Towards Sophisticated 3D Interphase Modelling of Advanced ...Halpin-Tsai model and Mori-Tanaka model...

Research ArticleTowards Sophisticated 3D Interphase Modelling of AdvancedBionanocomposites via Atomic Force Microscopy

Mohanad Mousa1,2 and Yu Dong 1

1School of Civil and Mechanical Engineering, Curtin University, GPO Box U1987, Perth, WA 6845, Australia2Shatrah Technical Institute, Southern Technical University, Basra, Iraq

Correspondence should be addressed to Yu Dong; [email protected]

Received 15 January 2020; Accepted 13 June 2020; Published 4 August 2020

Academic Editor: Laura Martinez Maestro

Copyright © 2020 Mohanad Mousa and Yu Dong. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original workis properly cited.

Nanomechanical properties and interphase dimensions of PVA bionanocomposites reinforced with halloysite nanotubes (HNTs)and Cloisite 30B montmorillonite (MMT) were evaluated by means of peak force quantitative nanomechanical mapping(PFQNM). A three-phase theoretical composite model was established based on hard-core–soft-shell structures consisting ofhard mono-/polydispersed anisotropic particles and soft interphase and matrices. Halpin-Tsai model and Mori-Tanaka modelwere employed to predict experimentally determined tensile moduli of PVA bionanocomposites where effective volume fractionof randomly oriented nanoparticles resulted from the inclusion of interphase properties and volume fractions. Overall, it wassuggested that the estimation of elastic modulus according to effective volume fraction of nanoparticles revealed betteragreement with experimental data as opposed to that based upon their nominal volume fraction. In particular, the use ofpolydispersed HNTs and Cloisite 30B MMT clays with Fuller particulate gradation was proven to yield the best prediction whencompared with experimental data among all proposed theoretical models. This study overcomes the neglected real interphasecharacteristics in modelling nanocomposite materials with much more accurate estimation of their mechanical properties.

1. Introduction

In the last decade, polymer nanocomposites reinforced witha small amount of nanoparticles with different shapes andsizes in order to enhance multifunctional properties, costeffectiveness, and light-weight structures have become themajor focus on the innovation of material development inplastics and composite materials. In a nanocomposite sys-tem, there are commonly three major nanofiller shapesincluding nanoplatelets such as MMT clays and graphenenanoplatelets, nanotubes like carbon nanotubes (CNTs)and HNTs, and nanospheroids including zinc oxide nano-particles or nanosillica.

The material merit of using a small amount of nanopar-ticles can significantly enhance mechanical, thermal, elec-tronic, and antimicrobial properties [1–4] with decreasedgas/liquid permeability, while some key features of net

polymer systems such as low density and easy processibility[5] can still be well implemented. The applications of poly-mer nanocomposites have been widely expanded in aerospaceand aircrafts, automobile manufacturing, food packaging,and medical devices [6]. It is well recognised that an inter-phase region in the vicinity of nanofillers or nanoparticlesin polymer nanocomposites can have a dramatic propertychange from those of polymer matrices [5], which in turnplays a prevalent role in the overall enhancement of materialperformance. Interphase dimensions, volume, and propertiescan be identified as typical features, which depend primarilyon matrix-filler interaction associated with nanoparticlestructures and shapes in polymer nanocomposites [7]. Suchmatrix-filler interaction has been investigated by atomisticand coarse-grained molecular simulations [8] though thelimitation of a computational environment may often restrictsuch simulation work to single-particle or two-particle

HindawiJournal of NanomaterialsVolume 2020, Article ID 4526108, 22 pageshttps://doi.org/10.1155/2020/4526108

https://orcid.org/0000-0003-1774-1553https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2020/4526108

systems [5, 8]. The PFQNM technique has a powerful charac-terisation capability to obtain the interphase dimensions andproperties of nanocomposites based on various nanome-chanical properties including elastic modulus and adhesionof nanocomposite constituents along with correspondingdimensions [7].

In simple micromechanical modelling of compositematerials using Halpin-Tsai model [9] and Mori-Tanakamodel [10], interphase properties and features between fillersand matrices are generally neglected for simplicity. Conse-quently, the mechanical properties of polymer nanocompos-ites may be overpredicted based on such conventionalcomposite theoretical models for polymer/CNT composites[11] and silk fibroin/graphene oxide nanocomposites [12],which was consistent with the numerical simulations usingthe finite element method (FEM) based on the representativevolume element (RVE) for polyethylene (PE)/CNT nano-composites [13, 14]. On the other hand, such propertiescan also be underestimated, as evidenced by polyamide 66(PA66)/calcium carbonate (CaCO3) nanocomposites [15].This drawback can inevitably inhibit accurate micromecha-nical modelling work in polymer nanocomposite systemsowing to the typical lack of interphase properties and fea-tures. Despite many recent attempts, the incorporation ofinterphase regions as the third phase in available Mori-Tanaka model [16] andMaxwell model [17] reveals little suc-cess, arising from the simple assumption that the interphasecan be only hypothesised as a 1D transitional material phasesurrounding nanofillers with uniform interphase thicknessand regular shapes. Whereas, it has been well documentedthat an irregular-shaped interphase with nonuniform thick-ness usually occurs in real morphological structures of com-posites [7, 18].

In particular, when a real interphase effect is taken intoaccount in the modelling work of nanocomposites, inter-phase volume fraction is one of the key interphase materialparameters to be predetermined. With an additional 5 vol%of monodispersed spherical nanoparticles (particle diameter:10 nm and interphase thickness: 0.5 nm), the interphase vol-ume fraction can reach as high as 25 vol%, according toMousa and Dong [7]. When particle diameter is furtherreduced to be only nomore than 5nm, the interphase volumefraction can be increased by over 50 vol%, as opposed to thatof the particles [7]. Amraei et al. [19] established a closed-form interphase model as a function of radial distance usingRVE, which was found to have the capability of estimatingthe effective mechanical properties of polymer nanocompos-ites reinforced with spherical inclusions. For the other work,Amraei et al. [20] particularly concentrated on a closed-form micromechanical interphase model in terms of CNTdiameter and interphase thickness, as well as the mechani-cal properties of individual constituents to influence overallmechanical properties of polymer nanocomposites, indicat-ing a critical role of the interphase. Moreover, Zare and Rhee[21] developed a new model to predict the tensile modulus ofpolymer/clay nanocomposites using not only clay size andmorphology but also interfacial shear modulus in goodaccordance with experimental values for the model valida-tion. The dimensions of clay thickness and length were

revealed to be key factors for the enhancement level of nano-composite modulus. Overall, a holistic understanding for theeffect of interphase volume fraction on the elastic modulus ofbulk nanocomposites still remains challenging when consid-ering the complexity of interphase structures as well as apotential overlap to neighbouring interfacial layers.

The aim of this study lies in the systematic developmentof a novel three-phase composite theoretical model by imple-menting experimentally measured 3D interphase nanome-chanical properties in PVA bionanocomposites reinforcedwith HNTs and Cloisite 30B MMT clays as the most populartubular and platelet-like clay nanofillers, respectively. Ulti-mately, missing real interphase characteristics, often encoun-tered in conventional composite modelling approaches, canbe recounted (rather than being completely ignored) foraccurate property prediction in advanced nanocomposites.

2. Experimental Work

2.1. Materials and Fabrication Process. PVA, as a popularwater-soluble polymer with a molecular weight of 89000-98000 g/mol and a degree of hydrolysis of 99.0-99.8%, wassupplied by Sigma-Aldrich Pty. Ltd., Australia. Cloisite 30Bclays modified with methyl, tallow, bis-2-hydroxyethyl, andquaternary ammonium were purchased from Southern ClayProducts, Gonzales, TX, USA. HNTs with an outer diameterof 120-140 nm, an inner diameter of 15-100 nm, and a lengthof 0.3-1.5μm were donated by Imerys Tableware Limited,New Zealand [22].

PVA bionanocomposites reinforced with HNTs andCloisite 30B clays were synthesised using solution casting fol-lowing the same procedure mentioned in our previous study[1]. Five wt%/v PVA aqueous solution was prepared aftermixing PVA powders with deionised water at a magnetic stir-ring speed of 400 rpm and a processing temperature of 90°Cfor 3 h to warrant the complete dissolution of PVA. In a sim-ilar manner, HNTs and Cloisite 30B clay powders were alsomixed in deionised water using a mechanical mixer at405 rpm and 40°C for 2 h. Subsequently, the ultrasonicationprocess was carried out using an ultrasonicating bath (model:ELMA Ti-H-5, IKA; Germany) at an oscillatory frequency of25 kHz and a power intensity of 70% at 40°C for 1 h. Aqueoussuspensions of HNTs and Cloisite 30B clays were graduallyadded in a dropwise manner into the PVA solution bymechanical mixing in order to obtain particle contents of 0,3, 5, and 10wt%. A further sonication took place for 30minto ensure a more uniform particle dispersion. In the end,20ml mixed solution was poured on a glass petri dish andsubsequently dried in an air-circulating oven at 40°C for48 h. Finally, prepared PVA bionanocomposite films werestored in a desiccator containing silica gels for subsequentmaterial testing and characterisation.

2.2. Material Characterisation via Atomic Force Microscopy(AFM). In this study, the nanomechanical properties of theinterphase in PVA bionanocomposites were determined bymeans of peak force quantitative mapping (PFQM) in a Bru-ker Dimension FastScan AFM system to acquire a singleforce-distance curve under ambient conditions. In particular,

2 Journal of Nanomaterials

an RTESPA-525A probe (nominal spring constant: 200N/m;nominal tip radius: 8 nm; and nominal resonant frequency:525 kHz) was employed to facilitate such direct measure-ments. During the calibration process, the deflection sensi-tivity was warranted with the acquisition of a force curveon a stiff sapphire-12 surface. The spring constant wasdetermined by using a thermal tuning method [23] inwhich cantilever mechanical response to thermal agitationwas measured with the Brownian motion of encompassingfluid molecules. Imaging analysis using atomic forcemicroscopy (AFM) was carried out with the TESPA probe(normal spring constant: 40N/m; tip radius: 8 nm). Thescan rate was set up at 2Hz with a digital pixel resolutionof 256 × 256. Unwanted features including noise, bow, andtilt were removed when AFM images were first-order flat-tened using Bruker NanoScope 1.5 software. At least threeAFM samples were utilised for each material batch to war-rant the test reproducibility.

3. Modelling Approach

3.1. 3D Interphase Modulus, Surface Area, and Volume. Asmentioned earlier, interphase properties such as interphasemodulus and features like interphase surface area and vol-ume were detected via PFQM. The interphase modulibetween PVA matrices and dispersed HNTs and Cloisite30B clays in various shapes and sizes were evaluated on thebasis of a dataset associated with elastic moduli collectedfrom PVA/HNT and PVA/Cloisite 30B interphases sur-rounding 75 different particles at 25 line scan regions (LSRs),respectively.

On the other hand, 3D interphase dimensions are clas-sified as interphase width WInterphase, interphase lengthLInterphase, and interphase height HInterphase. In particular,individual interphase width W i Interphase, interphase lengthLj Interphase , and interphase height Hk Interphase along the ithtransverse plane (i = 1, 2, 3⋯ ), the jth longitudinal plane(j = 1, 2, 3⋯ ), and kth height plane (k = 1, 2, 3⋯ ),respectively, were measured using the same scanningmethod mentioned in previous literature [7] so that typicalfeatures of distinct interphases between nanoparticles andpolymer matrices could be characterised according to thegreat variation in their nanomechanical properties with theaid of PFQM.

As illustrated in Figures 1(a), 1(b), 1(e), and 1(f) forAFM imaging analysis, it is clearly shown that nanofillerdispersion took place with two typical categories of fullyembedded and partially embedded HNTs and Cloisite30B clays in PVA bionanocomposites. The 3D interphaseregion can be surrounded between the inner interface areaand the outer interface area bound by nanofillers and PVAmatrices, respectively, as evidenced in Figures 1(c), 1(d), 1(g),and 1(h). Both surface areas of outer interface SAouter interfaceand inner interface SAinner interface with respect to a wide rangeof fully and partially embedded nanoparticles denoted bysubscripts “f” and “p” can be estimated in the following byrearranging analytical equations for surface areas of aniso-tropic particles developed by [24].

SAouter interfaceð Þf = a1 + b1 L2Interphase + c1W2Interphase+ d1H2Interphase,

ð1Þ

SAouter interfaceð Þp = a2 + b2 L′2Interphase‐effective

+ c2W′2Interphase‐effective

+ d2H′2Interphase‐effective,

ð2Þ

SAinner interfaceð Þf = a3 + b3 L2p + c3W2P + d3H2P, ð3Þ

SAinner interfaceð Þp = a4 + b4 L′2p‐effective + c4W′

2p‐effective

+ d4H′2p‐effective,

ð4Þ

where under the category of partially embedded nanopar-ticles shown in Figures 1(d) and 1(h), LInterphase‐effective′ ,WInterphase‐effective′ , and HInterphase‐effective′ are the maximumlength, width, and thickness for effective interphases,whereas Lp‐effective′ , Wp‐effective′ , and Hp‐effective′ represent themaximum length, width, and thickness for effective nanopar-ticles (excluding the nanoparticle portions without an inter-phase to PVA matrices in bionanocomposites). The rest ofthe letters ai, bi, ci, and di (i = 1, 2, 3, and 4) denote empiricalconstants determined by curve fitting with correspondingexperimental data of the surface areas obtained from AFMmeasurements (see more details in Supporting Information(available here)).

Additionally, with the supply of the aforementioned sur-face area data in equations (1)–(4), nanoparticle/interphasevolume Vp/Interphase and nanoparticle volume Vp for fullyembedded nanoparticles, as well as effective nanoparticle/in-terphase volume Vp/Interphase‐effective and effective nanoparticlevolume Vp‐effective for partially embedded nanoparticles canbe further determined according to the modified equationsderived from Behmer and Hawkins [24]:

SAouter interfaceð Þf = ℯ1Vf1p/Interphase, ð5Þ

SAouter interfaceð Þp = ℯ2Vf2p/Interphase‐effective, ð6Þ

SAinner interfaceð Þf = ℯ3V f3p , ð7Þ

SAinner interfaceð Þp = ℯ4Vf4p‐effective: ð8Þ

In a similar manner, empirical constants ei and f i(i = 1, 2, 3, and 4) can also be determined using a curve-fitting scheme with the experimental data of correspondingvolumes via AFM, as given in Supporting Information.

Finally, interphase volume V Interphase in relation to fullyand partially embedded nanoparticles in PVA bionanocom-posites depicted in Figure 1 is given by

V Interphase� �

f =Vp/Interphase −Vp, ð9Þ

V Interphase� �

p =Vp/Interphase‐effective −Vp‐effective: ð10Þ

3Journal of Nanomaterials

Partially embeddedHNT

Fully embeddedHNT

9.4 nm

1.65 nm

(a)

Partially embeddedHNT

Fully embeddedHNT

100 100200

300400 nm

200300

400 nm

1.65 nm9.4 nm

(b)

PVA matrices

Interphase

HNT

Inner interface

Outer interface

(c)

PVA matrices

HNT

Effective interphase

Inner interfaceOuter interface

(d)

Fully embeddedCloisite 30B

Partially embeddedCloisite 30B

5.6 nm

1.8 nm

(e)

100

50

10050 150300250200

150

200

250

1.8 nm

300.0 nm

5.6 nm Fully embeddedCloisite 30B

Partially embeddedCloisite 30B

(f)

PVA matrices

Interphase

Cloisite 30B

Inner interface

Outer interface

(g)

Cloisite 30B

PVA matrices

Effective interphase

Inner interfaceOuter interface

(h)

Figure 1: AFM height images of PVA bionanocomposites reinforced with fully embedded and partially embedded HNTs in (a) 2D view and(b) 3D view as well as corresponding proposed schematic diagrams (c and d). AFM height images of PVA bionanocomposites reinforced withfully embedded and partially embedded Cloisite 30B clays in (e) 2D view and (f) 3D view as well as corresponding proposed schematicdiagrams (g and h).


3.2. Interphase Volume Fraction. Interphase volume fraction∅Interphasecan be estimated using a nearest-surface distribu-tion theory [25] where composite media consist of 3D rigidanisotropic particles and voids (see Appendix A for moredetails). In a typical nanocomposite system, uniformly dis-persed nanoparticles with relatively similar sizes are knownas monodispersed nanoparticles as opposed to polydispersednanoparticles where more randomly dispersed nanoparticlesoccur with different sizes and diameters [26]. With respect toa monodispersed particle system, interfacial volume fraction∅Interphasecan be estimated as follows (see more details inAppendix A)

∅Interphase = 1 −∅p� �(

1 − exp"−6∅pλ

3

1 −∅p

"1Sλ2

+1λ

2 +3∅p

S2 1 −∅p� �

" #+43+

4∅pS 1 −∅p� �

+4m∅2p

3S3 1 −∅p� �2

##),

ð11Þ

where λ = t ′/Deq is the geometric size of anisotropic particlesin which t ′ is the interfacial dimension and Deq is a diameterof a sphere with the same volume of an anisotropic particle.∅p is the nominal volume fraction of nanofillers.m is consid-ered a parameter used for the theoretical estimation of aradial distribution function in a spherical particle system.In this study, m = 2 has been employed according to theCarnahan-Starling approximation [27]. Here, S is a morpho-logical descriptor of anisotropic particles in terms of theiraspect ratio α calculated based on the following:

S =1 + 1:5αð Þ2/3

1 + α: ð12Þ

As far as a polydispersed particle system is concerned, theimpact of particle size distribution (PSD) is critical on boththe interphase volume fraction and the reinforcement effi-ciency of nanocomposite systems. The gradation of irregularaggregates can be experimentally evaluated with the aid of asieve analyser or laser particle analyser in which each irregu-lar aggregate size is assessed relative to a correspondingspherical particle of equivalent size [28]. When an equivalentdiameter is determined, the PSD of spherical particles can betransformed into that of anisotropic particles accordingly[29]. Our study focuses on two particulate gradations,namely, the Fuller gradation [30] and the equal volume frac-tion (EVF) gradation [29, 30] in order to estimate the∅Interphase given as follows:

∅Interphase = 1 −∅p� �

1 − exp −6∅pD3eqD E e′t + d′t3 + g′t3� �

24

35

8<:

9=;,

ð13Þ

e′ =D2eqD E

S 1 −∅p� � , ð14Þ

d′ =2 Deq� �1 −∅p

+3∅p D2eq

D E2S2 1 −∅p� �2 D3eqD E , ð15Þ

g′ = 43 1 −∅p� � + 4∅p Deq

� �D2eqD E

S 1 −∅p� �2 D3eqD E

+4m∅p D2eq

D E33S3 1 −∅p� �3 D3eqD E2 ,

ð16Þ

DkeqD E

=ðDmax eqDmin eq

Dkeq f N Deq� �

dDeq, ð17Þ

f N Deq� �

=−q

D−qmax eq −D−qmin eq

� �Dq+1eq

�q = 2:5⟶ Fuller gradation

q = 3:0⟶ EVF gradation

(,

ð18Þ

where f NðDeqÞ is a number-based probability function ofanisotropic particles. hDkeqi, Deq‐min, and Deq‐max are the kthmoment and the minimum and maximum equivalent diam-eters of the anisotropic particles. Finally, the aforementionedparameters to calculate ∅Interphase can then be measured foreach nanoparticle based on AFM experimental data. Formore detailed derivations of ∅Interphase, one can refer toAppendix A.

3.3. Micromechanical Model Based on Nominal and EffectiveVolume Fractions. The prediction of the elastic moduli of aunidirectionally or randomly distributed filler-reinforcedcomposite is generally achieved by using conventional com-posite theoretical models such as Halpin-Tsai model [9] orMori-Tanaka model [10]. In particular, the elastic moduliof our PVA biocomposites in Halpin-Tsai model accordingto different nanofiller orientation states, namely, randomlyoriented and parallel (or well-aligned) nanofillers, can berepresented by Erandom and Eparallel, respectively, using thefollowing:

Erandom = Em38

1 + ηLξ∅p1 − ηL∅p

!+58

1 + 2ηT ∅p1 − ηT∅p

!" #, ð19Þ

Eparallel = Em1 + ηLξ∅p1 − ηL∅p

" #, ð20Þ

ηL =Ep/Em� �

− 1Ep/Em� �

+ ξ, ð21Þ


ηT =Ep/Em� �

− 1Ep/Em� �

+ 2, ð22Þ

ξ =2α3

=2ıp3tp

, ð23Þ

∅p =Wp

Wp + ρp/ρm� �

1 −Wp� � , ð24Þ

where Em and Ep are Young’s moduli of PVA matrices andnanoparticles (i.e., HNTs and Cloisite 30B clays), accord-ingly. lp and tp refer to the length and thickness of nanopar-ticles. Øp and Wp are nominal volume fraction and weightfraction of nanofillers in PVA bionanocomposites, respec-tively, while ρp and ρm are the densities of nanoparticlesand PVA.

Furthermore, Mori-Tanaka model is an effective theoret-ical model to predict the elastic moduli of polymer compos-ites, which is also employed in modelling our PVAbionanocomposites. It was originally employed by TandonandWeng [31] using Mori-Tanaka theory [10] and Eshelby’ssolution [32] to derive a complete analytical solution for cal-culating the elastic moduli of an isotropic matrix containingaligned spheroidal inclusions. Longitudinal and transversemoduli of polymer composites ðE11Þ and ðE22Þ can be exper-essed as follows:

E11Em

=1

1 +Øp Α1 + 2νmΑ2ð Þ/A, ð25Þ

E22Em

=1

1 +Øp −2νmΑ3 + 1 − νmð ÞΑ4 + 1 + νmð ÞΑ5Αð Þ/2Α,

ð26Þwhere νm is Poisson’s ratio of polymer matrices and Αi(i = 1‐5) and A are the functions of Eshelby’s tensors andproperties of the matrices and fillers such as Young’s moduli,Poisson’s ratio, aspect ratio, and volume fraction of fillers.When fillers are inclined to more random orientation, theelastic modulus of composites can be further predicted byusing a combination of the laminate theory [33] and Mori-Tanaka model given by

Ec ≅ 0:375E11 + 0:625E22: ð27Þ

In a nanocomposite system, large specific surface areas ofnanofillers yield more amounts of polymeric molecularchains to attach to nanofiller surfaces resulting in more effec-tive interphases of nanocomposites. Accordingly, the nomi-nal volume fraction of nanofillers may be altered whenreinforced within polymer matrices in nanocomposite sys-tems. It has been proven that the effective volume fractionof nanofillers ∅p′ is more applicable instead for accurateproperty estimation in modelling work using the following[32, 34, 35]:

∅p′ =Øp 1 + kxRgΑΤρp� �

, ð28Þ

where Rg is the radius gyration of a polymer, while ATis the specific surface area of nanofillers. The layer thicknessof absorbed polymeric chains in nanoparticles is xRg, whichmeans increasing up to x times of Rg. The alteration of kxdepends on interfacial interaction levels between polymermatrices and nanoparticles in different nanocomposite sys-tems. Additionally, the dynamic behaviour of polymericchains near an attractive interface may vary from that of abulk polymer phase and the effect of attractive surfaces cantake place for distances larger than Rg for polymers [36].The term of kx can be reconsidered based on the following[31, 33]:

kx =EmEp

tRg

!, ð29Þ

where t is regarded as the thickness of adsorbed layers.The effective volume fraction of nanofillers ∅p′ in

PVA/HNT bionanocomposites can be determined usingequation (28) in a general form. However, in polymer/plate-lete nanocomposites, ∅p′ should depend on intercalation andexfoliation levels of platelet-like nanofillers taking placewithin polymer matrices. With respect to clay intercalatedstructures in nanocomposites [31], ∅p′ can be calculatedusing the following derived equation:

1∅p′

= 1 +ρp′ 1 −Wp′ −Wp′Wp″s� �

d1 N − 1ð Þ + h½ �Wp′ρm d2 N − 1ð Þ + h½ �

, ð30Þ

where ρp′ is referred to as the clay density, Wp′ is the weightfraction of clays in nanocomposites, and Wp″ is the weightfraction of clay platelets within clays. s is the polymer uptakein a general expression s = ð1 −WipÞ/Wip to represent themass of polymer matrices swollen into the unit mass of inter-calated clays, where Wip is the weight fraction of intercalatedclay structures. d1 and d2 are basal plane spacing values of as-received clay particles and intercalated clays in nanocompos-ites, respectively. N and h are the average layer number perstack and thickness of a single platelet, respectively.

In the case of exfoliated clay structures in nanocompos-ites where individual clay platelets are dispersed homoge-neously in polymer matrices with an adsorption effect, ∅p′can be calculated according to equation (28) in a rewrittenform below:

∅p′ =Øp 1 + kxRgΑΤpρp″� �

, ð31Þ

where ΑΤp is the total surface area and ρp″ is the density ofsingle clay platelets by replacing AT and ρp accordingly inequation (28).


3.4. Volume Fraction of Nanofillers with Interphase Effect.The interphase features and properties are essential in ananocomposite system, which is often ignored in conven-tional modelling work. The interphases in PVA bionano-composites generally have nonuniform dimensions andcritical nanomechanical properties to significantly influencenanofiller-matrix interactions. For example, by increasingthe interphase volume from 2988 to 4363 nm3 in PVA/nano-diameter bamboo charcoal (NBC) bionanocomposites, theirinterphase modulus was found to be remarkably enhancedfrom 34.67 to 49.91GPa (i.e., an increase by 44%) [7]. Conse-quently, the application of 3D interphase features such asinterphase size and volume fraction to predict the elasticmodulus of polymer nanocomposites may yield a more reli-able modelling approach to estimate bulk nanocompositeproperties according to their nanomechanical behaviour.

Apparently, the volume fractions of nanoparticles andinterphase ∅p and ∅Interphase in a nanocomposite systemcan be expressed as follows:

∅p =VpVc

, ð32Þ

∅Interphase =V Interphase

Vc, ð33Þ

where Vc and V Interphase are the volumes of nanocompositesand interphase, respectively. In this case, Vp and V Interphasecan be estimated by using equations (7) and (9) accordingly.

B1 A1

200

200

400

400

600

600800

800 nm

16.4 GPa58.0 GPa

(a)

0 4 8 12 16 20

20

25

30

35

40

45

50

55

PVA zone HNT zoneInterphase zone

Elas

tic m

odul

us (E

) (G

Pa)

Scan distance (Sd) (nm)

A1 B1

(b)

100

200

200

100

300

300400 nm

400 nm

11.9 GPa

56.5 GPa

(c)

0 10 20 30 40

20

25

30

35

40

45

50

55

PVA zone Interphase zone Cloisite 30B zone

Elas

tic m

odul

us (E

) (G

Pa)

Scan distance (Sd) (nm)

B2A2

(d)

Figure 2: 3D AFM mapping images and corresponding typical profile of elastic modulus in PVA/3wt% HNT bionanocomposites (a and b),as well as PVA/3wt% Cloisite 30B clay bionanocomposites, respectively. A1B1 and A2B2 are the corresponding typical cut sections for scandistance Sd.


By rearranging equations ((32)) and ((33)), they yield anew proposed equation based on the interphase featuresshown as follows:

∅p =∅InterphaseVpV Interphase

, ð34Þ

where ∅Interphase can be determined according to the theoryof the nearest-surface function [25] elaborated in Section 3.2.

4. Results and Discussion

4.1. Elastic Properties of Interphase. As seen from Figure 1,both HNTs and Cloisite 30B clays when dispersed intoPVA matrices in bionanocomposites presented two similar

nanoparticle-embedding effects, namely fully embeddedand partially embedded formations. When nanoparticlesare fully embedded into continuous matrices, a full inter-phase configuration is manifested in Figures 1(c) and 1(g),while an effective interphase (also known as partial inter-phase without the consideration of noninteracting nanopar-ticle portions) is generally applied under the scenario ofpartial embedding in Figures 1(d) and 1(h) leading to differ-ent levels of filler-matrix interaction and reinforcement effi-ciency to impact the interphase modulus.

Furthermore, as a typical case, the AFM images and pro-files of the elastic modulus for PVA/HNT bionanocompo-sites and PVA/Cloisite 30B clay bionanocomposites at ananofiller content of 3wt% are depicted in Figure 2. Thefinal interphase modulus was determined by using the bestcurve fitting to discrete modulus datasets based on 25

0.2

0.4

0.6

0.8

1.0 𝜇m

0.20.4

0.60.8

1.0 𝜇m

9.0 nm

(a)

0 20 40 60 80 100

1

2

3

4

5

6

9.2

nm

18.7

nm

6.5

nm

HNT PVA

Hei

ght (

nm)

Scan distance (nm)

InterphaseInterphasePVA

A3 B3

(b)

100

100

200

200

300

300

400 nm

400 nm

0.1 nm3.0 nm

(c)

0 20 40 600.0

0.4

0.8

1.2

1.6

2.0 10.2

nm

31.2

nm

8.4

nm

2.4 Cloisite 30B

Hei

ght (

nm)

Scan distance (nm)

PVA PVA InterphaseInterphase

B4A4

(d)

Figure 3: 3D AFM height mapping images and typical height profiles of PVA/3wt% HNT bionancomposites (a and b) and PVA/3wt%Cloisite 30B clay bionanocomposites (c and d), respectively. A3B3 and A4B4 are the corresponding typical cut sections for scan distance.


representative line scan regions (LSRs) illustrated inFigure S9 in Supporting Information. Overall, the inter-phase modulus demonstrated an almost linearly increasingtrend with a modulus-gradient effect in terms of scandistance except for the interphase boundary regions aroundnanoparticles and PVA matrices regardless of additionalHNTs and Cloisite 30B clays in PVA bionanocomposites.In comparison, the interphase modulus of PVA/Cloisite30B clay bionanocomposites was increased from 20:6 ± 3:4GPa near PVA matrices to 41:6 ± 4:6GPa surroundingnanoclays as opposed to the variation of the interphasemodulus in the range from 22:2 ± 2:9 to 43:4 ± 3:1GPa inPVA/HNT bionanocomposites accordingly (Figures 2(b)and 2(d)). However, the interphase moduli measured forPVA bionanocomposites in this study were less than those

of silk fibroin (SF)/graphene oxide (GO) nanocomposites inthe range of approximately 10-250GPa [12] as well as thoseof epoxy/T300 carbon nanocomposites between 23 and90GPa [17]. Such variations in the interphase modulus aswell as the modulus-gradient effect in the interphase zonesfrom nanoparticles to polymer matrices may be associatedwith the gradient number of hydrogen bonding fromnanofiller surfaces to polymer matrices, which is believed toplay an important role in tailoring the mechanical propertiesof polymer nanocomposites [37, 38]. In a similar manner,Amraei et al. [19, 20] also identified interphase transitionalzones with the continuous variations of elastic modulusbetween the inclusions and matrices with the assumption ofa perfect bonding effect in terms of radial distance of RVE ina nanocomposite system.

17.5 nN5.6 nN

1.0 𝜇m

0.8

0.6

0.4

0.2

0.20.4

0.60.8

1.0 𝜇m

(a)

0 20 40 60 80 100

89

10111213141516171819

PVA HNT

Adh

esio

n (n

N)

Scan distance (nm)

InterphaseInterphase

A5 B5

6.5

nm

18.7

nm

9.2

nm

PVA

(b)

17.8 nN6.0 nN

400 nm

300

400

200

100

300200

100

(c)

0 20 40 60 80

89

10111213141516171819

Cloisite 30B PVA

8.4

nm

31.2

nm

10.2

nm

Adh

esio

n (n

N)

Scan distance (nm)

PVA InterphaseInterphase

A6 B6

(d)

Figure 4: 3D AFM adhesion mapping images and typical adhesion profiles of PVA/3wt% HNT bionanocomposites (a and b) andPVA/3wt% Cloisite 30B clay bionanocomposites (c and d), respectively. A5B5 and A6B6 are the corresponding typical cut sections for scandistance.


200 40 60 80 1000

2

4

6

8

10

t Int

erph

ase (

nm)

DHNT (nm)

(a)

500 100 150 200 2500

50

100

150

200

250

LInterphase-max = −6 + 0.77 LHNT

R2 = 0.77

LHNT (nm)

LIn

terp

hase

-max

(nm

)

(b)

20 400 60 80 100

4

8

12

16

20R2 = 0.68

WIn

terp

hase

-max

(nm

)

WInterphase-max = 0.91 + 0.16 DTHNT

DTHNT (nm)

(c)

20100 30 40 50 60 70 80 90

22

24

26

28

30

DLHNT (nm)

HIn

terp

hase

-max

(nm

)HInterphase-max = 28–0.097 DLHNTR2 = 0.87

(d)

3 6 9

3

6

9

12

00

t Int

erph

ase (

nm)

tCloisite 30B (nm)

(e)

20 40 60 80 100 120 1400

50

100

150

200

0

LInterphase-max = −15.9 + 1.1 LCloisite 30B

R2 = 0.75

LIn

terp

hase

-max

(nm

)

LCloisite 30B (nm)

(f)

Figure 5: Continued.


4.2. Interphase Dimensions. The elastic properties of inter-phases in composite materials generally vary to a differentextent when surrounded with individual particles or fillersin diverse sizes and shapes, thus resulting in the great changeof interphase dimensions. Interphase dimensions can beclearly specified according to the variation identified in termsof height and adhesion profiles in PVA bionanocompositesreinforced with 3wt% HNTs and Cloisite 30B clays, asdepicted in Figures 3 and 4, respectively. Interphase thicknesswas determined to be 6.5 and 9.2 nm on both sides of HNTsas opposed to corresponding relatively large dimensions of8.4 and 10.2 nm on those of Cloisite 30B clays, whichappeared to be consistent in view of both height and adhesionprofiles. Moreover, the tip adhesion to PVA matrices wasdetected to be approximately 14:24 ± 2:31 nN and becamegreater than those of HNTs and Cloisite 30B clays at 8:6 ±1:08 and 8:4 ± 1:1 nN, respectively. As clearly seen, the adhe-sion force of PVA matrices was much greater than those forHNTs and Cloisite 30B clays, which could be explained bymore hydroxyl groups identified in PVA when compared tothose of HNTs and Cloisite 30B clays.

Overall, interphase dimensions of PVA bionanocompo-sites reinforced with HNTs and Cloisite 30B clays revealedvery similar tendencies in terms of interphase thicknesstInterphase, maximum interphase length LInterphase‐max , maxi-mum interphase width WInterphase‐max, and maximum inter-phase height HInterphase‐max from a 3D point of viewdisplayed in Figure 5. In particular, tInterphase appeared to beindependent of the HNT diameter (DHNT) and platelet thick-ness of Cloisite 30B (tCloisite 30B), respectively (Figures 5(a) and5(e)). Nonetheless, both LInterphase‐max and WInterphase‐max

increased in a linear manner as a function of HNT lengthLHNT andHNT transverse diameterDTHNT in PVA/HNT bio-nanocomposites, as well as Cloisite 30B clay platelet lengthLCloisite 30B and width WCloisite 30B accordingly in Figures 5(b),5(c), 5(f), and 5(g) despite opposite linearly decreasing trendstaking place in HInterphase‐max in terms of HNT longitudinaldiameter DLHNT and HCloisite 30B depicted in Figures 5(d) and5(h). Such a phenomenon can be ascribed to an increase inthe contact surface areas between continuous polymer matri-ces and more dispersed nanoparticles in a nanocomposite sys-tem especially when nanoparticles are fully embedded orcovered by surrounding matrices [6]. Increasing DLHNT orHCloisite 30B could make it difficult for nanofillers to be fullyembedded within polymer matrices, thus resulting in thereduction in HInterphase‐max.

As demonstrated in Figure 1 for the proposed mecha-nism models in terms of nanofiller dispersion and particle-matrix interaction, it is worthwhile investigating these twotypical scenarios, namely the fully and partially embeddednanoparticles with PVA matrices in bionanocomposites forthe assessment of their interphase modulus. The formerapparently yields more effective interphases around eachside of nanoparticles (i.e., full coverage of nanoparticlesby interphases), which is generally deemed as a good rep-resentation of effective load transfer from matrices andnanofillers, while the latter gives rise to less pronouncedinterphase effectiveness since some remarkable portionsof nanoparticles were detected to be free of contact withPVA matrices, further reducing effective interfacial regions.In this study, the interphase surface area SAInterface and inter-phase volume V Interphase were characterised as two critical

0 20 40 60 80 100 1200

40

80

120

160

WInterphase-max = −3.1 + 0.95 WCloisite 30B

R2 = 0.76

WIn

terp

hase

-max

(nm

)

WCloisite 30B (nm)

(g)

0.0 2.5 5.0 7.5

2.5

5.0

7.5

10.0

HInterphase-max = 7.9–0.57 HCloisite 30B

R2 = 0.79

HIn

terp

hase

-max

(nm

)

HCloisite 30B (nm)

(h)

Figure 5: Correlation between maximum interphase dimensions and nanofiller dimensions of PVA/HNT bionanocomposites andPVA/Cloisite 30B clay bionanocomposites: (a) tInterphase vs. DHNT, (b) LInterphase−max vs. LHNT, (c) WInterphase−max vs. DTHNT, (d)HInterphase−max vs. DLHNT, (e) tInterphase vs. tCloisite 30B, (f) LInterphase−max vs. LCloisite 30B, (g) WInterphase−max vs. WCloisite 30B, and (h) HInterphase−maxvs. HCloisite 30B. tInterphase is interphase thickness, and DHNT is HNT diameter. LInterphase−max ,WInterphase−max, and HInterphase−max are maximuminterphase length, width, and height, respectively. LHNT, DLHNT, and DTHNT are the length, longitudinal diameter, and transverse diameterof HNTs while LCloisite 30B, WCloisite 30B, and tCloisite 30B are the length, width, and thickness of Cloisite 30B clay platelets.


interphase dimensional parameters to evaluate the impactson interphase modulus EInterphase with respect to fully or par-tially embedded nanoparticles in PVA bionanocomposites(Figure 6). In addition, SAInterface is further divided intoSAinner interface and SAouter interface when considering the innerinterfaces between nanoparticles and interphase regions, aswell as outer interfaces between the interphase regions andPVA matrices, respectively, as illustrated in Figures 1(c),1(d), 1(g), and 1(h). A very identical behaviour occurred in

PVA/HNT bionanocomposites and PVA/Cloisite 30B claybionanocomposites, which indicated that overall EInterphasetended to be consistently enhanced in a nonlinear mannerwith increasing SAInterface and V Interphase individually. Moreconsistently, fully embedded HNTs and Cloisite 30B claysyielded higher EInterphase as opposed to those based on par-tially embedded counterparts. Besides, SAinner interface led torelatively high overall EInterphase as opposed to those basedon corresponding SAouter interface. As mentioned earlier by

1500 3000

15

30

45

Inner interface-fully embedded HNTInner interface-partially embedded HNTOuter interface-fully embedded HNTOuter interface-partially embedded HNT

Inte

rpha

se m

odul

us (E

Inte

rpha

se) (

GPa

)

SAInterphase (nm2)

(a)

1500 3000 4500

25

50

Inte

rpha

se m

odul

us (E

Inte

rpha

se) (

GPa

)

Inner interface-fully embedded Cloisite 30BInner interface-partially embedded Cloisite 30BOuter interface-fully embedded Cloisite 30BOuter interface-partially embedded Cloisite 30B

SAInterphase (nm2)

(b)

0 2000 4000 6000 80000

15

30

45

Fully embedded HNTPartially embedded HNT

VInterphase (nm3)

Inte

rpha

se m

odul

us (E

Inte

rpha

se) (

GPa

)

(c)

0 2000 4000 6000 80000

20

40

Fully embedded Cloisite 30BPartially embedded Cloisite 30B

Inte

rpha

se m

odul

us (E

Inte

rpha

se) (

GPa

)

VInterphase (nm3)

(d)

Figure 6: Relationships between interphase modulus EInterphase and interphase surface area SAInterphase: (a) PVA/HNT bionanocomposites and(b) PVA/Cloisite 30B clay bionanocomposites. Relationships between interphase modulus EInterphase and interphase volume V Interphase: (c)PVA/HNT bionanocomposites and (d) PVA/Cloisite 30B clay bionanocomposites.


Liu et al. [39], the interphase region with a modulus gradienteffect can be divided into two different zones comprising thefirst zone in contact with nanoparticle areas with relativelyhigh interphase density as opposed to the second zone adja-cent to matrix regions. Fan et al. [40] reported that increas-ing interphase density certainly induced the modulusincrease in a nanostructure-specific hierarchy in good accor-dance with our higher EInterphase in the case of SAinner interfacein PVA bionanocomposites. The abovementioned resultsmay suggest that SAInterface and V Interphase as typical 2D and3D interphase dimensional parameters can play a vital rolein the improvement of EInterphase leading to the furtherenhancement in mechanical properties of PVA bionano-composites. Nevertheless, it is also admittedly mentionedhere that partially embedded nanoparticles with the imper-fect bonding effect within PVA matrices are inevitably detri-mental to their mechanical properties with much lessbonded matrix-filler interactions when compared with fullyembedded counterparts.

On the other hand, the aspect ratio is used as animportant factor to evaluate the reinforcement efficiencyof nanofillers within polymer matrices in nanocomposites.Its determination becomes much easier when dealing withnanofillers with regular sizes and shapes. However, irregularnanofillers with different shapes are quite common leading tothe complexity of real aspect ratios due to the effect of multi-stage dispersion processing techniques generally used in themanufacture of nanocomposites [25, 26]. Moreover, in addi-tion to the nanofiller aspect ratio, interphase dimensions andproperties can also be affected by nanofiller dispersion [26].Liu and Brinson [5] as well as Alishahi et al. [41] suggestedthe use of interphase volume per unit nanofiller volume(V Interphase/Vnanofiller) in theoretical modelling as an effectiveparameter in promoting the reinforcement efficiency of

nanofillers instead of V Interphase, whose relationship as afunction of Vnanofiller was presented in Figure 7 in this study.Overall, an increase in Vnanofiller caused a significant decreasein V Interphase/Vnanofiller for both PVA bionanocompositesdespite being more pronounced in PVA/Cloisite 30B claybionanocomposites. This is because Cloisite 30B clay plate-lets induced more efficient planar reinforcements whencompared to predominant longitudinal reinforcement oftubular HNTs.

4.3. Particle Debonding. With an increase in nanoparticleloading, interparticle spacing appeared to be smaller andnanoparticles tended to be interconnected with neighbouringcounterparts side by side with some nanoparticles free ofcontact with PVAmatrices in bionanocomposites. Moreover,a closely compacted joint particle-to-particle pattern mayinduce adverse phase separation resulting in scattered loadtransfer from PVAmatrices to nanoparticles. It was evidentlyshown in Figures 8(a) and 8(c) that large HNT aggregatesand clustered stack-up Cloisite 30B clays took place at a veryhigh nanofiller content up to 10wt% in PVA bionanocom-posites with the resulting weak interfacial bonding forparticle-matrix interactions. Two narrow zones near inter-phase regions were highlighted with a sharp decline in elasticmodulus for both PVA bionanocomposites with excessiveamounts of undispersed nanoparticles in Figures 8(b) and8(d), indicating an existing particle debonding effect withpolymer matrices [36]. A lower interphase modulus mayalso arise from a relatively low density near interphase zonesas compared to those of aggregated nanoparticles and poly-mer matrices [24]. In addition to nanoparticle sizes anddimensions, nanoparticle dispersion within continuousmatrices is also among the key factors in controlling theinterfacial bonding between fillers and matrices. When

0 2000 4000 6000 8000 10000

1.2

1.4

1.6

VIn

terp

hase

/Vna

nofil

ler

Vnanofiller (nm3)

PVA/Cloisite 30BPVA/HNT

Figure 7: Interphase volume per unit nanofiller volume (V Interphase/Vnanofiller) as a function ofVnanofiller in PVA bionanocomposites reinforcedwith HNTs and Cloisite 30B clays.


excessive amounts of HNTs and Cloisite 30B clays weredispersed within PVA matrices, those nanoparticles tendedto agglomerate owing to their weak Van der Waals inter-actions, while higher nanofiller content inevitably led toa significant reduction in interparticle spacing to hinderuniform nanoparticle dispersion [42, 43]. A nanofiller finedispersion method such as ultrasonication [41], on theother hand, may give rise to the possible damage of nano-particle structures especially at the high ultrasonic powerintensity resulting instead in declined mechanical proper-ties of bionanocomposites.

4.4. Prediction of Elastic Moduli of PVA Bionanocomposites.The prediction of the elastic moduli of PVA bionanocom-posites reinforced with HNTs and Cloisite 30B clays as afunction of nominal and effective volume fractions of nano-particles was presented in Figure 9 (without predefined par-ticle systems) and Figure 10 (with monodispersed andpolydispersed particle systems), respectively, using Halpin-Tsai model, Mori-Tanaka model, and a combination of

Mori-Tanaka model and laminate theory [4] along withassociated modelling parameters listed in Table 1. In bothbionanocomposites (without predefined particle systems),the estimated moduli did not coincide well with correspond-ing experimental data even at the very low volume fractionsof HNTs and Cloisite 30B clays, Figure 9. However, the useof an effective volume fraction and a randomly oriented dis-persion state of nanoparticles consistently gave rise to muchcloser correlation with experimental data regardless of thecomposite theoretical models implemented, as also con-firmed in previous studies [34, 35]. In particular, with respectto PVA/Cloisite 30B clay bionanocomposites, the predictedresults appeared to be in better agreement with experimentaldata at the low volume fraction of 0.061 vol% on the basis ofan effective volume fraction and exfoliated clay structures,while better correlation was manifested for those predictedin terms of effective volume fraction and intercalated claystructures at high volume fraction levels. As far as morpho-logical structures are concerned, it was expected that themajority of the Cloisite 30B clay platelets tended to be more

B7

130.0 nm

5.2 nm

A7

(a)

A7B7

0

10

50

40

20

30

0.0 0.5 3.02.52.01.51.0Scan distance (𝜇m)

Elas

tic m

odul

us (E

) (G

Pa)

Debonding Debonding

(b)

118.6 nn

15.3 nm

(c)

B8A8

Scan distance (nm)

Debonding Debonding

40

30

20

10

0

Elas

tic m

odul

us (E

) (G

Pa)

50

0 800600400200

(d)

Figure 8: AFM height mapping images and corresponding typical elastic modulus profiles of (a and b) PVA/10wt% HNTbionanocomposites, as well as (c and d) PVA/10wt% Cloisite 30B clay bionanocomposites indicating phase separation and agglomerationof nanoparticles, respectively. A7B7 and A8B8 are corresponding typical cut sections for scan distance.


exfoliated at low volume fractions as opposed to predomi-nant intercalated structures with an increase in their volumefraction, which further confirmed a mix of exfoliated andintercalated structures taking place in PVA/Cloisite 30B claybionanocomposites. The major drawback in using conven-tional Halpin-Tsai model and Mori-Tanaka model lies intheir common assumption that both nanofillers and polymer

matrices in nanocomposites are linearly elastic and isotropicmaterials with uniform nanofiller dispersion and the neglectof particle-particle interactions [44]. Generally speaking, iso-tropic nanoparticles are in possession of very large specificsurface areas on which a substantial amount of molecularchains of polymer matrices can be absorbed with the aid ofhydrogen bonding or electrostatic forces, resulting in the

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

kx = 0.1

H-T nominal (parallel)Experimental

H-T nominal (random)H-T effective (random)

EPV

A/H

NT (

GPa

)

Volume fraction of HNT (vol%)

(a)

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

ExperimentalM-T nominal (parallel)M-T nominal (random)

M-T-L nominal M-T-L (effective)

EPV

A/H

NT (

GPa

)


kx = 0.1

(b)

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

7.5

H-T nominal (parallel)ExperimentalH-T nominal (random)H-T effective (random-intercalated) H-T effective (random-exfoliated)

EPV

A/C

loisi

te 3

0B (G

Pa)

Volume fraction of Cloisite 30B (vol%)

kx = 0.12

(c)

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

7.5

ExperimentalM-T nominal (parallel)M-T nominal (random)M-T-L nominalM-T-L (effective-intercalated) M-T-L (effective-exfoliated)

EPV

A/C

loisi

te 3

0B (G

Pa)


kx = 0.12

(d)

Figure 9: Prediction of the elastic moduli of PVA/HNT bionanocomposites: (a) Halpin-Tsai model (H-T) and (b) Mori-Tanakamodel (M-T)and the combination of Mori-Tanaka model and laminate theory (M-T-L). Prediction of the elastic moduli of PVA/Cloisite 30B claybionanocomposites: (c) Halpin-Tsai model (H-T) and (d) Mori-Tanaka model (M-T) and the combination of Mori-Tanaka model andlaminate theory (M-T-L).


formation of interphase layers in nanocomposites. Conse-quently, such interphase layers behave as solid transitionalmaterial phases to restrict the mobility of other molecularchains of matrices, thus contributing positively to the totalvolume of reinforcements [31, 34]. This suggested that com-posite theoretical models in this study should use effective

volume fraction instead of nominal volume fraction for bet-ter accuracy of modelling work.

Although as mentioned earlier, the implementation of aneffective volume fraction can lead to a more accurate estima-tion of experimental data in PVA bionanocomposites, thelayer thickness of polymeric molecules absorbed onto

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

7.5

H-T effective-mono (random) H-T effective-Fuller (random) H-T effective-EVF (random)ExperimentalH-T nominal (random)

EPV

A/H

NT (

GPa

)


(a)

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

EPV

A/H

NT (

GPa

)


M-T-L effective-mono (random)M-T-L effective-Fuller (random)M-T-L effective-EVF (random)ExperimentalM-T-L nominal (random)

(b)

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

EPV

A/C

loisi

te 3

0B (G

Pa)


H-T effective-mono (random) H-T effective-Fuller (random) H-T effective-EVF (random)ExperimentalH-T nominal (random)

(c)

0.00 0.05 0.10 0.15 0.20 0.251.5

3.0

4.5

6.0

7.5

EPV

A/C

loisi

te 3

0B (G

Pa)


M-T-L effective-mono (random)M-T-L effective-Fuller (random)M-T-L effective-EVF (random)ExperimentalM-T-L nominal (random)

(d)

Figure 10: Prediction of the elastic moduli of PVA/HNT bionanocomposites: (a) Halpin-Tsai model (H-T) and (b) the combinationof Mori-Tanaka model and laminate theory (M-T-L). Prediction of the elastic moduli of PVA/Cloisite 30B clay bionanocomposites:(c) Halpin-Tsai model (H-T) and (d) the combination of Mori-Tanaka model and laminate theory (M-T-L).


nanofiller surfaces in terms of kx may vary even in the samegrade of polymers with different molecular structures andpolarities [32, 34]. Our aforementioned results demonstratedthat interphase features actually did not possess a uniforminterphase layer thickness, and the interphase dimensionsand properties could vary significantly when embedded withheterogeneous nanoparticles with different particle sizes anddimensions, as well as diverse nanomechanical propertiesdepending on matrix-filler interactions. As a result, inter-phase volume fraction ∅Interphase was incorporated into twodifferent particle systems, namely monodispersed particlesand polydispersed particles by considering the Fuller andEVF gradations, respectively. Modelling parameters pre-sented in Table 2 were substituted into equations (11) and(13), respectively, to estimate corresponding∅Interphase valuesused in PVA bionanocomposites in this study. Besides, inter-phase volume can be calculated according to equations (5),(6), (7), and (8) with associated results being used to deter-mine the volume fraction of nanofillers. Such recalculatedvolume fractions of nanoparticles with respect to the inter-phase effect were incorporated into Halpin-Tsai model andMori-Tanaka model accordingly in this study and illustratedin Figure 10 (with monodispersed and polydispersed particlesystems). In a consistent manner, all elastic moduli of PVA

bionanocomposites with the consideration of the interphaseeffect in our modelling work revealed a much closer relation-ship with experimental data as opposed to correspondingtheoretical models using both nominal and effective volumefractions without interphase. More evidently, our proposedmodels in a monodispersed particle system caused bettercurve fitting with experimental data at low volume fractionsup to 0.0604 and 0.061 vol% for HNTs and Cloisite 30B clays,respectively, as opposed to those in a polydispersed particlesystem with both the Fuller and EVF gradations, but viceversa beyond 0.1109 and 0.1105 vol%, accordingly. It wasunderstandable, since HNTs and Cloisite 30B clays tendedto be more uniformly dispersed in PVA matrices with rel-atively similar nanoparticle sizes (i.e., monodispersed par-ticle system) at their low volume fraction, while typicalnanoparticle agglomeration was evidently identified in bet-ter accordance with a polydispersed particle system. Whena particulate gradation effect was taken into account, thosepredictions according to the Fuller gradation seemed to bein slightly better agreement with corresponding experi-mental data in PVA bionanocomposites, which might beascribed to the theoretical assumption of finer particle dis-persion taking place in EVF gradation at the same volumefraction of nanocomposites. Larger specific surface areas of

Table 1: Modelling parameters used for PVA bionanocomposite films.

Modelling parameter PVA/HNT PVA/Cloisite 30B clay Ref.

Em (GPa) 2.08 2.08 [45]

Ep (GPa) 140a 178b

a[46]b[32]

lp (nm)

208 (3wt% HNTs) 109 (3wt% Cloisite 30B) [45]

410 (5wt% HNTs) 206 (5wt% Cloisite 30B) [45]

900.6 (10wt% HNTs) 560 (10wt% Cloisite 30B) [45]

tp (nm)

4.6 (3 wt% Cloisite 30B) [45]

15.8 (5 wt% Cloisite 30B) [45]

41.6 (10wt% Cloisite 30B) [45]

d (nm)

35.2 (3 wt% HNTs) [45]

66.5 (5 wt% HNTs) [45]

85 (10wt% HNTs) [45]

ρm (g cm-3) 0.39 0.39 [45]

ρp (g cm-3) 1.8 1.98 Material data sheets

t (nm) ~7.3 ~10.4 [45]Rg (nm) 10 10 [32]

νm 0.4 0.4 [34]

W″p 0.66 [32]d1 (nm) 1.87 [45]

d2 (nm) 3.6 [45]

N 5.6 [45]

h (nm) 0.98 [45]

ρp″ (g cm-3) 3.1 [45]

ΑΤ (m2 g-1) 40.3c 658d

c[47]d[32]


nanoparticles generally took place in the case of EVF grada-tion, thus resulting in increasing ∅Interphase and volume frac-tions of nanoparticles. However, it was not always the case inour PVA bionanocomposites especially at very high volumefractions of nanoparticles.

5. Conclusions

A pioneering modelling approach was successfully developedto determine the nanomechanical properties of PVA biona-nocomposites reinforced with HNTs and Cloisite 30B clays,as well as 3D interphase dimensions and modulus in termsof interphase surface area SAInterphase and volume V Interphase.It was clearly shown that the interphase modulus was consis-tently enhanced with increasing SAInterphase and V Interphase,respectively, regardless of the embedding status of nanoparti-cles and proposed interfaces. The interphase moduli ofPVA/Cloisite 30B clay bionanocomposites appeared to begreater than those of PVA/HNT bionanocomposites basedon V Interphase/Vnanofiller. The nanomechanical properties anddimensions of the interphases were found to depend greatlyon nanofiller dispersion states. As expected, increasing thenanofiller content inevitably decreased particle-particle spac-ing resulting in nanoparticle agglomeration with the visibleinterfacial debonding effect between nanoparticles and PVAmatrices. The incorporation of an effective volume fractionand monodispersed and polydispersed particle systems withthe interphase effect in conventional Halpin-Tsai modeland Mori-Tanaka model was validated to be in better agree-ment with experimental data as opposed to those based on anominal volume fraction of nanoparticles with the neglect ofinterphase features.

Appendix

Calculation of Interphase VolumeFraction (∅Interphase)

A theoretical interfacial volume fraction can be derived fromthe nearest-surface distribution theory [25], in which com-posite media are composed of 3D rigid particles and voids.Lu and Torquato [25] employed statistical geometries ofcomposites and geometric probability to determine a voidexclusion probability evðrÞ, which is defined as the probabil-ity of a designated empty region of composite media with theradius of particle cavities r at an arbitrary point. Accordingly,evðrÞ can be given by

ev rð Þ = 1 − ηð Þ exp −πρ er + dr3 + gr3� ��

, ðA:1Þ

e =4 R2� �1 − η

, ðA:2Þ

d =4 Rh i1 − η

+8πρ R2

� �21 − ηð Þ2 ,

ðA:3Þ

g =4

3 1 − ηð Þ +16πρ Rh i R2� �3 1 − ηð Þ2 +

64mπ2ρ2 R2� �3

27 1 − ηð Þ3 :

ðA:4ÞIn practice, evðrÞ represents the expected void fraction in

such a two-phase composite system [48]. m is a parameterassociated with the theoretical estimation of the radial distri-bution function in a spherical particle system. In particular,m = 2 has been used in this study based on the Carnahan-Starling approximation [28]. ρ is the number density of iso-tropic particles with a radius R. η can be further calculatedaccording to equation (A.5) as follows:

η = ρ Vh i = ρ π3/2 R3� �

Γ 1 + 3/2ð Þð Þ =4π3

ρ R3� �

, ðA:5Þ

where hVi is the average volume of hard particles and ΓðxÞ isthe gamma function. According to quantitative stereology[49], η denotes the volume fraction of 3D rigid particles.

Composite materials are supposed to consist of a packingof rigid particles and matrices evðrÞ as mentioned earlier,which can thus be considered as the matrices in a two-phase composite material. When a three-phase compositematerial, consisting of rigid nanoparticles, matrices, andsoft-shell interphases (layer thickness r = t) surrounding par-ticles, is taken into consideration, the combination of each ofthe isotropic particles and associated soft-shell interphasecan be regarded as a composite particle. Therefore, a three-phase composite system can be simplified as a two-phaseequivalent system including rigid composite particles (i.e.,the original particles and the corresponding interphases), aswell as matrices. Nonetheless, for such a three-phase com-posite system, evðtÞ is not applicable for equations (A.1)and (A.4), but it can be subjected to the geometric configura-tion of anisotropic particles instead. The incorporation of the

Table 2: Modelling parameters measured for the calculation of∅Interphasein PVA bionanocomposites.

Modellingparameter

Nanoparticlecontent (wt%)

PVA/HNTaPVA/Cloisite30B clay

Deq‐min (nm)

3 64.5 34.1

5 168.5 54.3

10 245.7 141.6

Deq‐max (nm)

3 836 436

5 2460 1836.2

10 4645 3141

Deq‐mean (nm)

3 208 109

5 410 206

10 900.6 560

tInterphaseb

(nm)5 8.6 10.7

Note. aDeq‐min, Deq‐max, and Deq‐mean are the maximum, minimum, and meanequivalent diameters of anisotropic particles, which represent the maximum,minimum, andmean equivalent lengths of HNTs, respectively, in PVA/HNTbionanocomposites according to equations (A.24)–(A.34) in Appendix A.btInterphase is the average interphase thickness for the model developmentbased on the assumption that the interphase generated betweennanoparticles and polymer matrices was typically considered at the fillercontent of 5 wt% in PVA bionanocomposites.


geometric details of particles yields the modified equationsgiven by

ev tð Þ = 1 − ηð Þ exp −πρ et + dt3 + gt3� ��

, ðA:6Þ

e =Sh i

π 1 − ηð Þ , ðA:7Þ

d =4 Rh i1 − η

+ρ R2� �

2π 1 − ηð Þ2 ,ðA:8Þ

g =4

3 1 − ηð Þ +4ρ Rh i Sh i3 1 − ηð Þ2 +

mρ2 Sh i327π 1 − ηð Þ3 ,

ðA:9Þ

where hSi is the average area of rigid particles. According toequations (A.6) and (A.7), it can be clearly shown that evðtÞdepends primarily on R, ρ, and the surface area of isotropicparticles S. Similarly, in an anisotropic particle system, evðtÞ should be calculated based on the geometric details of suchparticles. Hence, the key step is how to determine these char-acteristic parameters of anisotropic particles. According toprevious studies [30, 50], an equivalent diameter (Deq) iswidely used as an alternative dimension of anisotropic irreg-ular particles with complex geometries. The number densityof anisotropic particles can be estimated by a quantitative ste-reological theory [49], which is equal to the ratio of the vol-ume fraction of a solid phase to the average volume of rigidparticles, or the ratio of the specific surface area of a solidphase to the average surface area of rigid particles. In termsof Deq, the average volume hVi and the average surface areahSi of anisotropic particles can be calculated as follows:

Vh i = π6 D3eq

D E, ðA:10Þ

Sh i = πs

D2eqD E

: ðA:11Þ

The volume fraction of a solid phase with various geom-etries has been found to be relatively similar to that of rigidparticles [30]. As a result, the number density (NV) of aniso-tropic particles is given by the following stereological theory:

NV =VpVh i =

SVSh i =

6Vpπ D3eqD E , ðA:12Þ

where SV is the specific surface area of rigid anisotropicparticles. By substituting equations (A.10) and (A.11) intoequations (A.6)–(A.9), the evðtÞ for composite materials rein-forced with anisotropic particles can be expressed as

ev tð Þ = 1 −Vp� �

exp −6VpD3eqD E e′t + d′t3 + g′t3� �

24

35,ðA:13Þ

∅Interphase = 1 −Vp − ev tð Þ = 1 − Vp� �

� 1 − exp − 6VpD3eqD E e′t + d′t3 + g′t3� �

24

35

8<:

9=;:ðA:14Þ

In a PVA bionanocomposite system, Vp represents thenominal volume fraction of nanofillers (∅p). As such, equa-tion (A.14) can be rewritten as follows:

∅Interphase = 1 −∅p� �

1 − exp −6∅pD3eqD E e′t + d′t3 + g′t3� �

24

35

8<:

9=;,

ðA:15Þ

e′ =D2eqD E

S 1 −∅p� � , ðA:16Þ

d′ =2 Deq� �1 −∅p

+3∅p D2eq

D E2S2 1 −∅p� �2 D3eqD E , ðA:17Þ

g′ = 43 1 −∅p� � + 4∅p Deq

� �D2eqD E

S 1 −∅p� �2 D3eqD E

+4m∅p D2eq

D E33S3 1 −∅p� �3 D3eqD E2 ,

ðA:18Þ

S =1 + 1:5αð Þ2/3

1 + α: ðA:19Þ

In a typical nanocomposite system, nanoparticles can bedispersed uniformly with relatively similar sizes; these areknown as monodispersed nanoparticles [26]. On the otherhand, when nanoparticles with different sizes and diametersare dispersed randomly, they are called polydispersed nano-particles [26].

In the case of a monodispersed particle system, theparameters e′, d′, and g′ are expressed as follows:

e′ =D2eq

S 1 −∅p� � , ðA:20Þ

d′ =2Deq1 −∅p

+ 2 +3∅p

S2 1 −∅p� �

" #, ðA:21Þ

g′ = 43 1 −∅p� � + 1

3+

∅pS 1 −∅p� � + m∅2p

3S3 1 −∅p� �2

" #,

ðA:22Þ


By substituting equations (A.20)–(A.22) into equation(A.15) and then letting λ = t ′/Deq,∅Interphase, one can expressthe following:

∅Interphase = 1 −∅p� �(

1 − exp"−6∅pλ

3

1 −∅p

"1Sλ2

+1λ

2 +3∅p

S2 1 −∅p� �

" #+43+

4∅pS 1 −∅p� �

+4m∅2p

3S3 1 −∅p� �2

##),

ðA:23Þ

where λ represents the geometric size factor of anisotropicparticles.

On the contrary, with respect to a polydispersed particlesystem, it is necessary to evaluate the effect of particle sizedistribution (PSD) on both the volume fraction of inter-phases and the reinforcement efficiency of nanocomposites.The gradation of irregular aggregates can be experimentallyinvestigated using a sieve analyser or laser particle analyserwhere the size of each irregular aggregate is evaluated relativeto the corresponding size of spherical particles [28]. The PSDof spherical particles can be transformed into that of aniso-tropic particles when the equivalent diameter is definedaccording to previous research work [29]. In this study, twoparticulate gradations, namely the Fuller gradation [29] andthe equal volume fraction (EVF) gradation [29, 30], wereemployed with their specific equations given as follows:

FV Dð Þ =ffiffiffiffiD

p−

ffiffiffiffiffiffiffiffiffiffiDmin

pffiffiffiffiffiffiffiffiffiffiDmax

p−

ffiffiffiffiffiffiffiffiffiffiDmin

p , ðA:24Þ

FV Dð Þ =InD − InDmin

InDmax − InDmin, ðA:25Þ

where FVðDÞ is the cumulative volume percentage of isotopicparticles with their corresponding diameter of D, in whichDmax and Dmin are the maximum and minimum diametersof isotopic particles, respectively. The PSD of anisotropicparticles can be connected to that of the isotopic particlesby substituting Deq into D, as mentioned in equation(A.25). The optimised Fuller and EVF gradations for aniso-tropic particles are presented as follows:

FV Deq� �

=ffiffiffiffiffiffiffiDeq

p−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmin eq

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmax eq

p−

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmin eq

p , ðA:26Þ

FV Deq� �

=InDeq − InDmin eq

InDmax eq − InDmin eq, ðA:27Þ

where FVðDeqÞ should be derived to generate the number ofpolydispersed particles. The volume-based probability den-sity function f VðDeqÞ is determined in terms of Deq basedupon the first-order derivative of FVðDeqÞ.

f V Deq� �

=1ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Dmax eqp

−ffiffiffiffiffiffiffiffiffiffiffiffiffiffiDmin eq

p� � ffiffiffiffiffiffiffiDeq

p , ðA:28Þ

f V Deq� �

=1

InDmax eq − InDmin eq� �

Deq: ðA:29Þ

The number dN of particles with various sizes in therange of ½Deq,Deq + dDeq� is then calculated as follows:

dN =f V Deq� �

dDeqV Deq� � , ðA:30Þ

where VðDeqÞ is the volume of anisotropic particles. Conse-quently, the number-based probability density function f NðDeqÞ for anisotropic particles is expressed as follows:

f N Deq� �

=f V Deq� �

V Deq� �

N, ðA:31Þ

and N is defined by

N =ðDmax eqDmin eq

f V Deq� �

V Deq� � dDeq: ðA:32Þ

By substituting equations (A.26) and (A.27) into equa-tion (A.32), f NðDeqÞ is given by

f N Deq� �

=−q

D−qmax eq −D−qmin eq

� �Dq+1eq

�q = 2:5⟶ Fuller gradation

q = 3:0⟶ EVF gradation

(:

ðA:33Þ

Moreover, the kth moment hDkeqi of the area of f NðDeqÞis given by

DkeqD E

=ðDmax eqDmin eq

Dkeq f N Deq� �

dDeq: ðA:34Þ

By substituting equation (A.33) into equation (A.34),hDeqi, hD2eqi, and hD3eqi are obtained to determine the vol-ume fraction of interphases for an anisotropic polydispersedparticle system. In addition, the parameters required to cal-culate∅Interphase in terms of maximum, minimum, and meanequivalent diameters of anisotropic particles Deq‐min, Deq‐max,and Deq‐mean, as well as tInterphase, can be then measured foreach type of nanofillers.

Data Availability

All data generated or analysed during this study are includedin this manuscript and supplementary materials.


Conflicts of Interest

The authors declare that they have no conflicts of interest andno financial interest related to this study.

Acknowledgments

Dr. Mohanad Mousa acknowledges the Higher Committeefor Education Development in Iraq for awarding a researchscholarship for his PhD studies at Curtin University. Theauthors are also indebted to Dr. Thomas Becker from Nano-chemistry Research Institute, Curtin University, for his tech-nical assistance in PFQNM measurements.

Supplementary Materials

PVA/HNT bionanocomposite films. Figure S1: (a) schematicdiagrams of cross-sectional scanning of PVA/HNT inter-phases in PVA/HNT bionanocomposites along the trans-verse plane direction with (b) height profile and (c)adhesion profile. Figure S2: schematic diagrams of cross-sectional scanning of PVA/HNT interphases in PVA/HNTbionanocomposites along (a) a longitudinal plane directionfrom the top view and (b) a height plane direction from a sideview. Figure S3: relationship between the surface area of theouter interface (SAouter interface) and interphase length(LInterphase) for PVA/HNT phases in PVA/HNT bionano-composites. Figure S4: relationship between the surface areaof the outer interface (SAouter interface) and HNT/interphasevolume (VHNT/Interphase) in PVA/HNT bionanocompo-sites. Figure S5: (a) schematic diagrams of cross-sectionalscanning of PVA/Cloisite 30B interphases in PVA/Cloisite30B bionanocomposites along the transverse plane directionwith (b) height profile and (c) adhesion profile. Figure S6:schematic diagrams of cross-sectional scanning of PVA/Cloi-site 30B interphases in PVA/Cloisite 30B bionanocompositesalong (a) a longitudinal plane direction from the top viewand (b) a height plane direction from a side view. Figure S7:relationship between the surface area of the outer interface(SAouter interface) and interphase length (LInterphase) in PVA/-Cloisite 30B clay bionanocomposites. Figure S8: relationshipbetween the surface area of the outer interface (SAouter interface)and Cloisite 30B/interphase volume (VCloisite 30B/Interphase) inPVA/Cloisite 30B clay bionanocomposites. Figure S9: elas-tic modulus profiles based on typical datasets of 25 linescan regions (LSRs) with the best curve fitting in termsof scan distance Sd: (a) PVA/3wt% HNT bionanocompositesand (b) PVA/3wt% Cloisite 30B clay bionanocomposites.(Supplementary Materials)

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http://nanoscaleworld.bruker-axs.com/nanoscaleworld/media/p/143.aspxhttp://nanoscaleworld.bruker-axs.com/nanoscaleworld/media/p/143.aspxhttp://nanoscaleworld.bruker-axs.com/nanoscaleworld/media/p/143.aspx

Towards Sophisticated 3D Interphase Modelling of Advanced Bionanocomposites via Atomic Force Microscopy1. Introduction2. Experimental Work2.1. Materials and Fabrication Process2.2. Material Characterisation via Atomic Force Microscopy (AFM)

3. Modelling Approach3.1. 3D Interphase Modulus, Surface Area, and Volume3.2. Interphase Volume Fraction3.3. Micromechanical Model Based on Nominal and Effective Volume Fractions3.4. Volume Fraction of Nanofillers with Interphase Effect

4. Results and Discussion4.1. Elastic Properties of Interphase4.2. Interphase Dimensions4.3. Particle Debonding4.4. Prediction of Elastic Moduli of PVA Bionanocomposites

5. ConclusionsAppendixCalculation of Interphase Volume Fraction (&emptyv;Interphase)Data AvailabilityConflicts of InterestAcknowledgmentsSupplementary Materials

Towards Sophisticated 3D Interphase Modelling of Advanced ...Halpin-Tsai model and Mori-Tanaka model...

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