《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_review of interphase in nanoscale.pdf_大学文库

J Mater Sci(2008)43:6747-6757 DOI10.1007/10853-008-26920 STRETCHING THE ENDURANCE BOUNDARY OF COMPOSITE MATERIALS: PUSHING THE PERFORMANCE LIMIT OF COMPOSITE STRUCTURES Review of the role of the interphase in the control of composite performance on micro-and nano-length scales J.Jancar Received: 3 April 2008/ Accepted: 30 April 2008/ Published online: 16 August 2008 e Springer Science+Business Media, LLC 2008 Abstract In fiber reinforced composites(FRCs), exhib- re-define term interphase on the nano-scale. Thus, the iting heterogeneous structure at multiple length scales, the Rubinstein reptation model and a simple percolation model interphase phenomena at various length scales were shown were used to describe immobilization of chains near solid to be of pivotal importance for the control of the perfor- nano-particles and to explain the peculiarities in the vis- mance and reliability of such structures. Various models coleastic response of nano-scale"interphase. " It has also based on continuum mechanics were used to describe been shown that below 5 nm. Bernoulli-Euler mechanical response of laminates and large FRC parts, along with the proposed reptation dynamics approach, 3L effects of the macro- and meso-scale interphase on the elasticity becomes not valid and higher-order elasticity satisfactorily. At the micro-scale, the interphase is con- provide suitable means for bridging the gap in modeling sidered a 3D continuum with ascribed average properties. the transition between the mechanics of continuum matter Number of continuum mechanics models was derived over at the micro-scale and mechanics of discrete matter at the the last 50 years to describe the stress transfer between nano-scale. matrix and individual fiber with realtively good success In these models, the interphase was characterized by some average shear strength, ta, and elastic modulus, En. On the other hand, models for tranforming the properties of the Introduction micro-scale interphase around individual fiber into the mechanical response of macroscopic multifiber composite Continuum mechanics can be used to describe effects of have not been generally successfull. The anisotropy of micro-scale interphase on the stress transfer in single fiber these composite structures are the main reasons causing the composites considering the system a three phase material failure of these models. The strong thickness dependence in which the individual phases, i.e., solid inclusion, matrix of the elastic modulus of the micro-scale interphase sug- and interphase, can be characterized by some average gested the presence of its underlying sub-structure. On the properties [1-5]. Unlike at the micro-scale, extreme cau- nano-scale, the discrete molecular structure of the polymer tion has to be exercised when selecting suitable modelin has to be considered. The term interphase, originally scheme at the nano-scale when the discrete molecular roduced for continuum matter, has to be re-defined to structure of the polymer becomes obvious. One of the main include the discrete nature of the matter at this length scale. difficulties when considering nano-scale in composites is to The segmental immobilization resulting in retarded repta- determine the size of the representative volume in which tion of chains caused by interactions with solid surface the discrete nature of the composite structure has to be seems to be the primary phenomenon which can be used to taken into account [6]. Very little has been written so far on the laws governing the transition between the nano-and J. Jancar(凶 micro-length scales, especially, on the reliability of clas Institute of Materials Chemistry, Brno University of Technology, sical continuum mechanics when scaled outside their Brno, Czech Republic validity range, i.e., down to the nano-scale [7]. Thus, it e-mail: jancar@fch. vutbr cz seems desirable to perform a critical review of the current 2 Springer

STRETCHING THE ENDURANCE BOUNDARY OF COMPOSITE MATERIALS: PUSHING THE PERFORMANCE LIMIT OF COMPOSITE STRUCTURES Review of the role of the interphase in the control of composite performance on micro- and nano-length scales J. Jancar Received: 3 April 2008 / Accepted: 30 April 2008 / Published online: 16 August 2008 Springer Science+Business Media, LLC 2008 Abstract In fiber reinforced composites (FRCs), exhibiting heterogeneous structure at multiple length scales, the interphase phenomena at various length scales were shown to be of pivotal importance for the control of the performance and reliability of such structures. Various models based on continuum mechanics were used to describe effects of the macro- and meso-scale interphase on the mechanical response of laminates and large FRC parts, satisfactorilly. At the micro-scale, the interphase is considered a 3D continuum with ascribed average properties. Number of continuum mechanics models was derived over the last 50 years to describe the stress transfer between matrix and individual fiber with realtively good success. In these models, the interphase was characterized by some average shear strength, sa, and elastic modulus, Ea. On the other hand, models for tranforming the properties of the micro-scale interphase around individual fiber into the mechanical response of macroscopic multifiber composite have not been generally successfull. The anisotropy of these composite structures are the main reasons causing the failure of these models. The strong thickness dependence of the elastic modulus of the micro-scale interphase suggested the presence of its underlying sub-structure. On the nano-scale, the discrete molecular structure of the polymer has to be considered. The term interphase, originally introduced for continuum matter, has to be re-defined to include the discrete nature of the matter at this length scale. The segmental immobilization resulting in retarded reptation of chains caused by interactions with solid surface seems to be the primary phenomenon which can be used to re-define term interphase on the nano-scale. Thus, the Rubinstein reptation model and a simple percolation model were used to describe immobilization of chains near solid nano-particles and to explain the peculiarities in the viscoleastic response of nano-scale ‘‘interphase.’’ It has also been shown that below 5 nm, Bernoulli–Euler continuum elasticity becomes not valid and higher-order elasticity along with the proposed reptation dynamics approach can provide suitable means for bridging the gap in modeling the transition between the mechanics of continuum matter at the micro-scale and mechanics of discrete matter at the nano-scale. Introduction Continuum mechanics can be used to describe effects of micro-scale interphase on the stress transfer in single fiber composites considering the system a three phase material in which the individual phases, i.e., solid inclusion, matrix and interphase, can be characterized by some average properties [1–5]. Unlike at the micro-scale, extreme caution has to be exercised when selecting suitable modeling scheme at the nano-scale when the discrete molecular structure of the polymer becomes obvious. One of the main difficulties when considering nano-scale in composites is to determine the size of the representative volume in which the discrete nature of the composite structure has to be taken into account [6]. Very little has been written so far on the laws governing the transition between the nano- and micro-length scales, especially, on the reliability of classical continuum mechanics when scaled outside their validity range, i.e., down to the nano-scale [7]. Thus, it seems desirable to perform a critical review of the current J. Jancar (&) Institute of Materials Chemistry, Brno University of Technology, Brno, Czech Republic e-mail: jancar@fch.vutbr.cz 123 J Mater Sci (2008) 43:6747–6757 DOI 10.1007/s10853-008-2692-0

J Mater sci(2008)43:6747-6757 knowledge on the structure and properties of the micro- pivotal importance for the control of the reliability and and nano-scale interphases in polymer composites and the performance of multiscale FRC structures. There seems to methodologies for their modeling in order to provide be general agreement on using continuum mechanics means for bridging the gap between continuum and dis- models to account for interphase phenomena from macro- crete models useful for reliable design of future multiscale to micro-scale and the design schemes based on continuum hierarchical composite structures mechanics, variational principles or Finite Element Anal The design of multi-length-scale composite structures, ysis(FEA) have been validated [2]. The understanding of such as the fuselage of the Boeing 787(Fig. 1), represents the translation of the properties of the micro-scale inter the state-of-the-art engineering application of fiber rein- phases into the response of macroscopic FRC parts is far forced composites(FRCs). These large structures are less unambigious [9]. The greatest success have been designed from top to bottom using continuum mechanics achieved in understanding and modeling of the role of the methodologies and the transitions between the individual micro-scale interphase in the stress transfer from the matrix treated simply with down the to a single fiber structural features of the greater length scale. Such multi- attempts to transfer properties of the micro-scale interphase scale continuum mechanics modeling approach was in the performance of a multi-fiber FRC structures have demonstrated to provide reasonable means for transforming generally failed the mechanical response of polymer composites accross Over the last 20 years, substantial advances were made several length and time scales from macro- down to micro- in understanding the deformation behavior of hard tissues scale(Fig. 2)[8]. such as bones which can also be considered multiscale Since the FRCs exhibit heterogeneous structure at functionally hierarchical composite structures(Fig 3)[71 multiple length scales, the interphase phenomena are of Unlike the FRC fuselage, bone is designed bottom-up MACRO MESO mm MICRO NANO 10n micro-and nano-length scales considered in this review Fig. 1 Part of the fuselage of Boeing 787 Dreamliner can serve as an top-bottom methodology within the framework of continuum example of a large manmade multiscale composite structure. This mechanics. No functional hierarchy exists between the various length polymer composite structure has been designed using the engineering scales 2 Springer

knowledge on the structure and properties of the microand nano-scale interphases in polymer composites and the methodologies for their modeling in order to provide means for bridging the gap between continuum and discrete models useful for reliable design of future multiscale hierarchical composite structures. The design of multi-length-scale composite structures, such as the fuselage of the Boeing 787 (Fig. 1), represents the state-of-the-art engineering application of fiber reinforced composites (FRCs). These large structures are designed from top to bottom using continuum mechanics methodologies and the transitions between the individual length scales are treated simply with scalling down the structural features of the greater length scale. Such multiscale continuum mechanics modeling approach was demonstrated to provide reasonable means for transforming the mechanical response of polymer composites accross several length and time scales from macro- down to microscale (Fig. 2) [8]. Since the FRCs exhibit heterogeneous structure at multiple length scales, the interphase phenomena are of pivotal importance for the control of the reliability and performance of multiscale FRC structures. There seems to be general agreement on using continuum mechanics models to account for interphase phenomena from macroto micro-scale and the design schemes based on continuum mechanics, variational principles or Finite Element Analysis (FEA) have been validated [2]. The understanding of the translation of the properties of the micro-scale interphases into the response of macroscopic FRC parts is far less unambigious [9]. The greatest success have been achieved in understanding and modeling of the role of the micro-scale interphase in the stress transfer from the matrix to a single fiber in model composites [2–4, 8]. However, attempts to transfer properties of the micro-scale interphase in the performance of a multi-fiber FRC structures have generally failed. Over the last 20 years, substantial advances were made in understanding the deformation behavior of hard tissues such as bones which can also be considered multiscale functionally hierarchical composite structures (Fig. 3) [7]. Unlike the FRC fuselage, bone is designed bottom-up Fig. 1 Part of the fuselage of Boeing 787 Dreamliner can serve as an example of a large manmade multiscale composite structure. This polymer composite structure has been designed using the engineering top–bottom methodology within the framework of continuum mechanics. No functional hierarchy exists between the various length scales 6748 J Mater Sci (2008) 43:6747–6757 123

J Mater Sci(2008)43:6747-6757 [14]. Even though the molecular structure of the interphase temperatures of engineering thermoplastics ranging from has been anticipated in many papers, with some exceptions 230 to 350C can exceed the thermal stability of the [15-17]. the main effort has been devoted to the relation- commonly utilized organosilanes ship between the type, thickness and deposition conditions Thickness dependence of the elastic modulus of thin of the fiber coating and the average shear strength of the polycarbonate (PC) layers deposited on a flat E-glass interphase, ta, measured in a simple test employing model substrate was measured over the thickness interval ranging single fiber composite [18]. from 10 to 30 nm [ 9, 21, 22). In all cases investigated Mechanical properties and environmental stability of elastic moduli of the deposited layers, Ei, decreased composites are strongly dependent upon the stability of the constant bulk value for layers thicker than 5 X 10'mr9 both fiber reinforced and particulate filled thermoplastic monotonically with increasing layer thickness reaching interfacial region between the matrix and fibers, especially(Fig. 4). Thermally annealed PC and SiCl4 grafted oligo- when exposed to moist environment. This is of particular PC interphases, exhibited higher elastic moduli than the as importance in glass fiber reinforced thermoplastic compos- received solution deposited PC interphase. No effect of ites since the glass fibers are highly hygroscopic and the thermal annealing on elastic modulus of strongly bonded bond between the fibers and the thermoplastic matrix is oligo-PC interphase was observed. It has been shown that usually weak. Hence, the tailoring of well-bonded, durable the shear strength of the interface, Ta, measured in a sin- interphases between the thermoplastic matrix and glass glefiber fragmentation test exhibited strong dependence on reinforcement has become a critical concern. The use of the interphase Ei. coupling agents, chemically reactive with both matrix and Similarly to the PC interphases, elastic moduli of the reinforcement, and/or chemical modification of the surfaces deposited silane layers decreased monotonically with of one or both constituents have been the most successful increasing layer thickness reaching a bulk value for layers means of providing reasonably well controlled bond thicker than 10 nm [21, 22]. Reactive chlorine containing between matrix and the encapsulated reinforcement [ 19] silane formed always stiffer layers compared to its alkoxy From the published data, it seems clear that a mono- analogues most probably due to stronger interaction molecular interphase layer with engineered molecular between the chlorine and glass surface and, most probably structure specific for the desired combination of resin and due to less defective network structure (Fig. 5). This reinforcement should result in the most favorable mix of hypothesis was further supported by the observed strong properties in thermoplastic matrix composites. Reactive effect of deposition technique, controlling the layer su- end-capped polymers capable of chemically reacting with permolecular structure, on the layer elastic modulus the fiber surface or various methods of grafting matrix Solution deposition technique yielded always layers with molecules onto reinforcement surface are the most prom- lower elastic modulus compared to the layers formed by rf- ising candidates for further investigations [17, 20]. plasma or rf-plasma enhanced CVd deposition of the same Thickness of the interphase can be controlled via modifi- substance. A qualitative explanation of the observe cation of the molecular weight and chain stiffness of the behavior was provided assuming formation of strongly constituent molecules, its mechanical properties can be immobilized layer of constant thickness, t;, and elastic varied by selecting the backbone chain constitution and modulus, Ei, near the bonded interface. Strength of the configuration, and its surface free energy can also be interfacial bond and network density of the polysiloxane controlled by the chain constitution and by the polarity of interphase were proposed to be the factors determining the end-groups. Elastic properties of these layers are con- and Ei for the given external conditions. Experimental data trolled by the attraction forces at the interface as well as the showed that the contribution of this strongly immobilized conformation entropy of the chains forming the layer. layer started to play an important role for interphase Organofunctional silanes are so far the most widely used thickness below 10 nm. This"inner"layer has been coupling agents for improvement of the interfacial adhe- covered with weaker "outer"layer with more defective sion in glass reinforced materials [19]. Upon application of network structure. The thickness of the"outer"layer was a silane from either dilute solution or the vapor phase, a dependent on the concentration of the silane solution it was highly crosslinked multilayer siloxane "interphase"is deposited from. The difference in E; between the outer presumably formed with thickness ranging from 1.5 to inner interphase layer was increasing with strengthening 500 nm. Unlike in thermosetting matrices with extensive the layer-surface interaction interpenetration between organosilane layer and the matrix In order to enhance the performance and reliability of monomer,long chain molecules do not interpenetrate the the FRC structures at the macro-scale, the results obtained organosilane layers significantly. On the other hand, for the micro-scale interphase can be used to control the immobilization phenomena are of a greater importance in stress transfer between the matrix and the reinforcement hermoplastic matrix composites. Moreover, processing Stiff interphases provide very efficient stress transfer, less 2 Springer

[14]. Even though the molecular structure of the interphase has been anticipated in many papers, with some exceptions [15–17], the main effort has been devoted to the relationship between the type, thickness and deposition conditions of the fiber coating and the average shear strength of the interphase, sa, measured in a simple test employing model single fiber composite [18]. Mechanical properties and environmental stability of both fiber reinforced and particulate filled thermoplastic composites are strongly dependent upon the stability of the interfacial region between the matrix and fibers, especially when exposed to moist environment. This is of particular importance in glass fiber reinforced thermoplastic composites since the glass fibers are highly hygroscopic and the bond between the fibers and the thermoplastic matrix is usually weak. Hence, the tailoring of well-bonded, durable interphases between the thermoplastic matrix and glass reinforcement has become a critical concern. The use of coupling agents, chemically reactive with both matrix and reinforcement, and/or chemical modification of the surfaces of one or both constituents have been the most successful means of providing reasonably well controlled bond between matrix and the encapsulated reinforcement [19]. From the published data, it seems clear that a monomolecular interphase layer with engineered molecular structure specific for the desired combination of resin and reinforcement should result in the most favorable mix of properties in thermoplastic matrix composites. Reactive end-capped polymers capable of chemically reacting with the fiber surface or various methods of grafting matrix molecules onto reinforcement surface are the most promising candidates for further investigations [17, 20]. Thickness of the interphase can be controlled via modifi- cation of the molecular weight and chain stiffness of the constituent molecules, its mechanical properties can be varied by selecting the backbone chain constitution and configuration, and its surface free energy can also be controlled by the chain constitution and by the polarity of the end-groups. Elastic properties of these layers are controlled by the attraction forces at the interface as well as the conformation entropy of the chains forming the layer. Organofunctional silanes are so far the most widely used coupling agents for improvement of the interfacial adhesion in glass reinforced materials [19]. Upon application of a silane from either dilute solution or the vapor phase, a highly crosslinked multilayer siloxane ‘‘interphase’’ is presumably formed with thickness ranging from 1.5 to 500 nm. Unlike in thermosetting matrices with extensive interpenetration between organosilane layer and the matrix monomer, long chain molecules do not interpenetrate the organosilane layers significantly. On the other hand, immobilization phenomena are of a greater importance in thermoplastic matrix composites. Moreover, processing temperatures of engineering thermoplastics ranging from 230 to 350 C can exceed the thermal stability of the commonly utilized organosilanes. Thickness dependence of the elastic modulus of thin polycarbonate (PC) layers deposited on a flat E-glass substrate was measured over the thickness interval ranging from 106 to 30 nm [9, 21, 22]. In all cases investigated, elastic moduli of the deposited layers, Ei, decreased monotonically with increasing layer thickness reaching a constant bulk value for layers thicker than 5 9 105 mm (Fig. 4). Thermally annealed PC and SiCl4 grafted oligoPC interphases, exhibited higher elastic moduli than the as received solution deposited PC interphase. No effect of thermal annealing on elastic modulus of strongly bonded oligo-PC interphase was observed. It has been shown that the shear strength of the interface, sa, measured in a singlefiber fragmentation test exhibited strong dependence on the interphase Ei. Similarly to the PC interphases, elastic moduli of the deposited silane layers decreased monotonically with increasing layer thickness reaching a bulk value for layers thicker than 105 nm [21, 22]. Reactive chlorine containing silane formed always stiffer layers compared to its alkoxyanalogues most probably due to stronger interaction between the chlorine and glass surface and, most probably, due to less defective network structure (Fig. 5). This hypothesis was further supported by the observed strong effect of deposition technique, controlling the layer supermolecular structure, on the layer elastic modulus. Solution deposition technique yielded always layers with lower elastic modulus compared to the layers formed by rfplasma or rf-plasma enhanced CVD deposition of the same substance. A qualitative explanation of the observed behavior was provided assuming formation of strongly immobilized layer of constant thickness, ti, and elastic modulus, Ei, near the bonded interface. Strength of the interfacial bond and network density of the polysiloxane interphase were proposed to be the factors determining ti and Ei for the given external conditions. Experimental data showed that the contribution of this strongly immobilized layer started to play an important role for interphase thickness below 103 nm. This ‘‘inner’’ layer has been covered with weaker ‘‘outer’’ layer with more defective network structure. The thickness of the ‘‘outer’’ layer was dependent on the concentration of the silane solution it was deposited from. The difference in Ei between the outer and inner interphase layer was increasing with strengthening the layer-surface interaction. In order to enhance the performance and reliability of the FRC structures at the macro-scale, the results obtained for the micro-scale interphase can be used to control the stress transfer between the matrix and the reinforcement. Stiff interphases provide very efficient stress transfer, less J Mater Sci (2008) 43:6747–6757 6751 123

J Mater Sci(2008)43:6747-6757 753 elastic response of systems with coordinated movement of magnitude greater specific surface area of the true nano- large number of atoms, such as observed in polymer fillers, almost all the polymer chains are in contact with the opposites [23]- The role of the nano-scale"interphase"to control the addition, continuum mechanics has only limited validity at posites(vr 0.85). viscoelastic response of the nano-composite matrix e. rformance and reliability of the FrC parts has to be this length scale and the discrete molecular structure pre- considered from two perspectives: (i)low vr nano-com- vails resulting in strong effect of non-local character of The (i) represents the direction to preparing new nano- The interphases in high vr nano-composites were studied structured advanced matrices while the (ii) leads to using the abalone shells [36]. These shells represent a designing new nano-structured advanced reinforcements. laminated sheet reinforced composite with over 95 vol % o of With few exceptions, most of the published literature on the aligned 500 nm thin aragonite sheets embedded in a protein synthetic nanocomposites deals with the low vr nanocom- matrix in apparently mesh-like fibrillar form(Fig. 5). In the posites [24-31], while, on the other hand, most of the work of Hansma and co-workers [12, 13], the model literature published on high vr nano-composites is related to sacrificial bonds has been proposed to explain the observed the mechanics of bio-composites such as bones, teeth and high-fracture resistance of nacreous composites. It has been shells [10-13 shown by Zidek and Jancar [37 ], that the hypothesis of the Most of the experimental evidence related to the inter- sacrificial bonds can also be used to simulate deformation phase in the low vr nano-composites were obtained at response of lightly cross-linked long flexible chain network temperatures below the polymer Tg using meso-scale test polymer fibril. In order to apply the model [37] to the specimens. Assuming the chain immobilization to be the behavior of an ensamble of chains in the vicinity of rigid primary reinforcing mechanism on the nano-scale, spatial weakly attractive nanometer sized inclusion, the immoil- distribution of the conformation entropy within the poly- ization phenomenon has to be investigated as the source of mer phase is of primary importance. Hence, experimental the drastic change in the viscoelastic behavior of polymers data for nano-composites above the matrix Tg has to be with addition of small amount of nano-scale inclusion considered. Sternstein at al [32] published interpretation of the viscoelastic response of rubbery nanocomposite above the matrix Tg, i.e., the Payne effect. Kalfus and Jancar [33, Chain immobilization on the nanoscale 64] analyzed the viscoelastic response of polyvinylacetate filled with nano-sized hydroxyapatite over the temperature Reducing the size of rigid inclusions from micro-to nano- range from -40 to +120C and observed strain softening scale is accompanied by 2-3 orders of magnitude increase in similar to the Payne effect [35]. The modulus recovery the internal contact area between the chains and the inclu- experiments allowed to determine the terminal relaxation sions. Moreover, above 2 vol % o nano-particle content, the time of reptation motion of bulk and surface immobilized average interparticle distance is reduced below 2 radii of chains, supporting the hypothesis that there is no"inter- gyration, Rg, of the chains. Hence, almost all the chains are hase"per se when nano-scale is considered. In order to in contact with the solid surface, possess reduced segmenta bridge the gap between the continuum interphase on the mobility at temperatures T2 Tg Below Tg, main chain micro-scale and the discrete molecular structure of the segmental mobility is frozen and only secondary low tem- matrix consisting of freely reptating chains in the bulk and perature side chain mobility can be affected. In addition, the retarded reptating chains in contact with the inclusions, conformation statistics of chains near solid surface can be higher-order elasticity combined with a suitable molecular altered from Gaussian random coil to Langevin coil above dynamics model could be utilized Tg and this phenomenon can be transformed into the was demonstrated, that the large specific surface area behavior of immobilized chains also upon solidification of the nanosized filler is capable of immobilizing large below Tg entanglements causing the steep increase of E In order to characterize the reduction in chain mobility addition of nanoparticles. This observation in an entangled melt quantitatively, one can use the char- seemed to confirm the purely entropic character of the acteristic reptation relaxation time, Trep, introduced by reinforcement mechanism on the nanoscale. All the data de Gennes [38. The trep is given for an entangled chain as: published support the dominant role of the chain immobi- L2 NL2 lization as the main reinforcing mechanism. light of the seems that the term "interphase"defined as a continuum where L is the length of the reptation path, N the number of phase of limited extent looses its physical meaning when monomer units in a chain, De and Do are diffusion considering true nano-composites. Due to two orders of constants of a chain and a monomer, respectively. The 2 Springer

elastic response of systems with coordinated movement of large number of atoms, such as observed in polymer composites [23]. The role of the nano-scale ‘‘interphase’’ to control the performance and reliability of the FRC parts has to be considered from two perspectives: (i) low vf nano-composites (vf\0.05) and high vf nano-composites (vf[0.85). The (i) represents the direction to preparing new nanostructured advanced matrices while the (ii) leads to designing new nano-structured advanced reinforcements. With few exceptions, most of the published literature on the synthetic nanocomposites deals with the low vf nanocomposites [24–31], while, on the other hand, most of the literature published on high vf nano-composites is related to the mechanics of bio-composites such as bones, teeth and shells [10–13]. Most of the experimental evidence related to the interphase in the low vf nano-composites were obtained at temperatures below the polymer Tg using meso-scale test specimens. Assuming the chain immobilization to be the primary reinforcing mechanism on the nano-scale, spatial distribution of the conformation entropy within the polymer phase is of primary importance. Hence, experimental data for nano-composites above the matrix Tg has to be considered. Sternstein at al [32] published interpretation of the viscoelastic response of rubbery nanocomposite above the matrix Tg, i.e., the Payne effect. Kalfus and Jancar [33, 34] analyzed the viscoelastic response of polyvinylacetate filled with nano-sized hydroxyapatite over the temperature range from -40 to ?120 C and observed strain softening similar to the Payne effect [35]. The modulus recovery experiments allowed to determine the terminal relaxation time of reptation motion of bulk and surface immobilized chains, supporting the hypothesis that there is no ‘‘interphase’’ per se when nano-scale is considered. In order to bridge the gap between the continuum interphase on the micro-scale and the discrete molecular structure of the matrix consisting of freely reptating chains in the bulk and retarded reptating chains in contact with the inclusions, higher-order elasticity combined with a suitable molecular dynamics model could be utilized. It was demonstrated, that the large specific surface area of the nanosized filler is capable of immobilizing large amount of entanglements causing the steep increase of E0 with small addition of nanoparticles. This observation seemed to confirm the purely entropic character of the reinforcement mechanism on the nanoscale. All the data published support the dominant role of the chain immobilization as the main reinforcing mechanism. In the light of the existing experimental evidence, it seems that the term ‘‘interphase’’ defined as a continuum phase of limited extent looses its physical meaning when considering true nano-composites. Due to two orders of magnitude greater specific surface area of the true nano- fillers, almost all the polymer chains are in contact with the surface at very low filler loadings above 2 vol.%. In addition, continuum mechanics has only limited validity at this length scale and the discrete molecular structure prevails resulting in strong effect of non-local character of viscoelastic response of the nano-composite matrix. The interphases in high vf nano-composites were studied using the abalone shells [36]. These shells represent a laminated sheet reinforced composite with over 95 vol.% of aligned 500 nm thin aragonite sheets embedded in a protein matrix in apparently mesh-like fibrillar form (Fig. 5). In the work of Hansma and co-workers [12, 13], the model of sacrificial bonds has been proposed to explain the observed high-fracture resistance of nacreous composites. It has been shown by Zidek and Jancar [37], that the hypothesis of the sacrificial bonds can also be used to simulate deformation response of lightly cross-linked long flexible chain network polymer fibril. In order to apply the model [37] to the behavior of an ensamble of chains in the vicinity of rigid weakly attractive nanometer sized inclusion, the immoilization phenomenon has to be investigated as the source of the drastic change in the viscoelastic behavior of polymers with addition of small amount of nano-scale inclusions. Chain immobilization on the nanoscale Reducing the size of rigid inclusions from micro- to nanoscale is accompanied by 2–3 orders of magnitude increase in the internal contact area between the chains and the inclusions. Moreover, above 2 vol.% nano-particle content, the average interparticle distance is reduced below 2 radii of gyration, Rg, of the chains. Hence, almost all the chains are in contact with the solid surface, possess reduced segmental mobility at temperatures T C Tg. Below Tg, main chain segmental mobility is frozen and only secondary low temperature side chain mobility can be affected. In addition, the conformation statistics of chains near solid surface can be altered from Gaussian random coil to Langevin coil above Tg and this phenomenon can be transformed into the behavior of immobilized chains also upon solidification below Tg. In order to characterize the reduction in chain mobility in an entangled melt quantitatively, one can use the characteristic reptation relaxation time, srep, introduced by deGennes [38]. The srep is given for an entangled chain as: srep ffi L2 Dc ffi NL2 D0 ; ð1Þ where L is the length of the reptation path, N the number of monomer units in a chain, Dc and D0 are diffusion constants of a chain and a monomer, respectively. The J Mater Sci (2008) 43:6747–6757 6753 123

6754 J Mater sci(2008)43:6747-6757 terminal relaxation time of a chain in a neat polymer melt substantially depending on the surface-polymer interaction can be expressed in a number of ways. Lin [39] has energy, efp, under given conditions. Assuming the chain expressed the trep, taking chain contour length fluctuation friction coefficient, sc, in the form [40, 41] into account. in the form (3 b-soN/M 2kT(M (2) where Sa is the friction coefficient of an adsorbed monomer unit and the number monomer units in trains is N.= N2 for the weakly interacting surface, the terminal relaxation where So is the monomer friction coefficient, b the length of time is in the form the statistical segment, kb the Boltzmann constant, T the absolute temperature, Ne is the number of monomer units -ads L2 b2N5/2 reP 2D per one entanglement strand. In the case of a chain interacting with a filler surface and Kalfus and Jancar [33 extended the use above entangled with neighboring chains, the question of primary Rubinstein model [40, 41] to describe the reptation time of importance is how to establish a connection between the a linear chain weakly interacting with nano-filler surface static conformation structure and the chain dynamics. In Friction coefficient, Sa, is very difficult to measure and it spite of certain intra-molecular order, the chain in a melt is known just for the system silica-polystyrene [42]at can be considered a random Gaussian coil. If such a chain 153C. Estimation of the Sa was based on the theoretical approaches a solid surface, its conformation transfers to the analysis given by Subbotin et al. [43]. Thus, one can train-loop-tail structure and the chain conformational establish a relation for the reptation time of a surface entropy, as well as, the chain internal energy can alter very adsorbed chain as follows Fig6(a) Schematic drawing of the nano-scale"interphase and the models used to translate behavior of discrete matter consisting of molecules with segmental mobility reduced due to the presence of nano-scale Reptation solid inclusions. Crystalline 10m can be modeled as a continuum while amorphous inclusions with the extent of non-locality Elasticity has to b considered discrete as well.(b) Molecular relaxation processes on the background of the time, temperature and elementary ingle chain (b) r。≠nc(M.) M(Rouse 10-10mm3 LOGEI 2 Springer

terminal relaxation time of a chain in a neat polymer melt can be expressed in a number of ways. Lin [39] has expressed the srep, taking chain contour length fluctuation into account, in the form: srep ¼ L2 0 p2Dc ffi b2f0N2 p2kbT M Me 1 Me M 1=2 " #; ð2Þ where f0 is the monomer friction coefficient, b the length of the statistical segment, kb the Boltzmann constant, T the absolute temperature, Ne is the number of monomer units per one entanglement strand. In the case of a chain interacting with a filler surface and entangled with neighboring chains, the question of primary importance is how to establish a connection between the static conformation structure and the chain dynamics. In spite of certain intra-molecular order, the chain in a melt can be considered a random Gaussian coil. If such a chain approaches a solid surface, its conformation transfers to the train-loop-tail structure and the chain conformational entropy, as well as, the chain internal energy can alter very substantially depending on the surface-polymer interaction energy, efp, under given conditions. Assuming the chain friction coefficient, fc, in the form [40, 41]: fc ¼ f0N þ faN1=2 ; ð3Þ where fa is the friction coefficient of an adsorbed monomer unit and the number monomer units in trains is Na = N1/2 for the weakly interacting surface, the terminal relaxation time is in the form: sads rep ¼ L2 2Dc ¼ b2N5=2 2kbTNe f0N1=2 þ fa h i ð4Þ Kalfus and Jancar [33] extended the use the above Rubinstein model [40, 41] to describe the reptation time of a linear chain weakly interacting with nano-filler surface. Friction coefficient, fa, is very difficult to measure and it is known just for the system silica-polystyrene [42] at 153 C. Estimation of the fa was based on the theoretical analysis given by Subbotin et al. [43]. Thus, one can establish a relation for the reptation time of a surface adsorbed chain as follows: Fig. 6 (a) Schematic drawing of the nano-scale ‘‘interphase’’ and the models used to translate behavior of discrete matter consisting of molecules with segmental mobility reduced due to the presence of nano-scale solid inclusions. Crystalline inclusions surrounded by a number of long chain molecules can be modeled as a continuum while amorphous inclusions with the extent of non-locality similar to polymers has to be considered discrete as well. (b) Molecular relaxation processes on the background of the time, temperature and elementary volume scale [6] 6754 J Mater Sci (2008) 43:6747–6757 123

J Mater Sci(2008)43:6747-6757 6755 b2N2 relaxation( Fig. 6)(46]. In the case of the non-local normal khTN ISo(N-Na)+ saNa] mode of relaxation, its characteristic volume is the upper In the case that Na=N, the reptation time takes the size. Below this upper limiting characteristic volume V aro N2. where r is the chain end-to-end distance b2N5/2 and n is the number of monomer units in the chain. The =2k.[wN2+5 (6) characteristic time, te, for each particular relaxation pro- cess varies from 10 s for bond vibrations above Tsto To describe the change in reptation dynamics of the chains the infinitely long times below Tg. Thus, the macroscopic as a function of nanoparticle volume fraction, percolation viscoelastic response of a polymer is a manifestation of a model was used. At the percolation threshold, physical range of molecular relaxations localized in some charac network formed by interconnection of immobilized chains teristic volume and the rate of the relaxation mode on individual nanoparticles penetrates the entire sample indirectly proportional to its locality (Figs. 7 and 8) volume. In this case, only physical"cross-links" are The physical reasons for the expected breakdown of considered and the terminal relaxation time reaches the ontinuum elasticity on the nano-scale include increasing value characteristic for the life time of the physical filler- importance of surface energy due to appreciable surface to polymer bond. Thus, the relaxation time near the percolation volume ratio [47], the discrete molecular nature of the hreshold is expressed in the form [44] polymer matrix resulting in non-local behavior in contrary to local character of classical elasticity [48], the presence of nano-scale particles with the length scale similar to the here v* is critical effective filler volume fraction (veff=0.04 for PVAc-HAP at 90C)and b is the perco- lation exponent(b= 4 for the same system). The veff is a sum of the filler volume fraction and the volume fraction of immobilized Snt=42m2/g the percolation, random clustering of effective hard spheres 8 o.249 immobilized chains and was shown to equal 0.04 for a PVAc-HAP nanocomposites at 90C. In order to simpli E was considered only in the way similar to that originally outlined by Jancar et al. [45] for micro-scale composites Percolation threshold Percolation threshold at approximately 2 m of the filler- were immobilized at the internal contact area of 42 mper B LER SuP G polymer contact area per l g of the composite was found in AREA PER 1g OF NANOCOMPOSITE(m) PVAC-HA ( Fig. 6). all the chains 1 g of the Characteristic length scale for transition between continuum and discrete elasticity in polymer composites layer pproximately R, The classical continuum mechanics is designed to be size- independent. For nano-composites, however, size-depen surface dent elastic properties have been observed which cannot be readilly explained using continuum mechanics and, thus, prevent simple scalling down the existing continuum elasticity models [23]. Polymers are unique systems with macroscopic viscoelastic response driven by the relaxation processes on the molecular level [46]. These relaxation processes represent particular molecular motions occurring in some characteristic volume, Ve. The V depends on the type of the relaxation process and temperature. The char Fig. 7 Simple approach combining the reptation dynamics and percolation model to describe the retarded reptation of chains in the acteristic volumes vary from 10-3 nm for localized bond vicinity of solid nano-sized inclusions representing the nano-scale ibrations to 10 nm for the non-local normal mode of 2 Springer

sads rep ¼ b2N2 p2kbTNe ½ ð f0ð Þþ N Na faNa 5Þ In the case that Na = N1/2, the reptation time takes the form: sads rep ¼ b2N5=2 2p2kbTNe f0N1=2 þ fa h i ð6Þ To describe the change in reptation dynamics of the chains as a function of nanoparticle volume fraction, percolation model was used. At the percolation threshold, physical network formed by interconnection of immobilized chains on individual nanoparticles penetrates the entire sample volume. In this case, only physical ‘‘cross-links’’ are considered and the terminal relaxation time reaches the value characteristic for the life time of the physical fillerpolymer bond. Thus, the relaxation time near the percolation threshold is expressed in the form [44]: srec composite ¼ sads rep veff veff v eff 1 v eff b ð7Þ where v eff is critical effective filler volume fraction (v eff = 0.04 for PVAc-HAP at 90 C) and b is the percolation exponent (b = 4 for the same system). The v eff is a sum of the filler volume fraction and the volume fraction of immobilized chains and was shown to equal 0.04 for PVAc-HAP nanocomposites at 90 C. In order to simplify the percolation, random clustering of effective hard spheres was considered only in the way similar to that originally outlined by Jancar et al. [45] for micro-scale composites. Percolation threshold at approximately 2 m2 of the fillerpolymer contact area per 1 g of the composite was found in PVAc-HA nanocomposite system (Fig. 6). All the chains were immobilized at the internal contact area of 42 m2 per 1 g of the nanocomposite. Characteristic length scale for transition between continuum and discrete elasticity in polymer composites The classical continuum mechanics is designed to be sizeindependent. For nano-composites, however, size-dependent elastic properties have been observed which cannot be readilly explained using continuum mechanics and, thus, prevent simple scalling down the existing continuum elasticity models [23]. Polymers are unique systems with macroscopic viscoelastic response driven by the relaxation processes on the molecular level [46]. These relaxation processes represent particular molecular motions occurring in some characteristic volume, Vc. The Vc depends on the type of the relaxation process and temperature. The characteristic volumes vary from 10-3 nm3 for localized bond vibrations to 106 nm for the non-local normal mode of relaxation (Fig. 6) [46]. In the case of the non-local normal mode of relaxation, its characteristic volume is the upper limit for Vc displaying strong dependence on the chain size. Below this upper limiting characteristic volume, Vc * R3 N3/2, where R is the chain end-to-end distance and N is the number of monomer units in the chain. The characteristic time, sc, for each particular relaxation process varies from 10-14 s for bond vibrations above Tg to the infinitely long times below Tg. Thus, the macroscopic viscoelastic response of a polymer is a manifestation of a range of molecular relaxations localized in some characteristic volume and the rate of the relaxation mode is indirectly proportional to its locality (Figs. 7 and 8). The physical reasons for the expected breakdown of continuum elasticity on the nano-scale include increasing importance of surface energy due to appreciable surface to volume ratio [47], the discrete molecular nature of the polymer matrix resulting in non-local behavior in contrary to local character of classical elasticity [48], the presence of nano-scale particles with the length scale similar to the Fig. 7 Simple approach combining the reptation dynamics and percolation model to describe the retarded reptation of chains in the vicinity of solid nano-sized inclusions representing the nano-scale ‘‘interphase’’ J Mater Sci (2008) 43:6747–6757 6755 123

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 Springer

radius of gyration of the polymer chains [49, 50] and internal strain due to molecular motion within a nonprimitive 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 corresponding 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 nonaffine deformation associated with occurence of highmoment stresses. Consequently, for such systems, taking strain-gradient effects into account while investigating nanoscale elastic phenomena may impart significant sizedependent 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 decreasing 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 phenomena 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 modulus, 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 nanoscale [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

《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_review of interphase in nanoscale

《复合材料 Composites》课程教学资源（学习资料）第五章陶瓷基复合材料_review of interphase in nanoscale