Modeling the strength and thickness of the interphase in polymer nanocomposite reinforced with spherical nanoparticles by a coupling methodology

Percolation onset and conductivity of nanocomposites assuming an incomplete dispersion of graphene nanosheets in a polymer matrix

Herein, stacks of graphene nanosheets resulting from an incomplete dispersion of nanoparticles in polymer graphene nanocomposites are considered. The volume fraction, aspect ratio and conduction of stacks are expressed by the distance between nanosheets (s), thickness of an individual nanosheet (t), nanosheet diameter (D), thickness of the interphase zone (ti) and tunneling length (d). Moreover, the percolation onset, actual filler quantity and portion of networked nanosheets are stated by the stacks of nanosheets, interphase depth and tunneling length. Finally, an advanced model for the conductivity of a graphene-based system is presented using the mentioned terms. The influence of all properties of stacks, tunneling and interphase areas on the percolation onset, portion of percolated nanosheets and conductivity are examined. Furthermore, the tested values of conductivity are applied to confirm the predictability of the model. The larger quantity of thin sheets included in stacks produces a higher conductivity for samples. In addition, a thicker interphase and smaller tunnels can result in higher conductivity. The calculations of conductivity match the tested data at all filler amounts.

Predicting of tunneling resistivity between adjacent nanosheets in graphene-polymer systems

In this work, the tunneling resistivity between neighboring nanosheets in grapheme-polymer nanocomposites is expressed by a simple equation as a function of the characteristics of graphene and tunnels. This expression is obtained by connecting two advanced models for the conductivity of graphene-filled materials reflecting tunneling role and interphase area. The predictions of the applied models are linked to the tested data of several samples. The impressions of all factors on the tunneling resistivity are evaluated and interpreted using the suggested equation. The calculations of tunneling resistivity for the studied examples by the model and suggested equation demonstrate the same levels, which confirm the presented methodology. The results indicate that the tunneling resistivity decreases by super-conductive graphene, small tunneling width, numerous contacts among nanosheets and short tunneling length.

Effect of contact number among graphene nanosheets on the conductivities of tunnels and polymer composites

Simple equations are expressed for tunnel conductivity, tunnel resistance and conductivity of a graphene-filled composite by the number of contacts and interphase part. More specially, the active filler amount is suggested by interphase depth, which changes the contact number. The conductivity of nanocomposite is presented by filler content, filler dimensions, tunneling length and interphase depth. The innovative model is surveyed by the experimented conductivity of real examples. Too, the impacts of numerous issues on the tunnel resistance, tunnel conductivity and conductivity of nanocomposite are discussed to validate the novel equations. The estimates agree with the experimented data and the impacts of several terms on the tunnel resistance, tunnel conductivity and conductivity of system are sensible. Thin and big nanosheets positively affect the nanocomposite's conductivity, but thick nanosheets improve the tunnel conductivity. High conductivity is found at short tunnels, while the nanocomposite's conductivity directly depends on the tunneling length. The dissimilar effects of these features on the tunneling properties and conductivity are described.

Simulating of effective conductivity for grapheme-polymer nanocomposites

The efficient conductivity of graphene-polymer systems is expressed supposing graphene, tunneling and interphase components. The volume shares and inherent resistances of the mentioned components are used to define the efficient conductivity. Besides, the percolation start and the share of graphene and interphase pieces in the nets are formulated by simple equations. Also, the resistances of tunneling and interphase parts are correlated to graphene conductivity and their specifications. Suitable arrangements among experimented data and model's estimates as well as the proper trends between efficient conductivity and model's parameters validate the correctness of the novel model. The calculations disclose that the efficient conductivity improves by low percolation level, dense interphase, short tunnel, large tunneling pieces and poor polymer tunnel resistivity. Furthermore, only the tunneling resistance can govern the electron transportation between nanosheets and efficient conductivity, while the big amounts of graphene and interphase conductivity cannot play a role in the efficient conductivity.

Progressing of a power model for electrical conductivity of graphene-based composites

This work presents a power equation for the conductivity of graphene-based polymer composites by the tunneling length, interphase deepness and filler size. The impressions of these factors on the effective concentration and percolation beginning of graphene nano-sheets in nanocomposites are also expressed. The developed equations for percolation beginning and conductivity are examined by the experimented data of some examples, which can guesstimate the interphase depth, tunneling size and percolation exponent. Besides, the impacts of numerous factors on the percolation beginning and conductivity are designed. The developed equation for percolation beginning shows the formation of thick interphase and large tunnels in the reported samples. So, disregarding of tunneling and interphase spaces in polymer graphene nanocomposites overpredicts the percolation beginning. Additionally, the developed model presents the acceptable calculations for the conductivity of samples. Among the mentioned parameters, the concentration and graphene conductivity in addition to the interphase depth induce the strongest effects on the conductivity of composites.

Estimation of the tensile modulus of polymer carbon nanotube nanocomposites containing filler networks and interphase regions by development of the Kolarik model

The Kolarik model for the tensile modulus of co-continuous blends is developed for polymer/carbon nanotube (CNT) nanocomposites assuming continuous CNT networks and the reinforcing and percolating efficiencies of the interphase.

Dependence of Z Parameter for Tensile Strength of Multi-Layered Interphase in Polymer Nanocomposites to Material and Interphase Properties

In this work, the Z interphase parameter which determines the tensile strength of interphase layers in polymer nanocomposites is presented as a function of various material and interphase properties. In this regard, the simple Pukanszky model for tensile strength of polymer nanocomposites is applied and the dependency of Z to different characteristics of constituents and interphase are illustrated by contour plots. The interphase strength (σ _i) and B interfacial parameter in Pukanszky model show direct links with Z parameter. Also, it is found that the volume fractions of nanoparticles and interphase reveal dissimilar effects on Z. A high Z is obtained by a low nanoparticle volume fraction and high content of interphase, but the best values of Z are associated with the level of B parameter.

Expansion of Kolarik model for tensile strength of polymer particulate nanocomposites as a function of matrix, nanoparticles and interphase properties

Kolarik proposed a model for tensile strength of polymer particulate composites based on the cubic orthogonal skeleton or three perpendicular plates (3PP) system. In this paper, Kolarik model is expanded for tensile strength of polymer nanocomposites containing spherical nanoparticles assuming the interphase properties. This model expresses the strength as a function of interphase properties. This development is performed using some models such as Pukanszky and Nicolais-Narkis. The expanded model is applied to calculate the thickness and strength of interphase by the experimental results. Furthermore, the strength of polymer nanocomposites is evaluated at different levels of material and interphase properties. The experimental data show good agreement with the predictions of the developed model.

Development and modification of conventional Ouali model for tensile modulus of polymer/carbon nanotubes nanocomposites assuming the roles of dispersed and networked nanoparticles and surrounding interphases

In this paper, conventional Ouali model for tensile modulus of composites is developed for polymer/carbon nanotubes (CNT) nanocomposites (PCNT) assuming the influences of filler network and dispersed nanoparticles above percolation threshold as well as the interphases between polymer host and nanoparticles which reinforce the nanocomposite and facilitate the networking. The developed model is simplified, because the characteristics of dispersed nanoparticles and surrounding interphase cannot significantly change the modulus of PCNT. The suggested model is compared to the experimentally measured modulus of some samples, which can calculate the percolation threshold of interphase regions and the possessions of interphase and filler network. The suggested model correctly predicts the influences of all parameters on the modulus. Thinner and longer CNT in addition to thicker interphase enhance the volume fraction of interphase which shifts the connectivity of interphase regions to smaller nanoparticle fraction and improves the modulus of PCNT. A very low level of percolation threshold significantly develops the modulus, but its high ranges have not any role. Among the studied parameters, the thickness and modulus of interphase between polymer host and networked nanoparticles play the most important roles in the modulus of PCNT.