Cooperative rearranging region and dynamical heterogeneity of nanocomposites in poly(l-lactide) and functionalized carbon nanotubes systems
Introduction
Dynamics of different polymer chains can be compared considering the glass transition temperature as a simple criterion. In 1965, the concept of cooperative rearranging region (CRR) was introduced by Adam and Gibbs to characterize dynamics of polymer chains at the glass transition temperature (Tg) [1]. Above the glass transition temperature, molecular motions of macromolecules occur independently. The corresponding structural relaxation becomes a kinetic phenomenon which arises from the non-equilibrium characteristic of the glassy state [2,3]. The rearranging movements of some molecules (or segments implying several chemical repeat units) are only possible through the simultaneous movement of a certain number of neighboring molecules [4]. The CRR is defined as a subsystem, which can rearrange its configuration independently of its environment. According to the method developed by Donth [5,6], the size of the CRR is determined by spatial aspects based on the statistical independence of thermal fluctuations. These in turn can be calculated from the complex heat capacity measurement using temperature modulated differential scanning calorimetry (TMDSC).
Each CRR is defined as a subsystem having its own glass transition temperature and its own free volume, which are obviously linked to a characteristic relaxation time. According to Donth et al. [4,7] the cooperativy length at the glass transition, , corresponds to the size of a CRR. This size can be easily estimated using the temperature fluctuation of the amorphous phase. The cooperativity length is associated with the volume of a CRR, , and the number of relaxing structural units per CRR, Na (i.e. the also called the cooperativity degree). The indicated parameters can be estimated by using the following equations:where Tα is the dynamic glass transition temperature, is the difference in the inverse of the isobaric heat capacity between the liquid and the glass at Tα, ρ is the density at Tα, kB is the Boltzmann constant, NA is the Avogadro’s number, m0is the molar mass of the relaxing structural unit, and δT is the temperature fluctuation in a CRR.
Quantification of these parameters is important because the dynamics of polymers can be affected by additives or modifiers while sometimes the glass transition temperature remains unchanged. There are several studies which focus on the CRR measurements of neat polymers and nanocomposites with different glass transition temperatures [[8], [9], [10], [11], [12]], but authors did not investigate the effect of nanofillers on dynamical behaviour of polymeric systems having the same glass transition temperatures. In recent years, various types of fillers and additives have been incorporated in polymer matrices in order to improve polymer properties and expand the application boundary of polymers [[13], [14], [15], [16], [17]]. Among these fillers, carbon nanotubes (CNTs) were identified as a unique material to render extraordinary thermal, mechanical, optical and electrical properties when were incorporated into a polymer matrix. Polymer chains can be attracted to nanoparticle surfaces depending on the chemistry and physics of particles. Thus, even at relatively small particle volume fractions significant changes in properties can be observed in nanocomposite materials [[18], [19], [20]]. Relative motion between polymer chains is logically retarded by their immobilization at the nanoparticle surfaces. As the affinity between polymer molecules and particles increases, polymer chains show solid like behavior especially near nanoparticle surfaces. Finally, it should be pointed out that adsorbed polymer molecules enhance the effective filler volume fraction in nanocomposites [14,21].
Rheological measurement is another way to evaluate the polymer chain dynamics affected by nanofillers or chain modifiers in polymeric systems. The study of the rheological behavior of polymer nanocomposites is highly important for the analysis and design of processing operations, the determination of the influence of the corresponding parameters, and the understanding of the structure–property relationships of nanocomposites [22]. In addition, some methods obtained by rheological data can clearly show the difference between the structural dynamics in polymeric systems whereas the melt viscosity and modulus are not able to detect the phenomena [[23], [24], [25]].
In this study, cooperative rearranging region and dynamical heterogeneity of PLLA were evaluated in order to determine the influence caused by the polymer chain extension and the functionalization of nanofillers. To this end, the effects caused by the incorporation of both pristine and functionalized MWCNTs were investigated and quantified. Furthermore, two types of PLLA matrices were considered (i.e. those prepared by non-reactive and reactive melt mixing processes). Results were significant since pointed out a significant effect of chain extension and functionalization on flexibility and dynamical heterogeneity of the studied polymeric system by these two simple methods. A simple model was developed to quantify relatively, the amount of heterogeneity in polymeric systems which demonstrated the variation of PLLA chain dynamics in the presence of chain extender and functionalized CNT.
Section snippets
Materials
Polylactide (PLLA), grade 4032D, was purchased from Natureworks LLC, USA. It is a semi-crystalline material containing 2% of D-lactide units. Multiwalled carbon nanotubes (Nanocyl®-7000 with average diameter, length and specific surface area of 9.5 nm, 1.5 μm and 250–300 m2g−1, respectively) was procured from Nanocyl Korea Ltd. Commercial multifunctional styrene-acrylic oligomers (BASF, Joncryl®ADR-4368) as a reactive agent were employed. Nitric acid (65%) and chloroform (CHCl3) were purchased
Cooperative rearranging region
Dynamics of polymer chains at temperatures close to the glass transition can be evaluated by measuring the cooperativity length (Eq. (1)) and the number of relaxing structural units per CRR (Eq. (2)). The average CRR sizes are calculated by taking ρ = 1.12 g/cm3 at 60 °C, M0 = 72 g/mol for the unit repeat of PLLA amorphous phase and a temperature fluctuation δT determined as the half-width at half-height of the out of phase Cp spectrum.
As mentioned before, assumes that the mean temperature
Conclusions
In this study, PLLA chain rearrangement at temperatures around the glass transition and PLLA chain dynamics in solid and melt states were studied in the presence of functionalized MWCNTs using calorimetric (TMDSC) and rheological data, respectively. It was found that incorporation of MWCNTs in a PLLA matrix did not change significantly the glass transition temperature whereas the flexibility and dynamics of polymer chains were extremely influenced in this region. In addition, different
Acknowledgements
The authors would like to thank Miss Kiany for her kind assistance in conducting Rheometry experiments. J.P. is grateful to support from MINECO and FEDER (MAT2015-69547-R) and the Generalitat de Catalunya (2014SGR188).
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