The effect of fibre concentration on the α to β-phase transformation, degree of crystallinity and electrical properties of vapour grown carbon nanofibre/poly(vinylidene fluoride) composites

Abstract

Vapour growth carbon nanofibres/poly(vinilidene fluoride) – VGCNF/PVDF – composites prepared by solution casting were studied. The spherulitic crystallisation morphology of the pure polymer is maintained for the composites. Mechanical stretching of the composite films induces the α to β-phase transformation within the polymer matrix. This phase transition is accompanied by the destruction of the spherulitic microstructure in favour of a microfibrillar one. The incorporation of the VGCNF in the PVDF matrix increases the degree of crystallinity of the polymer composites for concentrations lower than ∼1%, remaining stable for higher VGCNF concentrations. With respect to the electrical properties, the stretching associated to the phase transformation induces a change in the conduction mechanism: the α-phase composite demonstrates a percolative behaviour on the measured conductivity whereas the β-phase demonstrates typical ionic conduction behaviour. Dielectric measurements in conjunction with the the two exponent percolation phenomenological equation demonstrates that in the β-phase an effective reduction in the ratio VGCNF length/domain length could induce the observed percolation behaviour.

Introduction

Conductive nanofiller/polymer composites have been considerably investigated in past decades due to their exceptional mechanical and electric properties. In particular, the focus has been on composites with fillers with high aspect ratio such as carbon nanotubes (CNTs) and vapour grown carbon nanofibres (VGCNFs). For applications where weight, stiffness, and strength are relevant, polymers reinforced with VGCNFs or CNTs offer the potential for significant improvement over systems such as glass and conventional carbon fibre reinforced polymers [1]. CNTs have received greater research attention compared to VGCNFs due to their better mechanical properties, smaller diameters and low density [2], [3]. However, due to the VGCNF structure and dimensions, that facilitates dispersion during composites preparation [2], [3], and also due to their availability in large quantities with consistent quality at a pricing significantly lower than CNTs, VGCNFs are interesting for large-scale applications [2]. Furthermore, VGCNFs can be easily functionalised to improve interaction with the surrounding matrix due to a better accessibility to the graphene planes because of their ‘stacked cup’ structure [4].

The electric and mechanical properties of VGCNF/polymeric composites are intrinsically related to the polymer type [2]. In current literature, several types of polymers – polypropylene (PP), polycarbonate (PC) and poly(vinylidene fluoride) (PVDF) – were used to study several physical properties in VGCNF composites. PVDF is the main representative of a family of polymeric materials with interesting scientific and technological properties. This polymer is known for its outstanding electroactive properties with respect to other polymers, non-linear optical susceptibility and an unusually high dielectric constant, among polymers [5]. The electroactive properties of PVDF heavily depend on the phase content, microstructure and degree of crystallinity of the material, which in turn depend on the processing conditions. In particular the microstructure of α-PVDF plays an important role during the α- to β-phase transformation induced by stretching [6], [7]. The stretching process is the typical way for obtaining the most common electroactive polymorph, the β-phase, [8], [9] and deeply influences the properties of this phase.

In this work VGCNF/PVDF composites were prepared by a solution method for different concentrations of VGCNFs. The crystalline phase of the matrix was the non polar α-PVDF and the composites were uniaxially stretched in order to achieve the phase transformation of the polymer matrix to the polar β-phase. The PVDF α to β-phase transformation has been investigated. The influence of the VGCNFs on the degree of crystallinity of the polymer and melting temperature, quasistatic mechanical behaviour and electrical response of the composites was studied. In this work, the most relevant issues are how the presence of VGCNFs influences the β-phase content, degree of crystallinity and the electrical and mechanical macroscopic physical response.

Related to these issues, Suiac et al. [10] studied VGCNF/polypropylene (PP) composites. The degree of crystallinity of the PP matrix within the composites exhibited an increasing trend with VGCNF loading up to 3 wt.%, followed by a moderate decrease at 5 wt.% loading. It was shown that VGCNF loading in VGCNF/PP composites affects the properties of the composites both directly as conductive fillers and indirectly by influencing the crystalline structure of the polymer matrix. Wu et al. [11] studied VGCNF/polymer composites using three types of polymers with different degree of crystallisation, i.e., weakly-crystallized low density polyethylene (LDPE), strongly crystallized high density polyethylene (HDPE) and amorphous polystyrene (PS). They reported a distinct behaviour in the electrical conductivity as a function of loading concentration. The low crystalline composite (LPDE) demonstrates a typical percolation behaviour (S shape curve) and the high crystalline composite an exponential curve until the threshold near the 16%. The authors stated that the high percolation threshold for the HDPE/VGCNF composites is due to the VGCNF agglomeration in HDPE matrix, thereby reducing the aspect ratio of VGCNFs noticeably. Also the dielectric constant exhibits similar trends, but a deviation from the dielectric power law is observed: the expected decrease after the percolation threshold is not observed. The amorphous polymer composite shows a percolation behaviour and the same deviation for the dielectric constant and the conductivity curve: a small increase after the percolation threshold.

In related PVDF composites, Zhang et al. [12] studied the conductive network assembling in VGCNF/PVDF composites. Their results indicate that the conductive network of the composites was related to the interaction between PVDF molecules and VGCFs. According to a thermodynamic percolation model, a self-assembly velocity model for conductive network formation was proposed, and the results indicate that self-assembly velocity was a function of annealing time and temperature. Xu and Dang [13] analyzed four systems of conductive filler/PVDF composites. Their results demonstrate that the crystallinity is diminished and that the final value depends on the filler type. They also reported a non-uniform distribution of the fillers: the fillers aggregate in the amorphous region of the semicrystalline PVDF.

Another important topic in the present work is the composite electrical properties. In carbonaceous composites, the electrical response is usually understood in terms of the percolation theory framework [14]. The inclusion of high aspect ratio fillers like CNTs and VGCNFs into a polymeric matrix increases the electrical conductivity and the dielectric constant several orders of magnitude relative to the polymer matrix [2], [15]. The composite transition from an insulator state to the conductive one is observed at a critical filler concentration – the percolation threshold. This transition is explained by the formation of a continuous network inside the polymeric matrix as stated by the percolation theory [14]. The value for the percolation threshold depends on the dimensionality of the domain and the geometry of the filler. Several percolation thresholds have been reported even for the same type of polymer and fibre aspect ratio, as can been seen in a recent review on VGCNFs [2]. At the percolation threshold there are several physical properties that can diverge, for instance the conductivity and the dielectric constant. The behaviour of the conductivity and the dielectric constant at the composite critical concentration was earlier studied by Bergman and Imry in 1977 [16] for heterogeneous mixtures of a conducting phase and an insulating matrix. An important result in this work is the divergence at the percolation threshold. Bergman and Imry [16] also explained that the physical meaning of the effective dielectric constant divergence is related with the existence of conductive channels stretching across the entire length of the system, blocked by very thin barriers. Also according to Bergman and Imry [16] the channels are connected in parallel and contribute to the high capacitance value. The theoretical prediction was later completed in a following work by Stroud and Bergman [17], which using a scaling assumption analyzed the critical behaviour of the composite dielectric constant. The scaling assumption is valid for $|{\epsilon }_{\mathit{matrix}}/{\epsilon }_{\mathit{filler}}|\ll 1$ and $|p-p_c|\ll 1$, with p being the filler fraction, p_c the critical filler fraction, ε_matrix is the matrix dielectric constant and ε_filler is the filler dielectric constant. Bergman and Stroud [17], demonstrated for metallic inclusions in an insulating matrix that the dielectric constant has a peak at ω = 0 Hz, and that the height of the peak is proportional to ${\epsilon }_{\mathit{matrix}}|p-p_c{|}^{-s}$, diverging at p_c. The later yields a well known relation (Eq. (1)) that holds for p < p_c and p > p_c:

$${\epsilon }_{\mathit{eff}}\propto {\epsilon }_{\mathit{matrix}}|p-p_c{|}^{-s}$$

In the same article [17] Bergman also demonstrates, using the same scaling relations, that for p > p_c the composite conductivity is given by the following relation:

$${\sigma }_{\mathit{eff}}\propto {\sigma }_{\text{VGCNF}}(p-p_c{)}^t$$

On Eqs. (1), (2)t and s are called the conductivity, t, and superconductivity, s, critical exponents; these are believed to be universal depending only in the dimension of the system. In Eq. (2)σ_VGCNF is the VGCNF conductivity. In Eqs. (1), (2)σ_eff and ε_eff refers to the composite effective conductivity and dielectric constant. The values for the conductivity exponent (t) were determined by Kirkpatrick [18] using three different models. The value for 3D system was 1.5 ± 0.2. In more recent works the accepted value is ∼1.8. For the superconductivity exponent, using a bond percolation model in 3D systems, in conjugation with a transfer matrix algorithm, Herrmann and Derrida [19] found that the value is 0.75 ± 0.04. The current accepted values are in the range of 0.87. An important development was made by McLachlan et al. [20], [21], [22], [23], [24] in the context of the effective mean field approximation (EMA). They proposed the two exponent percolation phenomenological equation (TEPPE), Eq. (3). This equation relates the critical exponents s and t with the dependence in the critical concentration transversal to EMA models. In limiting cases this equation reduces to the effective mean field Bruggeman model [25] for p < p_c and to the percolation model when p ≈ p_c

$$(1-p)\frac{({\epsilon }_{\mathit{matrix}}^{1/s}-{\epsilon }_{\mathit{eff}}^{1/s})}{{\epsilon }_{\mathit{matrix}}^{1/s}+[(1-p_c)/p_c]{\epsilon }_{\mathit{eff}}^{1/s}}+p\frac{({\epsilon }_{\mathit{filler}}^{1/t}-{\epsilon }_{\mathit{eff}}^{1/t})}{{\epsilon }_{\mathit{filler}}^{1/t}+[(1-p_c)/p_c]{\epsilon }_{\mathit{eff}}^{1/t}}=0$$

For fibres with a capped cylinder shape, the theoretical framework developed by Celzard et al. [26] based on the Balberg model [27] provides the bounds for the percolation threshold. In general, the percolation threshold is defined in the following bounds:

$$1-e^{\frac{-1.4V}{〈V_e〉}}⩽p_c⩽1-e^{\frac{-2.8V}{〈V_e〉}}$$

Eq. (4) links the average excluded volume, $〈V_e〉$, the volume around an object in which the center of another similarly shaped object is not allowed to penetrate averaged over the orientation distribution and the critical concentration (p_c), where the value 1.4 corresponds to the lower limit – infinitely thin cylinders – and the value 2.8 to spheres. The values where obtained by simulation. The derivation of this equation and related discussion can be seen in [26]. The later equation imposes a bound in the percolation threshold for the formation of the percolation cluster.