified Model for Explaining Effects Imposed on Concentration of Particle−Polymer Contact Points (Proportional to Specific Surface Area25) by (from Left to Right) Grafting of Small (∼2−3 nm) Nanoparticles on the Surface of Silica (Particles of ∼10 nm in Size) Aggregates (≥200 nm)9 and by (from Top to Bottom) Increasing the Size of Initial Nanoparticles28,30
Scheme 2. Simplified Model for the Description of the Different Polymer Chain Conformations in PNCs and the Respective Changes Imposed by Increasing of Molecular Weight (Chain Length, Vertical Arrow Direction) and by Increasing Surface Roughness of the Hosting Particles (Surface Area, Horizontal Arrow)
particles (Scheme 1). For PNCs of linear PDMS-1000 adsorbed at 40 wt % on silica aggregates of a wide range of specific surface area (from 25 to 380 m2/g, dash-dotted line in Figure 9a),25 we demonstrated the systematic and nonlinear increase in RAFint with SAr. Results were interpreted there and in similar work28,70 by the following scenario. As SAr increases, the surface silica pores, in addition to increasing in number (concentration), they also approach each other (Scheme 1). Then, the concentration of surface silanols (potential contact points with PDMS) increases in these pores, which act as strongly attracting sites and, finally, pocket-free PDMS chains in their vicinity. Results for the SAr dependence of RAFint here in Figure 9a follow the respective trend shown in previous work;25 therefore, they can be interpreted by the same scenario. It is interesting to report, in this context, that the average distance between pores depends on initial particles size (Scheme 1); thus, it may vary from ∼10 nm (SAr ≥ 300 m2/ g, our case) to ∼80 nm (SAr ≥ 25 m2/g). In the particular case of large initial particles and low SAr (e.g., case of titanium dioxide,30,70 bottom of Scheme 1), results by following a similar methodology as in the present study suggested nonuniform coverage of particles surfaces by PDMS due to quite distant contact points, while the opposite was observed for initially smaller particles.29 To the best of our knowledge, this is the first time that polymer−filler interaction in PNCs was screened simultaneously via two physical phenomena (namely, by αint and S relaxation) and, furthermore, by the same technique. It is
can be considered responsible for the molecular mobility recorded by BDS as interfacial αint process. According to this model interfacial polymer consists, on the one hand, of extended tails with bulk like density but strongly reduced mobility and cooperativity and, on the other hand, of loops (flattened chain segments) in the inner quite dense region. It is further considered that during the initial stage of adsorption tail-like conformations are favored.9,10,28 Tail-like conformations for PDMS PNCs are probably more strongly attached to the oxide surfaces,10,84 while weaker interactions84 have been demonstrated for the loops, accompanied by the possibility for reorganization10 and, further, for abruption from the surface.9,29,31 According to simulations, it is necessary, from the thermodynamic point of view, that a third type of conformation coexists with loops and tails (outer part of interfacial layer), i.e., the “train” conformation (Scheme 3) in the inner part of interfacial layer16,36,85 ( Wm,e. Cheng et al.32 commented recently on changes in the fraction and density of interfacial polymer in silica/ poly(vinyl acetates) with Wms > Wm,e PNCs in terms of an interplay between formation of looplike conformations of the polymer at interfaces and of chain (loops) bridges between neighboring nanoparticles. We should keep in mind that implementation of entanglement effects in polymer mobility may arise, also, from measurement conditions (e.g., annealing temperature and time46). Regarding, now, effects imposed here by surface modification of silica (left side of Scheme 2), it is most probable that grafting of small CeO2 particles results in reduction of the number of accessible silanols,52−54 the potential contact points. For the sake of clarity, we recall that the number density of surface silanols of neat silica is not expected to change by applying surface modification;52,54 therefore, modification is expected to lead to reduced accessibility of polymer chains to surface silanols. In other words, the number of free silanols, i.e., silanols that have not interacted with PDMS chains, is expected to increase at the expenses of engaged silanols. Thus, independently of Wm (chain length−concentration of chain ends), the polymer adsorption is in general hindered (lowering of RAFint), and the finally adsorbed chains are less and more sparsely distributed at the surface of silica, resulting, this way, in low cooperativity (large cooperativity length) and slower and weaker αint relaxation (Scheme 2). Nevertheless, RAFint remains larger (Figure 9a) for the lower Wm (more chain ends, lower left in Scheme 2). Thermogravimetric analysis (TGA) measurements54 on the same systems revealed enhanced polymer degradation in the samples based on surface modified silica, as compared to the unmodified ones, suggesting weaker (less) oxide−polymer interaction(s) after CeO2 grafting. Another interesting point in the frame of the bimodal conformations model refers to the temperature dependence of Δε of αint relaxation. According to the model, for low Wm, where tails dominate interfacial dynamics, it is expected that with increasing temperature the mobility of the tails gradually increases, drifted by the increasing of bulk (free) polymer mobility.9 Thus, the degree of “orientation” of the tails at the interfaces is expected to reduce, leading to lowering of Δε for αint with temperature.9 The latter was observed here in Figures 7b and 8b for PDMS-20-based samples. On the other hand, for larger Wm, where loops govern interfacial dynamics, Δε of αint is expected to increase with temperature, as the looplike conformed chains are more weakly attached on the surfaces.10 In addition, their concentration may increase as temperature increases, without any change in interfacial polymer density, e.g., by a simultaneous decrease of loops’ height.10 This was also confirmed here in Figures 7b and 8b for the larger Wm PDMS samples. A final comment in this section refers to involvement of water in the phenomena studied in this work, in particular phenomena in the interfacial layer, as silica surfaces offer sites (silanols) for hydrophilic interactions. In addition, the type of interaction between silanols (−Si−OH) and water molecules
Scheme 3. Simplified Model for Explaining Differences between (Left) DSC and (Right) Dielectric Techniques in Recording Polymer Mobility in the Interfacial Layer with the Filler in PNCs (Details in the Text)
interfacial polymer recorded by BDS in PNCs, in particular models involving mobility of loops for polymers of large Wm32 and tails/loops for polymers of small Wm.28−30 As mentioned in section 3.1, the significant reduction of ΔCp,n in PNCs is interpreted in terms of polymer in the interfacial layer being immobilized, RAFint, in agreement with results obtained previously.5,20,21 Thus, we may conclude on the basis of these results that none of the three types of polymer conformations in the interfacial layer (Scheme 3) contribute to the glass transition in PNCs measured by DSC. We suggest, for the first time to the best of our knowledge, that this is the reason for recording larger RAFint by DSC than by BDS (Scheme 3) with PDMS-based systems.6,28,30 On the basis of this suggestion, we may proceed to a rough calculation of the fraction of trains as the difference between RAFint by DSC and RAFint by DRS. We obtain values between 0.1 and 0.2 for the samples with different molecular weight and specific surface area, with an average value of 0.15 and a tendency of increasing for the highest molecular weight (PDMS-1000). These should be considered as preliminary results, interesting to be compared in future work with related results obtained with other PNCs and/or by other methodologies. Coming back to the present study, results can be explained as follows (Scheme 2). The increased concentration of free chain ends in the case of PDMS-20 (short chains) results in the adoption of many contact points (Scheme 1) at the surfaces of silica (lower right in Scheme 2). Thus, RAFint is relatively large consisting mainly of tails (lower right in Scheme 2), which may not easily fold and/or cooperate with each other in the interfacial layer. These characteristics explain the recorded large Δε of αint and the slowing down of dynamics (slow αint) with almost eliminated cooperativity (m, Figure 7a) in the frame of Adam−Gibbs theory.86 With increasing Wm, the concentration of free chain ends decreases and, consequently, adoption of neighboring contact points becomes difficult; nevertheless, polymer chains are now longer and show increased ability to fold and to cooperate with each other. Thus, the adoption of multiple contact points (however, not so close to each other) per chain is enhanced, and polymer adsorption favors looplike conformations (upper right in Scheme 2). This explains the recorded suppression of RAFint, simultaneously with the enhanced cooperativity and faster dynamics for PDMS-200 and, further, for PDMS-1000 based PNCs (Adam−Gibbs 9468
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DSC and BDS in PNCs) has been reported previously for PDMS9,29 and other polymers71,75 and has been explained in terms of effects of geometrical confinement of the polymer in the voids formed between initial silica nanoparticles in their aggregates9 and, in general, between neighboring nanosized fillers.71 The most interesting effect of Wm on Tg is demonstrated again for interfacial polymer, namely on Tg,diel of the interfacial polymer (calculated by extrapolation of the VTHF fit of αint at 1.6 × 10−3 Hz, Figure 7a). Interfacial Tg,diel gradually decreases by ∼6 K with increasing Wm (from −99 °C to −101 and −105 °C for PDMS-20, PDMS-200, and PDMS-1000, respectively, Figure 10). It would be interesting to study in future work silica/PDMS based on linear PDMS of Wm ≫ 8000 g/mol and examine as to whether Tg saturates in PNCs similarly to neat polymers. Combining these results with the model employed in section 3.4 that considers adoption of different polymer conformations in the interfacial layer, namely, tail- and looplike, for low and higher Wm, respectively, the lowering of Tg,diel could be possibly explained by an increasing of free volume at the interface. This situation resembles changes suggested in Scheme 1 (more sparse polymer distribution in the case of loops than of tails) and the previously suggested increased number of the nonengaged surface hydroxyls of silica (Figure 9b). In the inset to Figure 10 we have replotted interfacial Tg,diel for the PNCs studied here against the apparent thickness of the interfacial layer, dint (details of calculation in section D of the Supporting Information). Results show an increase in Tg,diel (from −105 to −99 °C) with dint (from 0.7 to 1.5 nm). Having in mind the formation of strong interactions between silica and PDMS (hydrogen bonds), we may compare our findings with those for polymers in the form of thin films supported on an attractive solid surface (refs 40, 41, 50, and 51 and references therein). Schönhals and co-workers40 studied by specific heat spectroscopy (AC-chip calorimetry) ultrathin poly(2-vinylpyridine) (P2VP) films, of 10−405 nm in thickness, d, supported on acid-cleaned SiO2 surface and revealed the existence of a mobile surface layer (higher mobility than that in bulk). Moreover, they showed that Tg of the surface layer increases sharply by about ∼6 K with increasing of d from 5 to ∼80 nm, while Tg saturates for larger d. Changes imposed on d dependence of Tg and ΔCp were considered there to be influenced by the adsorbed interfacial layer (quite mobile) and geometrical confinement, respectively.40 It is remarkable that the dint (although apparent) dependence of interfacial Tg,diel here (sharp increase, inset to Figure 10) resembles that of thin supported films,40 suggesting significant similarities between differently prepared polymer layers, similar origins of effects on the interfacial polymer, and, from the methodological point of view, similarities between in principle different experimental techniques (calorimetry vs dielectric spectroscopy). This is a point worth to be followed in future work. Finally, we should comment on another significant discrepancy between DSC and dielectric techniques revealed in relation to Tg in PNCs. Tg of neat PDMS remains practically unchanged on the addition of particles when measured by DSC (Table 1), while it decreases when measured by BDS (Figure 10). Such discrepancies between Tg (unchanged) and time scale of the α relaxation (faster in the PNCs) have been observed in previous work69,71 and discussed in terms of BDS being able (DSC however not) to detect specific effects on segmental mobility, for example effects of spatial confinement,
(H−OH) is the same with that between silanols and PDMS, namely hydrogen bonding. In this connection, Gee et al.87 showed that dehydration of PDMS/silica PNCs similar to those studied in this work results in a decrease of polymer−silica contact distance, accompanied by decreased mobility of interfacial polymer. Preliminary results obtained with hydrated/dehydrated samples within this work (not shown here) seem to agree with those by Gee et al.87 Effects of hydration in PNCs are worth to be systematically followed in future work. 3.5. Glass Transition Temperature. Figure 10 compares the Wm dependence of glass transition temperature, Tg, as
Figure 10. Molecular weight, Wm, dependence of (a) glass transition temperature, Tg, for neat PDMS (open symbols) and A300/PDMS PNCs (solid symbols), results from the present [DSC (squares), BDS (cicles, spheres)] and previous studies [DSC (gray solid lines)43 and BDS (crossed triangles)44]. The inset shows the dependence of dielectric Tg of the interfacial layer on the apparent thickness of the interfacial polymer layer (details in text). The red line in the inset was added to guide the eyes.
recorded in the present study by DSC and BDS with respective results from the literature for linear neat PDMS.43,44 We should note that the dielectric Tg values, Tg,diel, in Figure 10 were obtained from BDS data by extrapolating the VTFH fits of Figures 7a and 7b to the frequency of 1.6 × 10−3 Hz (i.e., relaxation time τ = 100 s) (eq 9).67,71 Our results for Tg of neat polymers, in the Wm range studied, agree very well with those in the literature (Figure 10), demonstrating an increase in Tg of about 5 K with Wm increasing from 1700 to 7960 g/mol (increase from −134 °C in amorphous PDMS-20 to −129 °C in amorphous PDMS-1000 in Table 1). Results by DSC and BDS are in very close agreement with each other (Figure 10). Interestingly, Sokolov and co-workers47 reported recently the opposite effect of Wm on Tg, namely, decrease of Tg with increasing Wm, for −OH-terminated PDMS, this effect being assigned to the development of hydrogen bonds between PDMS chains at large extent (modifications in polymer structure) along with possible microphase separation of hydroxyl groups. Regarding PNCs here, the Tg(Wm) dependence of bulklike polymer in PNCs based on unmodified A-300 shows in Figure 10 a similar trend with that in neat polymers (results by DSC in Table 1); absolute values by BDS (Tg,diel) are, however, systematically lower by 4 K, on average, as compared to Tg by DSC. The latter effect (discrepancy between 9469
DOI: 10.1021/acs.macromol.6b01931 Macromolecules 2016, 49, 9457−9473
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Macromolecules
below Wm,e, while, as recently discussed by Sokolov and coworkers,32 an interplay between uniquely looplike conformations should dominate polymer (including the interfacial polymer) dynamics above Wm,e. BDS enabled the estimation of Tg (actually, dynamic Tg,diel) of the polymer in the interfacial layer. Values of Tg,diel were found to decrease with increasing Wm, opposite to Tg in bulk. However, in terms of increasing of interfacial layer thickness, dint (in the range between 1 and 2 nm), interfacial Tg,diel increases sharply. Interestingly, this result on interfacial polymer mobility in PNCs resembles that in ultrathin (≥5 nm in thickness) supported polymer films studied by specific heat spectroscopy,40 revealing effects imposed on Tg by geometrical confinement arising from the low film thickness. Important issues remain to be further clarified, and new questions arise from the present study. Future work on samples with alternated polymer structure (e.g., with −OH endgroups18,47 against −CH3 in the present study), chemically grafted chains on silica, lower polymer loadings (
