1 Introduction

Polymers are molecules made of long chains of repeated units known as monomers. Their intrinsic features of flexibility, light-weight and low production cost, allow them to have wide applications in our daily life such as food packaging, painting, and automobile industries, etc. Although the monomer structure and selection of polymerization methods allow good control on some of the polymer properties, certain functions cannot be achieved by polymer itself. Therefore, polymers are compounded with other additives to achieve new properties. This final product is called composite [1].

Polymer nanocomposites (PNCs) are defined as the polymer matrixes reinforced with fillers with at least one dimension within 100 nm range. Nanofillers can be categorized based on their dimensions, e.g. 0D particle, 1D tube/fiber, and 2D sheets [2]. The PNCs have attracted great attention due to their drastically enhanced properties [3,4,5]. For instance, thermally insulating polymers can be transformed into thermal conductors after reinforcing with carbon nanotubes (CNTs) [6,7,8]. Moreover, PNCs have demonstrated improved mechanical, gas barrier, solvent resistance, and flammability properties compared to the corresponding neat matrices [3, 4, 9]. The significant differences in properties of PNCs can be explained by the extremely large interface area of nanofiller. The interfacial area of nanofillers is orders of magnitude higher than traditional macro- or micron-sized additives [10, 11]. Therefore, the dispersion quality of nanofillers in polymer matrix becomes critically important. The techniques of incorporating nanofillers, dispersion control, and their impacts on the physicochemical properties of PNCs have been reviewed broadly [12,13,14,15].

Although the type and chemistry of the nanofillers are important for the prediction of their composite properties, the experimental and modeling results have not completely been in compliance with the predicted behavior. Therefore, there should have been other parameters which have either underestimated or not been considered in the prediction of composite behavior. In this regard, the interfacial interaction between polymer matrix and nanofiller became one of the parameters which have raised attention [16,17,18,19]. The presence of nanofillers in the matrix and their interfacial interaction can affect the mobility of polymer chains [20]. At high filler content (over threshold), they can form a network which further restrains the mobility of the polymer chains [21]. Moreover, it has been reported that the property enhancement of polymer matrix filled with nanoparticles is a function of inter-filler distance, interfacial interactions, and interfacial area [22]. Hence, in addition to the characteristics of the constituents of the composites, the properties such as their interfacial areas, play a key role in the overall performance of composites. In this review, we described the type of interactions between the constituents, interaction characterization, improvement techniques, and the effect of interfacial interactions on thermal, mechanical, and electrical properties of PNCs.

2 Interfacial interactions in PNCs

The involved interactions in PNCs can be categorized into filler-filler and filler-polymer interactions. For instance, the interaction between the nanofillers (in the filler bundles) [23] or between different shells of the nanofillers such as multiwalled carbon nanotube (MWCNT) [24] is only related to the fillers and their properties. While the interaction between filler and polymer matrix [25] depends on the properties of both. The “interface/interphase” is defined as the region where the filler and matrix are either chemically or physically attached to each other [26]. A schematic model for the interface of filler in polymer matrix is shown in Fig. 1. The interfacial bonding plays a key role in polymer chain mobility and transferring the forces from the surrounding matrix to the filler. Therefore, it affects the mechanical properties of the polymer composites [17]. Following, the attributes of the fillers influencing the interfacial interactions, types of interfacial interactions, and the modification methods are reviewed.

Fig. 1
figure 1

Schematic model for the filler interface in a polymer composite

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2.1 Effect of filler surface chemistry

Surface chemistry of the fillers can impact the filler-matrix and filler-filler interactions as well as the isotropic dispersion of fillers in the matrix. Stronger interfacial interaction between the composite constituents than the inter-filler interactions can lead to a better isotropic distribution [27, 28]. The inter-filler interaction is the reason for potential agglomeration of fillers. If the inter-filler interaction is highly attractive, the fillers can accumulate and then act as a bigger reinforcing cluster rather than individual particles. However, in the case of weak inter-filler interaction, the deformation of the aggregated fillers will affect the storage/loss of applied energy [28].

2.2 Effect of filler size and shape

As discussed earlier, the high surface to volume (SV) ratio of nanofillers is responsible for the significantly enhanced properties. Therefore, it can be counted as the primary motivation for nanocomposite development [28, 29]. This parameter in addition to the stress transfer [28, 30] is responsible for “new structural arrangement” at microscale in the composites. As a result, improving the interfacial regions can increase the chance of introducing new properties to the composites [28]. Based on Eq. (1), SV ratio of spherical fillers is a function of (1/r):

$$ \frac{A_s}{V_s}=\frac{4\bullet \pi \bullet {r}^2}{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.\bullet \pi \bullet {r}^3}=\frac{3}{r} $$
(1)

where As is the available surface area, Vs is the volume of the filler, and r stands for spherical radius. To investigate the effect of the interfacial area, the whole interfacial area involved in the composites should be considered. For this purpose, in addition to surface volume ratio of individual fillers, the volume fraction (φ) of the fillers should be considered as well (Eq. (2)):

$$ \frac{A_{,\mathrm{total}}}{V_{\mathrm{total}}}=\frac{3}{r}\bullet \varphi $$
(2)

where A,total is the total surface area of the fillers and Vtotal is the total volume occupied by the fillers. Therefore, the overall surface to volume ratio is a function of (1/r) and φ. This means that in a constant volume fraction, by decreasing the size of fillers, the overall interfacial area will be increased and followed by increment of the interfacial interactions. As a result, the interfacial stress transfer will be more efficient. Additionally, for a specific size of fillers, by increasing the content of filler in the composite, the interfacial regions can be increased as well.

For cylindrical fillers, this ratio can be expressed in Eq. (3):

$$ \frac{A_c}{V_c}=\frac{2\bullet \pi \bullet {r}^2+2\bullet \pi \bullet r\bullet L}{\pi \bullet {r}^2\bullet L}=\frac{2}{r}+\frac{2}{L} $$
(3)

Comparing the spherical and cylindrical shaped fillers, their SV ratio can be expressed in Eq. (4):

$$ \frac{SV_s}{SV_c}=\frac{3}{2\bullet \left(1+\raisebox{1ex}{$r$}\!\left/ \!\raisebox{-1ex}{$L$}\right.\right)} $$
(4)

Hence, for plates (r > L) and short rods (L < 2r) the SV ratio of cylindrical fillers is larger than spherical fillers’, while the SV ratio of long fibers (L > 2r) is smaller than the spherical filler. Although it seems that due to high SV ratio of cylindrical fillers, it is better to use them as reinforcing agents, but there are other factors that may influence the selection of filler shape. For example, rigid cylindrical fillers can hardly disperse isotropically at high concentrations [28]. For thermal conduction, composites with smaller fillers (larger interfacial area) have severe phonon scattering resulting in lower thermal conductivity (TC) [31]. For example, Wu et al. investigated the effect of graphite nanoplatelet size (1 to 15 μm) on thermal conductivity of polyetherimide (PEI) composites. It was shown that although the smaller particles formed a better network, the thermal conductivity of the composites was higher with larger particles. It was suggested that the interfacial thermal resistance is the dominant parameter that determines the TC of the composites [32]. Eventhough larger enhancement of TC was also reported in other composites with larger fillers [33, 34], there are some contradictory reports as well [35, 36]. For instance, Pashayi et al. found that nano-sized silver particles outperformed micron-sized particles in enhancing TC of epoxy-silver composites. SEM observations revealed that nano-sized fillers formed a continuous network which was not observed for micron-sized fillers [37]. However, it is known that TC is not only a function of particle size; other parameters such as surface chemistry, morphology, and dispersion of fillers could affect TC as well. Therefore, more likely, the effect of size should be discussed with other parameters when interpreting the thermal conduction in polymer composites [38]. Fu et al. reported higher TC for epoxy adhesives filled with nano-sized Al2O3compared with micron-sized filled ones. The authors believed that higher polydispersity of nano-sized fillers helped to construct an effective filler network for heat transfer [36]. In contrary to high interfacial thermal resistance in polymer nanocomposites, combination of nanoparticles with microparticles could synergistically enhance the TC of composites. This phenomenon has been observed in several systems, which was attributed to bridging effect of nanofillers between micron-sized fillers [36].

With filler size down to nanometer, the SV ratio and surface energy of nanofillers become large enough that lead to a dramatic change in physicochemical properties of PNCs due to the presence of large interface area between filler and polymer matrix. It should be also considered that homogenous dispersion of the nanofillers is essential for achieving the desired mechanical properties.

In terms of stiffness, the effect of filler size seems more complicated. It was reported that the size of fillers in a constant volume fraction cannot significantly affect the stiffness (or called Young’s modulus) [39, 40]. However, Ji et al. have theoretically proved that there is a critical size for fillers in nylon 6/montmorillonite nanocomposites, below which the filler size can affect the stiffness (Fig. 2) [41]. This phenomenon has been experimentally proved in separate studies [42, 43]. Therefore, the stiffness of the composites can be either unaffected or decreased by increasing the filler size [44].

Fig. 2
figure 2

Normalized modulus as a function of particle size [41]

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2.3 Types of interfacial interactions

The properties of the composite materials are framed based on the interfacial characteristics of the fillers and matrixes [45, 46]. Generally, the interactions between the filler and matrix are categorized as covalent and noncovalent interactions (i.e., van der Waals (VDW) [45], electrostatic [45], and hydrogen bonding [47,48,49]). Depending on interactions between the constituents of the composite, different types of improvement techniques were developed [16].

2.3.1 Noncovalent interaction

The noncovalent interaction between the matrix and fillers can be enhanced by employing bridging, increment of interfacial area, and polymer wrapping [16]. Bridging happens when a polymer chain interacts with two or more reinforcing fillers simultaneously (Fig. 3). The probability of the presence of bridging in the composite depends on the ratio of the radius of gyration (Rg) of the polymer chain to the average distance of nearest reinforcing filler. Therefore, by increasing the filler content and using higher molecular weight polymer, the chance of bridging phenomenon will be higher [50].

Fig. 3
figure 3

Schematic drawing of bridging incident in polymer composites

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Specific interaction area in the composite is another factor which can affect the properties of the composite. It is defined as interfacial area of polymer-filler per unit volume and it is related to the density ratio of polymer matrix to the fillers, the concentration, and diameter of the filler [50]. In this regard, Cadek et al. have shown that the reinforcement of polymer composites is linearly related to the overall interfacial area of fillers, meaning that the smaller fillers can have higher impact on the property of the final product [29].

Wrapping fillers by polymer chains, in addition to increment of the interaction, is useful for better dispersion of the fillers in the matrix [51,52,53,54]. Wrapping of the nanotubes by the polymer chains has been explained by presence of π-π stacking [55,56,57,58,59], hydrophobic [60], and VDW interactions [61, 62]. Figure 4 shows the schematic of a wrapped single wall carbon nanotube (SWCNT) by DNA which is due to π-π stacking interaction between the SWCNT wall and the aromatic bases of DNA [63].

Fig. 4
figure 4

Schematic drawing of a single wall CNT wrapped with DNA [63]

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Wrapping fillers by polymer is related to the chemical composition and stiffness of the polymer backbone [60] and geometric parameters [50] of the constituents in the composites. Thus, higher molecular weight polymers and nanotubes with smaller diameters are more likely to go through the wrapping mechanism [16].

Finally, it should be noted that crystallization of the semi-crystalline polymer host at the interface is another way for improving the interfacial interactions. In this process, the fillers will act as a nuclei and the semi-crystalline host will crystallize at the interface [64].

2.3.2 Covalent interactions

Covalent interaction happens when polymer chains are chemically connected to the reinforcing fillers [16]. For that purpose, proper chemical treatments are required to attach functional groups to filler surface which can react with the matrix [65,66,67,68,69,70]. Figure 5a–c shows three types of surface functionalization of CNT with polymer chains, hydroxyl, and carboxyl groups, respectively. Functionalized fillers not only enhance their interaction with the host, but improve their dispersion and the final properties of the composites compared to the pristine fillers [71,72,73]. The functional group of the fillers should react with an active group on the polymer chains of the host. One of the suitable methods for chemical bonds formation is the in situ polymerization, where the monomers react with each other and the fillers simultaneously [74,75,76,77,78]. The other way is to modify the host prior to the chemical attachement of the fillers [79].

Fig. 5
figure 5

a, b Schematic drawing of modification of CNT’s surface by addition of polymer chains and functional groups, respectively. c Functionalization of multiwall CNT (MWCNT) by plasma functionalization [83]

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Although covalent bonding between the fillers and the host can enhance the interfacial strength more effectively (due to stronger adhesion), the involved pretreatment process requires special attention. For instance, even though the functionalized fillers could achieve better dispersion, but introduction of surface defects could deteriorate the intrinsic properties of the filler [16]. Grafting polymer chains on filler surface have been demonstrated effective approach to improve the interfacial interaction and thus enhanced property of the composites [80,81,82].

3 Experimental methods of measuring interfacial interactions

3.1 Interfacial wetting properties

For strong adhesion between the fillers and matrix, good wettability of the reinforcements by the matrix is required [84], which makes it important to evaluate the wettability of the fillers. In the following section, contact angle [85] and surface tension [86] methods will be introduced for wettability measurement.

The concept of contact angle was first introduced by Thomas Young in 1805 [87]. He proposed that the contact angle of a drop of a liquid on a solid surface is the result of mechanical equilibrium between three surface tensions. The involved surface tensions at the interface are liquid/vapor (γLV), solid/vapor (γSV), and liquid/solid (γLS). This equilibrium results in the following Eq. (5) [88]:

$$ {\gamma}_{SV}-{\gamma}_{SL}={\gamma}_{LV}.\cos \theta \kern13.5em $$
(5)

This concept is important as the angle of the liquid drop at equilibrium state gives information on wettability and spreadability of the liquid on the solid surface [88]. The contact angle (θ) below 90° indicates that wetting is favorable while for angle above 90° (θ > 90°) is not (Fig. 6) [89]. In other words, the lower the angle, the better the wettability. Complete wetting can be achieved when contact angle approaches to 0° [90].

Fig. 6
figure 6

The schematic presentation of the relationship between contact angle and wettability [89]

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Contact angle measurements of the nanofillers with polymer matrixes have been studied in both microscopic and macroscopic scales [84]. For instance, the wetting property of carbon nanotubes in macroscopic scale was evaluated by placing the liquefied matrix (or the powder followed by applying heat to convert it to liquid) on the nanotube sample. The aim was to see whether the liquefied matrix would absorb (wetting contact angle) by the surface or it would make a spherical bead (nonwetting contact angle).

Further, using drop-on-fiber techniques [85] and characterization by scanning electron microscopy (SEM) [84], transmission electron microscopy (TEM) [86] and optical microscope [91], the shape and symmetry of the drop on the cylindrical fiber can be studied. In drop-on-fiber method, the drop will be symmetrically shaped along the cylindrical axis when the contact angle is zero, in contrast to the high contact angle which results in nonsymmetrical conformation [92, 93]. For instance, Qian et al. used the drop-on-fiber approach to evaluate the wettability of carbon fiber (CF) and its CNT-grafted version with poly (methyl methacrylate) (PMMA) as matrix (Fig. 7). The contact angle of CF changed from 27.4 ± 0.8 to 25.7 ± 0.8° after oxidation, while grafting CNT to CF resulted in further drop of the contact angle to 21.6 ± 0.7° [94].

Fig. 7
figure 7

Optical images of PMMA droplets on a as-received, b oxidized, and c CNT-grafted carbon fibers [94]

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Wetting property of the fibers at microscale has been studied with the Wilhelmy model [95, 96]. Combination of the Wilhelmy model with atomic force microscopy (AFM) makes it a useful technique for measuring the wetting properties of the carbon nanotubes. For this purpose, carbon nanotube will be attached to a calibrated AFM tip and will be brought down to immerse CNT in the polymer melt. This process will be followed by inducing a downward force on the CNT, which will be recorded by the cantilever deflection. The deflection force can be converted to the contact angle by knowing the surface tension of the liquid. The following Eqs. (6) and (7) will be used for this conversion:

$$ {F}_r={\gamma}_L\pi .d.\cos \theta $$
(6)
$$ {F}_r={\gamma}_L.\pi .\left({d}_{\mathrm{out}}.\cos {\theta}_{\mathrm{out}}+{d}_{\mathrm{in}}\cos {\theta}_{\mathrm{in}}\right) $$
(7)

where γL is the surface tension of the liquid (N/m), θ is the contact angle in degree, θin and θout are the inside and outside contact angles of the nanotube, d is the diameter of the nanotube, and din and dout are the inside and outside diameters of the nanotube [97,98,99].

Although the wetting measurements are known as simple method to estimate of the interfacial adhesion, significantly different values are reported even for the same materials. For example, the contact angle of PEG-MWCNT was reported to be in the wide range of 25–73° in different studies. The difference between observed results could be explained by the different size of fillers and also temperature variations in the system [84, 99]. Therefore, these methods could provide an initial estimation for the recognition of strong or weak interactions [16]. Thereafter, researchers found surface tension measurement a better technique for wettability studies [84, 98]. In this method, the surface tension of the polymer will be compared with the critical surface tension of the nanotube (γc) (in the plot of cosθ versus γL of various liquid, the intercept at cosθ = 1 shows the critical surface tension) [95]. In theory, liquids with surface tension equal or less than the critical surface tension of substrate (γc) can completely wet the surface [90].

3.2 Spectroscopy techniques

The spectroscopy techniques such X-ray diffraction, Raman, and Fourier transform infrared (FTIR) are well-known methods for material characterization. Raman spectroscopy was first conducted on CNTs in 1993, and since then, it has been used for characterization of nanocomposites [100]. Raman spectroscopy can be used for detection of the type of functionalization [101] and the diameter of the nanotubes [102, 103]. Furthermore, the chemical peak shifts in Raman/FTIR can be used to distinguish the VDW interactions between the nanotubes in the bundle [104, 105], the hydrogen [106], and covalent bonding between the nanotubes and the polymer matrix [107].

3.3 Atomic force microscopy involved techniques

As mentioned earlier, recent developments in the force microscopy techniques makes it feasible to measure the force between the cantilever and the substrate even in atomic resolution [108] e.g. for measuring the interactions in the nanotube composites. Two major approaches have been developed for this purpose. In the first approach, a nanotube attached tip will be prepared and a polymer melt will be used as the substrate [97,98,99, 109] (similar to the contact angle measurement mentioned in previous section), while in the second approach, the tip will be coated with the polymer and the nanotube is placed as the substrate [110].

3.3.1 CNT-on-tip/cantilever approach

This approach involves two different methods for strength measurement: (i) pull out method [111] and (ii) peeling force microscopy method [112]. Figure 8 shows the pull out technique which was used by Barber et al. for the first time. Using this method, they could measure the critical force required for interfacial failure between CNT and a copolymer melt [113]. In the pull out method, the CNT attached tip will approach the polymer melt, while the applied force on the cantilever is simultaneously recorded as a function of time. When the tip is close enough to the polymer surface, a jump-in force is usually observed in the force curve. Afterwards, by pushing the CNT further into the bath and keeping it stationary for a while, the polymer will solidify around it and later will be pulled out from the matrix (Fig. 9). For this procedure, it is required to investigate the length and diameter of the nanotube after pull out process to see if any changes have occurred [111, 114, 115].

Fig. 8
figure 8

CNT attached AFM tip is immersed in the resin followed by pulling out and measuring its required force simultaneously [113]

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Fig. 9
figure 9

Force vs. time plot for the pull out approach: a the nanotube is already in the polymer bath; b by pulling out the nanotube, the cantilever will be deflected until it reaches its maximum deflection at c. At d, the pull out is occurring, while at e, it is completely out of the bath [111]

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The other method is the peeling force microscopy. In this method, the CNT is attached to a tipless cantilever and it will be in touch with the substrate. In next step, the nanotube will be peeled off from the surface, generating the force curve simultaneously. During this process, the nanotube will go through different geometrical configurations with regards to its contact with the substrate: line contact (s shape), point contact (arc shape), and finally no contact or freestanding mode (Fig. 10). Based on a proposed theoretical model, each of these configurations represent specific kind of involved energy in separating the nanotube from the substrate and the applied work in s-shape mode will mostly change the interfacial energies of constituents. Although this technique is useful for interaction measurement, it cannot measure the interfacial energy per unit area due to difficulty of measuring the contact area during this process [112, 116].

Fig. 10
figure 10

The s-shape and arc-shape CNT configuration on the substrate [112, 116]

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3.3.2 CNT-on-substrate approach

In contrast to the previous approach, CNT will be placed as the substrate, and a modified AFM tip (chemically modified either by applying the polymer as a coating or binding functional groups to it) will be used. Later, the force curve between the cantilever and the substrate will be recorded and used to measure the corresponding adhesion. This type of measurement is useful to show the effect of present chemical groups on the adhesion between the polymer matrix and the nanotubes [110, 117,118,119,120]. However, it worth mentioning that in this method only the maximum adhesion force will be considered, which is the summation of all forces applied on different locations of the cantilever. Therefore, the tip-substrate distance will influence the final value of the adhesion force. Recent studies have introduced a new parameter for measuring the adhesion force which is also a function of separation distance, called interaction stress. This parameter is “the state of stress (i.e., a tensor) at any given point of an object as a result of its vicinity to a secondary object” [121]. In order to get this factor, a stepwise discretization method was applied to the force curve of AFM followed by determination of the noncovalent interactions versus separation distance. Furthermore, all the other interaction parameters can be calculated (e.g., interaction forces, energy and internal stress) from interaction stress as well [120, 121]. Additionally, each of these factors can be used for measuring the other parameters such as the stress field at nanoscale [121, 122].

4 Influence of interface on mechanical properties

It is known that incorporation of fillers in a matrix can modify its properties. In conventional composites, micrometer-sized inorganic fillers such as calcium carbonate, talc, and glass beads have been extensively used for mechanical property enhancement [123,124,125]. Such properties can be further improved by decreasing the fillers’ size to nanoscale and increasing their aspect ratio.

Since the behavior of PNCs is greatly influenced by their microstructures, the properties of matrix and fillers, filler distributions, interfacial bonding, and processing method should all be considered [123, 126]. Mechanical properties of composites are more related to particle size, loading, and filler-matrix interfacial adhesion [44]. The interfacial property is important for the evaluation of the mechanical load transfer from polymer matrix to fillers [127, 128]. For instance, strength and toughness of the composites strongly depend on the interfacial adhesion. Therefore, the dispersion, interfacial adhesion, geometric dimensions, etc., play key roles in mechanical property enhancement [76, 129,130,131]. The mechanical properties can be evaluated by either conventional methods such as dynamic mechanical analysis (DMA) [27, 132]; tensile, compression, and shear tests [25, 133,134,135]; or the new methods such as copper grid technique [136, 137] and strain-induced elastic buckling instability for mechanical measurements [138,139,140]. Since stiffness is not significantly affected by the degree of interfacial bonding in polymer composites [141, 142], it is not reviewed here.

4.1 Strength

The tensile strength of the composite depends on the efficiency of stress transfer between the constituents of the composite. If the applied load efficiently transfer to the fillers, the strength will be improved [143, 144]. The smaller particles have larger interface area at a constant volume fractions of fillers, leading to a large portion of stress transfer regions [44].

The efficiency of the load transfer also depends on the strength of interfacial bonding between the composite constituents [44, 145]. Contrary to the composites with strong interfacial interaction [142], strength will be decreased in composites with poorly bonded fillers. This is due to the presence of discontinuity because of de-bonding at the interface, which prevents the filler from carrying the applied load efficiently. There are many studies on filler surface modification that lead to higher dispersion and interfacial interaction and subsequently higher tensile strength of the composites [76, 146,147,148,149]; suggesting that, the introduction of chemical bonding to filler-matrix interfaces can effectively enhance the strength of composites [150, 151].

An et al. incorporated functionalized rod-shaped silicates known as attapulgite (ATT) into the polyimide (PI) films. For that the fillers’ surface was grafted with polymer chains similar to the matrix. The functionalization of the silicates resulted in better dispersion of ATT and more efficient stress transfer between filler and matrix. The final composite showed an increase of 70% in tensile modulus, 45% in tensile strength, and 54% in elongation at break. The enhanced mechanical properties were explained by considering the predominant factors such as the percolated particle networks, interfacial interactions, and introduced free volume due to addition of the fillers. The enhanced properties were induced at three different stages: (i) at low concentration of fillers, the reinforcement was due to interfacial interactions, leading to effective stress transfer between fillers and matrix; (ii) after reaching the percolation threshold, in addition to the interfacial interactions, percolated particle network also enhanced the strength of the composite; (iii) further increasing the fillers’ concentration beyond percolation increases free volume and decreases the tensile strength by crack initiation and propagation. Therefore, depending on the concentration of reinforcing agents in the composite, the mechanical properties could be enhanced by interfacial interaction, percolated network, or both of them. At high loading degrees, the strength will be decreased due to crack formations [152]. Results mentioned above, are consistent with other studies stating that the addition of nanoplatelets into the polymer matrixes can improve their stiffness and toughness and possibility of de-bonding at the interfaces at high volume fraction of the fillers [153].

In addition to the surface modification of fillers, interfacial crystallization can also enhance the interfacial interactions followed by more load transfer. The mechanism of such mechanical property enhancement has been systematically studied and been explained by: (i) improvement of interfacial interactions in the filler/crystalline polymer compared to the filler/amorphous polymers, (ii) crystalline phase of polymer acts as an additional stiff constituent in the composite, and (iii) reduction of filler aggregation due to the formation of crystalline phase at the boundaries [64, 154].

4.2 Toughness

The role of nanofillers in development of tough polymeric products have been reported [155, 156]. However, the enhancement of the strength of composites are accompanied with sacrificing toughness of the products [157]. Likewise, toughening agents such as rubbers which are used to enhance the extensibility and the fracture resistance of polymers, reduce the strength of product [158, 159]. Therefore, the balance between these two properties should be considered when designing desired properties in composites [160, 161]. The fracture behavior of polymer nanocomposites which defines their toughness is a function of the type of polymeric matrix [44], size and shape of fillers [152], and the interfacial interactions [152]. For instance, toughness can be significantly enhanced by the enhancement of the interfacial adhesion between the thermoplastic matrix and filler; but not in composites with thermosetting matrix [44]. Yet, the simultaneous enhancement of toughness and strength in glassy polymeric matrix is unclear [152].

Sakai et al. investigated the mechanical properties of brittle carbon matrix reinforced with carbon fiber. They proposed that if inappropriate interaction was embedded between the components, the cracking of matrix would propagate along the fibers. In that case, the fibers could not bridge the crack and lead to weak toughening of the composite. On the other hand, for the interactions which were strong enough for stress transfer and weak for de-bonding to happen, the crack pattern changed significantly (crack deflection, voiding, and de-bonding). This phenomenon resulted in fiber pull out followed by bridging the crack and toughening the composite (Fig. 11) [162]. Boo et al. studied the exfoliated epoxy/α-zirconium phosphate nanocomposite. They claimed that since fillers had strong bonding with the matrix, no crack blunting and deflection occurred. The crack went through fillers by breaking them; thus, there was no improvement in toughness [163].

Fig. 11
figure 11

Crack interaction with fibers for a strong and b weak interactions [162]

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Moloney et al. also reported that though epoxy/glass bead composite had a low strength due to the poor bonding and the toughness was enhanced due to crack tip blunting [159, 164]. Similarly, Liu et al. explained the toughening of intercalated epoxy/clay nanocomposite due to the crack deflection and de-bonding process. The toughness of epoxy resin was enhanced by 70% after adding 4 wt% of clay [165]. The same result was reported by Zuiderduin et al. for toughening of aliphatic polyketone by stearic acid-coated calcium carbonate particles. They claimed that rigid particles can enhance the toughness of composites with reduction of the volume strain. That required the particles to de-bond from the host [166]. For this mechanism to happen, fillers should have a round shape (no stress concentration) and their size should be less than 5 μm (in this study, it was around 0.7 μm; otherwise, the created voids would cause fracture initiation), well dispersity of fillers, and moderate interfacial interactions. The stearic acid coating used in this study was for enhancing the dispersion of the particles and lowering the interaction with the matrix. Thus, due to de-bonding mechanism, the toughness of the composite was increased [166, 167]. On the other hand, Levita et al. believed that at high enough adhesion between the filler and the matrix, the crack will be arrested (pinned) by reaching the filler (known as crack pinning model). Further propagation of the crack, needed higher tension. It was mentioned that the size of the filler was important to be able to interact with the crack [168].

Fiedler et al. investigated the effect of CNT on the toughness of epoxy composites. They showed that although untreated CNT could enhance the toughness due to void nucleation and crack deflection, the amino-functionalized carbon nanotube had a better performance. The fracture toughness of the resin was enhanced 45% by incorporation of just 0.3% of amino-functionalized double-walled CNT. They concluded that crack bridging by fiber can further enhance the toughness of composites [169]. Gojny et al. summarized the possible fracture mechanisms of CNT-filled composites as shown in Fig. 12 [170]. Table 1 briefly summarizes the change of mechanical properties of polymer composites after introducing different fillers. To sum up, depending on the dominant toughening mechanism and the type of matrix (thermoplastic vs. thermoset), higher interfacial interaction may have positive or negligible impacts on the toughness of composites.

Fig. 12
figure 12

Schematic representation of fracture mechanisms of CNT-filled composites. a Initial position of CNT in a matrix. b CNT-pull out as a result of CNT-polymer debonding (weak interfacial interaction). c CNT’s rupture which is caused by strong interfacial adhesion and fast local deformation. d Telescopic pull out resulting in outer layer fracture (due to strong adhesion) and inner layer pull out. e Crack bridging phenomenon combined with partial debonding [170]

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Table 1 Mechanical property of polymer composites with different fillers and bonding types
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5 Influence of interfacial interactions on thermal properties

Investigation of the thermal behavior of nanocomposites is essential for determining the applicable temperature range of the materials [180]. In this section, we will review the effect of fillers and proximity to the fillers’ surfaces on the thermal properties of composites, such as glass transition, thermal stability, and interfacial thermal resistance.

5.1 Glass transition (T g)

The impacts of the size and confinement on the glass transition and dynamics of polymer chains at the interface have been reviewed earlier. Evidence of the effect of interface has been found on the variations of the glass transition temperature or the dynamics of molecules [20, 181, 182]. Presence of reinforcing particles in the polymers can affect the local segmental mobility of polymer chains. This parameter can be evaluated either by measuring the segmental relaxation time or the Tg behavior before and after filler addition [20]. The relaxation time was mainly measured using dielectric spectroscopy [183, 184], NMR spectroscopy [185,186,187,188,189,190,191,192], and neutron scattering [193, 194]. Tg was determined using dynamic mechanical spectroscopy [195,196,197,198,199], calorimetry [191, 200,201,202], and dilatometry [184, 203] techniques. Since the mobility of the polymer chains around the fillers is related to the interfacial interaction, the presence of the interaction and their strength can be estimated by measuring Tg and relaxation time [11, 204]. For example, stronger interactions will cause reduction of the dynamic loss, decrement of thermal expansion coefficient and increment of Tg [205]. On the other hand, in NMR measurements, bonding strength between the polymer chains and the filler particles show different relaxation times [185].

For different polymer nanocomposites, Tg was shown to be increased [206, 207], decreased [180, 208], or even unaffected [182, 209] by the introduction of fillers into the system. More studies are summarized in Table 2.

Table 2 Glass transition behavior of polymer composites after incorporation of fillers
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The presence of strong interaction between the matrix and the fillers (e.g., H-bonding [30, 220], electrostatic interaction [220, 221], and covalent bonding [222]) increase the Tg while the free space at the interface of nonwetted fillers lead to reduced Tg [204, 223]. The absence of strong interfacial interaction of wetted fillers have no substantial impact on Tg [182, 204]. This phenomenon was explained by the thermomechanical similarities of planar polymer films and polymer nanocomposites [223]. If the interaction between the fillers and surrounding matrix is the same as the interfacial interaction between ultrathin layer of the bulk polymer and the substrate, Tg will be invariant [204]. Additionally, it was reported that there may be more than one Tg in polymer nanocomposites with strong interactions between the fillers and polymer chains [196]. In that case, higher Tg belongs to the regions adjacent to the fillers with irreversible adsorption of polymer chains to the particles, while the lower Tg represents for the polymer bulk farther from the fillers [182]. It should be mentioned that different Tg values have been reported for the same materials, which can be the result of incorporating different methods of analysis [20], neglecting the effect of fillers on the degree and nature of crystallinity of the matrix [20], or different methods of preparation [224].

5.2 Thermal stability

The improved thermal stability of the PMMA/montmorillonite PNCs was first reported by Blumstein in 1965 [225]. Higher thermal stability and improved flammability performance make them suitable for high-temperature applications. Additionally, since many of the polymer composites are produced through melt mixing at high temperatures, it is essential to know the degradation temperatures for a better process design [4, 226].

The presence of reinforcing agents in the matrix can increase the thermal stability in different ways. First, they can act as a barrier, which makes them useful for flame retardation applications [209, 227, 228]. Second, they can create a network which can protect the polymer from degradation [229,230,231,232]. Third, they can act as radical traps [233]; and lastly, they are capable of altering the microstructure of the product [4, 222]. Moreover, strong adhesion between the filler and matrix causes lower mobility of polymer chains followed by reduction of decomposition rate [234, 235]. Therefore, using any method which can increase the strength of the interaction between the composite constituents would improve its thermal stability.

5.3 Thermal conductivity

In many literatures, it has been confirmed that the interface in the composites play a significant role in their thermal conductivity [236,237,238,239,240,241]. Heat transfer at the interface of two different materials mostly happens with a temperature discontinuity [242]. This phenomenon was observed first at the interface of a metal and liquid helium [243], while later it has been found at the interface of two solids [244]. The heat loss at the interface of two different materials is due to the phonon scattering at this region [236, 238, 239]. Phonon scattering can be significantly impacted by dimensions of fillers, the matrix, and their interfacial regions. Therefore, the interfacial zones predominantly affect the thermal conductivity of the composite [245, 246]. As a result, anything that can affect the interfacial regions (e.g., geometry of particles [247,248,249,250,251,252,253], aggregation [254,255,256], interfacial pressure [257], roughness [258,259,260], and the strength of interactions at the interfaces [261,262,263,264,265]) in the composites would influence their thermal conductivity. In this section, we will review the parameters affecting the interfacial interactions and their subsequent impact on the thermal conductivity of the composites.

The heat transport in the macroscopic scale can be described by the Fourier law (k = Q/ΔT), where k is the thermal conduction coefficients and it relates the heat flux (Q) to the temperature gradient. The thermal conductivity at the boundaries is explained by the following equation, hBD = Q1/ΔT1, where hBD is the thermal boundary conductance, Q1 is the heat flux perpendicular to the interface, and ΔT1 is the temperature discontinuity. The thermal boundary conductance, which is the inverse of the interfacial thermal resistance, was studied first by Kapitza in 1941 [243]. The effects of interfacial phonons transport are merged into this factor [238]. Although in macroscopic scale k is the controlling parameter for heat flux, it is strongly affected by hBD at nanoscale [266, 267]. In this regard, interface plays a key role because of influence of factors such as lattice mismatch [256, 268] and phonon scattering [267, 269]. Wang et al. reported that the interfacial resistance and phonon scattering are due to the incomplete contact at the interface (MWCNTs in their study) [270]. Moreover, it has been reported that the resistance of the solid-liquid interface is a function of properties of adsorbed liquid layers [271]. Presence of adsorbed polymer layers around the fillers prevent the formation of percolation network and filler-filler phonon transfer. Even if the fillers are in direct contact with each other, due to their small contact area, the matrix and its interfacial resistance play a key role in heat transfer [272].

Noncovalent functionalization has been used for dispersion of fillers (i.e., CNTs [273, 274] and graphene [171, 275]) in polymer matrix. This type of functionalization enhances the dispersion quality of fillers. However, its impact on the thermal conductivity is still not clear. In some studies, it was observed that contrary to the dispersion of fillers, the thermal conductivity was decreased compared to the untreated fillers [251]. The authors believed that the noncovalent functionalization leads to the formation of more filler-matrix interfaces and higher phonon scattering. Additionally, it was proposed that this type of bonding at the interface cannot effectively transfer the thermal vibration from the filler to the matrix [251]. Contrary to these studies, some other authors showed thermal conductivity improvements with employing the noncovalent functionalization [171, 275, 276]. For example, Teng et al. functionalized graphene nanosheets (GNSs) through π-π stacking with functionalized pyrene molecules containing functional segmented polymer chains poly(glycidyl methacrylate) (PGMA), Py-PGMA. They showed that Py-PGMA-GNS fillers could form covalent bonding with epoxy. The strong interaction between Py-PGMA-GNS fillers and matrix resulted in a much higher thermal conductivity comparing to composites filled with pristine GNS and MWCNT. Optimized Py-PGMA-GNS-epoxy composite showed 20 and 267% higher thermal conductivity than pristine GNS-epoxy and pristine MWCNT-epoxy, respectively [275].

In the presence of strong bonding, the phonon scattering and the local thermal resistance could be decreased and subsequently improved the thermal conductivity of the composite [277,278,279]. This phenomenon was explained by increasing the transmission coefficient of the phonons [263, 278]. Modification of the end groups of the polymer chains [261] and surface modification of the fillers (either with functionalization [237, 280,281,282,283,284] or applying specific coatings [285,286,287]) are common methods for improving the adhesion at the interfaces with subsequent thermal conductivity enhancement. However, it should be considered that the functionalization of the filler may create defects and decrease the intrinsic thermal conductivity of them [288]. This is caused by higher phonon scattering at the grafted area. On the other hand, the phonon scattering at the interface will be decreased due to higher compatibility of fillers and matrix after functionalization. Therefore, the reduction of intrinsic thermal conductivity of fillers due to their modification and increment of interfacial thermal conductance at the interface are competing parameters [251].

Huang et al. proposed that there is a critical concentration for thermal conductivity enhancement by chemical bonding. Below this concentration, covalent bonding improved the thermal conductivity; above this concentration, chemical bonding became not as much effective. Although increasing the filler loading could enhance the thermal conductivity through direct contact of the fillers, formation of voids and defects at higher filler concentration could suppress the thermal conductivity enhancement as well (Fig. 13) [280].

Fig. 13
figure 13

Proposed microstructure evolution in polymer-filler [280]

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In addition to the introduction of conductive fillers in polymeric matrix, the thermal conductivity can be enhanced by engineering the inter-chain interactions [289]. This approach is accompanied with introduction of large crystallinity [290, 291] or hydrogen bonding [289, 292,293,294] in polymer blends.

Mu et al. studied the effect of incorporation of different types of amino acids (AAs) in poly(vinyl alcohol) (PVA). They showed that depending on the type of PVA-AA interaction, two crystal patterns were formed, continuous and discrete, as shown in Fig. 14. They emphasized the important role of interface surrounding the crystalline pattern. The continuous crystal network created continuous interface with facilitated phonon transfer while the phonon scattering was higher in discrete network. They concluded that high PVA-AA interaction and self-organized continuous crystal structure resulted in higher thermal conductivity in the composite [290].

Fig. 14
figure 14

Schematic illustration of different crystalline structure and subsequent micro- and nanoscale phonon transfer in different PVA-AA blends [290]

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In another study, the effect of induced H-bonding in PVA-biopolymers (i.e., lignin and gelatin) blend and its subsequent impact on thermal conductivity was investigated by Mu et al. They found that stronger H-bonding caused larger polymer coils which created a continuous microstructure. As a result, these formed continuous microstructures of polymer coils led to continuous pathways for better phonon transfer (Fig. 15) [292].

Fig. 15
figure 15

Schematic drawing of intermolecular interactions in PVA-lignin-gelatin blend via H-bonding and achieved continuous coil microstructures [292]

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The advantageous of nanofiller incorporation in some other polymeric composites has been summarized in Table 3. In summary, incorporation of thermally conductive fillers, reduction of phonon scattering at the interfacial regions, and enhancement of phonon transfer by enhancing the inter-chain interaction can improve the TC of polymeric materials.

Table 3 Effect of filler type and surface functionalization on thermal conductivity of polymer composites
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6 Influence of interfacial interactions on electrical conductivity

Contrary to the thermal and mechanical properties of the composites, where homogenous distribution and strong adhesion between the fillers and the matrix is required, electrical conductivity (EC) is based on formation of continuous electrical conductive network between the fillers [307,308,309,310,311,312]. The electrical conductivity enhancement appears in three main stages, (i) prior to, (ii) within, and (iii) after percolation threshold [313,314,315]. Figure 16 [316] shows the three steps for carbon fibers into a polymer host, respectively. In the first stage, due to presence of few CFs, EC is close to the EC of the host. Gradually by aggregation and connection through CFs, the EC increases slightly by tunneling effect (Fig. 16b). However, there is no complete pathway for conduction yet. Further increasing the amount of fillers, creates the first conductive pathway (red lines in state c). The volume fraction of fillers at this stage is known as percolation threshold. Adding more filler into the host creates more conductive pathways, which results in the formation of a more conductive network (Fig. 16d). The percolation threshold is determined by a sharp drop of electrical resistance and it depends on the size and shape (aspect ratio) of fillers [308, 317,318,319], their dispersion [317, 320, 321], interfacial interactions, and alignment [322,323,324].

Fig. 16
figure 16

a–d Percolation stages in conductive composite and the corresponding electrical conductivity in each step [316]

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The presence of thin layer of polymer matrix around the fillers prevents the formation of continuous network and cause a tunneling barrier between them [325, 326]. Hence, the functionalization of the fillers has two different effects. As it was mentioned earlier, they will enhance the distribution of the fillers into the host [234, 307, 317, 327]. Well-dispersed fillers result in the formation of continuous conductive pathways which in turn enhance electrical conductivity [308, 320, 328]. On the other hand, the interaction of the host with functionalized filler forms an insulating layer on filler’s surface [307, 329], which is detrimental for EC enhancement. In general, it has been reported that the negative influence of functionalization was outweighed by its positive effect on dispersion of fillers [310, 326]. Some other related literatures are summarized in Table 4.

Table 4 Effect of filler functionalization on electrical conductivity of polymer composites
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7 Summary and outlook

In this review, an overview of the interfacial region and its important role in overall properties of the composites and especially polymer nanocomposites were provided. Different types of interactions at the interface and the common techniques for their enhancement were introduced. Additionally, it was described how the properties of fillers, such as their aspect ratio and chemistry will impact the interfacial interaction. Moreover, the techniques used for measuring the adhesion between nanotube fillers and polymer matrixes were described. Finally, the influence of interfacial interactions on the mechanical, thermal, and electrical properties of composites was reviewed. In general, the strength of interfacial bonding plays a key role in the properties of composite. For mechanical properties, it influences the load transfer at the boundary. While for thermal properties, it affects the Tg of polymer host, its degradation rate, and thermal conduction across the interface. Lastly, due to the impact of interfacial bonding on the dispersion of fillers in the matrix, it will subsequently affect formation of percolated network and electrical conductivity.

Numerous studies on the polymer composites and their properties show the importance of the polymer-filler interfaces in these types of materials. It has been confirmed that their performance (mechanical, thermal, electrical, etc.) relies significantly on the quality of the interfacial interactions. Therefore, in-depth studies on the impact of interfacial interactions on each property of polymer composites are required. Insight of these fundamental understandings followed by employing suitable methods for achieving optimum interfacial interactions would lead to enhanced performance of polymer composites.