6756 J Mater sci(2008)43:6747-6757 Fig8(a)Cleavage of the (a) balone shell at various length scales revealing the discrete character of the"interphase when visualized on the nano- scale [36].(b)Schematic representation of the effect of sacrificial bonds on the cleavage strength of the discrete molecularly designed interphase shown in (a)[12, 13] sacrificial bond Extra toughness M……点…“ 200250 Pulling distance(nn radius of gyration of the polymer chains [49, 50] and by Park and Gao[48]. The bending rigidity of a rectangular internal strain due to molecular motion within a non- beam was calculated for various length scales [23]. For primitive lattice [51, 52]. Quantum confinement effects can polyethylene, the bending rigidity increased with decreas- also play a role inducing a strain field on the nano-scale ing beam dimensions and was double that of the classical without the presence of external loading, however, its Bernoulli-Euler bending rigidity at beam dimensions of importance is limited to the size range below 2 nm [53]. 5 nm. On the basis of the arguments put forward above, the In order to estimate the length scale at which the classical one may consider to carefully revise published data on the lasticity becomes non-valid, the MD on a polyethylene elastic properties of carbon nanotubes measured using chain in a cubic simulation cell was performed under classical elasticity. periodic boundary conditions at 50 K [23]. The corre- sponding length scales for the longitudinal and transverse directions were 1.85 and 3.81 nm, respectively. A recent Conclusions work by Nikolov et al. [53] estimated that rubbers above their Tg should have non-local length scale approximately In polymer matrix composites exhibiting heterogeneous 5 nm. The high non-locality in polymers most probably structure at multiple length scales, the interphase phe- stems from a cooperative behavior of large number of chain nomena are of pivotal importance for the control of their segments characteristic for entangled polymers. As a result, performance and reliability. In this paper, a review of the parts of the material system may undergo considerable non- current knowledge on the interphase phenomena at various affine deformation associated with occurence of high- length scales has been attempted comparing multiscale moment stresses. Consequently, for such systems, taking manmade composite structure with natural multiscale strain-gradient effects into account while investigating functionally hierarchical composite structure. On the nanoscale elastic phenomena may impart significant size- micro-scale, the interphase is considered a 3D continuum dependent corrections to the results obtained from classical possessing some average properties such as elastic modu continuum elasticity [23]. The magnitude of corrections that lus, shear strength and fracture toughness. Existing strain-gradient effects may impart to results obtained by continuum mechanics models provide satisfactory means classical continuum elasticity has recently been proposed to relate these properties to the stress transfer from matrix 2 Springerradius of gyration of the polymer chains [49, 50] and internal strain due to molecular motion within a non￾primitive lattice [51, 52]. Quantum confinement effects can also play a role inducing a strain field on the nano-scale without the presence of external loading, however, its importance is limited to the size range below 2 nm [53]. In order to estimate the length scale at which the classical elasticity becomes non-valid, the MD on a polyethylene chain in a cubic simulation cell was performed under periodic boundary conditions at 50 K [23]. The corre￾sponding length scales for the longitudinal and transverse directions were 1.85 and 3.81 nm, respectively. A recent work by Nikolov et al. [53] estimated that rubbers above their Tg should have non-local length scale approximately 5 nm. The high non-locality in polymers most probably stems from a cooperative behavior of large number of chain segments characteristic for entangled polymers. As a result, parts of the material system may undergo considerable non￾affine deformation associated with occurence of high￾moment stresses. Consequently, for such systems, taking strain-gradient effects into account while investigating nanoscale elastic phenomena may impart significant size￾dependent corrections to the results obtained from classical continuum elasticity [23]. The magnitude of corrections that strain-gradient effects may impart to results obtained by classical continuum elasticity has recently been proposed by Park and Gao [48]. The bending rigidity of a rectangular beam was calculated for various length scales [23]. For polyethylene, the bending rigidity increased with decreas￾ing beam dimensions and was double that of the classical Bernoulli–Euler bending rigidity at beam dimensions of 5 nm. On the basis of the arguments put forward above, the one may consider to carefully revise published data on the elastic properties of carbon nanotubes measured using classical elasticity. Conclusions In polymer matrix composites exhibiting heterogeneous structure at multiple length scales, the interphase phe￾nomena are of pivotal importance for the control of their performance and reliability. In this paper, a review of the current knowledge on the interphase phenomena at various length scales has been attempted comparing multiscale manmade composite structure with natural multiscale functionally hierarchical composite structure. On the micro-scale, the interphase is considered a 3D continuum possessing some average properties such as elastic modu￾lus, shear strength and fracture toughness. Existing continuum mechanics models provide satisfactory means to relate these properties to the stress transfer from matrix Fig. 8 (a) Cleavage of the abalone shell at various length scales revealing the discrete character of the ‘‘interphase’’ when visualized on the nano￾scale [36]. (b) Schematic representation of the effect of sacrificial bonds on the cleavage strength of the discrete molecularly designed interphase shown in (a) [12, 13] 6756 J Mater Sci (2008) 43:6747–6757 123