Hygrothermal aging effect on the properties of PMMA nanocomposites reinforced by ceramic nanoparticles

Abstract

This paper aimed to evaluate hygrothermal aging effects on polymethyl methacrylate modified with TiO₂, SiO₂, and Al₂O₃ nanoparticles in 0.5, 1, and 2% weight fractions. The distribution of nanoparticles was characterized by the scanning electron microscopy (SEM) method. Moisture absorption behavior and mechanical properties of samples in terms of elastic modulus, tensile strength, impact strength, and hardness were investigated. Furthermore, the coefficient of hygrothermal expansion (CHE) for each sample was calculated thanks to experimental data. Finally, by applying the multi-criteria decision making (MCDM) technique, the optimum composition for superior performance was obtained in 0.5 wt% of nanoparticles, more specifically for SiO₂.

Keywords

Hygrothermal effect Thermoplastic resin Environmental degradation Nanocomposite

Introduction

Polymeric materials typically face different types of aging, which occur due to many environmental causes during service conditions. According to the reported statistics of the French Association for Composite Material (AMAC), among environmental causes in material failures, the hygrothermal effect by 36% is the most reported that happens due to the combination of moisture and temperature.¹ The certain absorbed moisture amount by a polymeric composite is usually at low levels (below 2 wt%). However, studies have revealed that just this level affects the performance of material that intensifies durability concerns.² For this reason, the accelerated artificial aging method generally has been used to predict the long-term performance of a material in which it attempts to replicate the natural aging effects to get results faster.³

With respect to the extension of nanotechnology, many studies have concentrated on developing polymeric-based nanocomposites (PMNCs) with paramount properties.^4,5 The addition of nanoparticles has shown great promise to improve barrier properties such as reducing moisture absorption and diffusivity of polymers under wet conditions.^6–9 Related research shows that the diffusion path lengthened because of increasing tortuosity by the presence of nanoparticles, which is directly dependent on the exfoliation degree in polymers.¹⁰ Despite this, Agwa et al. ¹¹ reported a different behavior in their study. They immersed reinforced nanocomposites with Al₂O₃ and SiO₂ in distilled water at 25°C for 100 days. Their results show that the addition of nanoparticles could reduce the moisture amount only at low concentration (0.5 wt%) of nano-fillers, and conversely, for the higher content of nanoparticles (1.5 and 3 wt%), moisture amount and diffusion rate increased compared to the neat sample. In other research, Zhao and Li ¹² evaluated the absorbed moisture effect on the mechanical properties of epoxy resin nanocomposite mixed with Al₂O₃ nanoparticles. They found that the addition of Al₂O₃ nanoparticles caused enhancement in both elastic modulus and tensile strength compared to neat epoxy after immersion in water. The obtained tensile stress–strain curves show increasing ductility and reduction in tensile properties for both filled and un-filled wet epoxy compared to dry specimens, while this reduction is lower for nanocomposite containing Al₂O₃ nanoparticles. Their study also showed that the moisture amount decreased with adding the Al₂O₃ nanoparticles in 55±1°C de-ionized water bath by increasing exposing time. Besides, the presence of Al₂O₃ did not change the water absorption curve of neat epoxy.

This research focuses on studying the hygrothermal aging effects on polymeric nanocomposites regarding the use of polymethyl methacrylate (PMMA) as the matrix, which has not been studied yet. PMMA is a prominent amorphous thermoplastic that is extensively used in medicine. However, by considering different medical applications based on human body physiology, PMMA would confront a particular form of hygrothermal aging that directly affects its performance. Related to this issue, the influence of adding three multi-functional types of ceramic nanoparticles with biomedical applications on moisture absorption behavior, diffusion coefficient, structural durability, and swelling of PMMA is studied. In addition, the mechanical properties of hygrothermally aged nanocomposites in terms of fracture behavior, tensile strength, elastic modulus, impact strength, and hardness are examined. Finally, the optimum combination of nanocomposites with prominent properties, by using the multi-criteria decision making (MCDM) methods and considering the lowest production cost, is introduced.

Experimental

Specimen preparation

The materials used for preparing nanocomposite are PMMA resin with the trade name of Acryrex CM-205 (melt flow index = 1.9 mL/10 min at 230°C under a load of 3.8 kg, density = 1.19 g.cm⁻³) purchased from Chi Mei Corporation of Taiwan and TiO₂ (Titania), SiO₂ (Silica), and Al₂O₃ (Alumina) nanoparticles with the purity of 99% provided by US-Nano Inc. Table 1 represents the physical properties and specification of ceramic nanoparticles used as reinforcement.

Table 1.

Physical properties and specification of TiO₂, SiO₂, and Al₂O₃ nanoparticles.¹³

Properties	Nanoparticles
Properties	TiO₂	SiO₂	Al₂O₃
Trade code	US 3500	US 3438	US 3023
Purity (%)	+99	99.5	+99
Average particle size (nm)	20	20–30	20
Specific surface area (m²/g)	10–45	180–600	>138
Morphology	Spherical
Color	White

For preparing nanocomposite specimens, PMMA was first dried for 12 h at 80°C in order to eliminate the humidity before processing. Then, PMMA was melt compounded with 2 wt% of each nanoparticle as masterbatch, using a ZSK-25 twin-screw extruder (D = 25 and L/D = 48 mm) with the rotation speed of 250 rpm at 210°C. The rest of the intended compounds (with 0.5 and 1 wt% of nanoparticles) were prepared by diluting the mixed masterbatch. After preparing the final mixtures, nanocomposite granules were re-dried in the hopper unit of the injection molding machine at 80°C for 2 h. Then, the tensile and impact test specimens based on the desirable standards were manufactured using an NBM HXF-128 injection molding machine. The machine was adjusted to the constant parameters in all production procedures (Table 2) to reduce the possible effects of processing factors on the study. Figure 1 shows mixed granules and final produced nanocomposites; the pure specimens were also made to have a better evaluation of nanoparticle effects on test variables. In order to analyze the morphology and possibility of nanoparticles agglomeration in matrix, the scanning electron microscopy (SEM) technique was proceeded by mentioned specification including a Hitachi S-4160 FE (Field Emission)-SEM, with an operating voltage of 20 kV.

Table 2.

Adjusted processing parameters of injection molding.

Parameter	Injection temperature (°C)	Mold temperature (°C)	Injection pressure (MPa)	Holding pressure (MPa)	Cooling time (s)	Shot size (cm)
Value	260	60	110	80	25	172

Figure 1.

a) Prepared nano-mixed and pure granules, b) Injection-molded nanocomposite specimens.

Hygrothermal conditioning

In order to simulate the hygrothermal condition, a distilled-water bath chamber was designed. Polyethylene (PE) was used as chamber’s sidewall to reduce the thermal conductivity with outdoor environment. A digital thermoregulator was also used to adjust and fix the water temperature at 36°C (biological body temperature). The mass measurements of specimens were performed at consecutive periods of time, by a digital balance (A&D FX-300GD) with an accuracy of 0.001 g. At each step, firstly, the specimens were removed from the chamber, and the droplets of water were cleaned off, then the specimens were returned to the chamber immediately after measurement. The moisture absorption amount of specimens was calculated using

M_{t} = \frac{W_{t} - W_{d}}{W_{d}} \times 100

(1)

where M_t is the moisture absorption content (wt%) at time t, W_d and W_t are the weights of the dry and wet specimens, respectively.

Mechanical tests

After the aging process, the mechanical properties of wet specimens in terms of tensile strength, elastic modulus, impact strength, and hardness were measured. Tensile test was carried out using a universal STM-150 (SANTAM) machine according to the general specifications of the ASTM D638 standard. The specimens were loaded with a cross-head speed of 5 mm/min rate and the gauge length of 88 mm. Charpy impact test was tested by SIT-200 (SANTAM) with a maximum capacity of 200 J and impact speed of 5.2 ± 0.1 m²/s, based on the ASTM D6110 standard; before starting impact test, all specimens were notched as V-form with 2 mm deep and notch angel of α = 45°. Hardness test was also accomplished based on the Rockwell-M method according to the ASTM-D785 by a Zwik/Roell Indentec Universal machine.

Note: All measurements and tests were performed at room temperature. Moreover, for each nanocomposite, at least three specimens were examined, and the mean of the data was considered.

Analytical formulation

Moisture absorption behavior

Investigation of the kinetics of the moisture absorption process as a time-dependent aspect is essential to predict the structural durability of nanocomposites.¹⁴ When a nanocomposite is subjected to a hygrothermal environment, the absorbed fluids may degrade the matrix and the filler-matrix interface by hydrolysis and chemical reactions that provide the weakening of filler-matrix bonds.¹⁵ Ouled Ahmed et al. ¹⁴ discussed that according to the absorption kinetic, any continuous increment in moisture absorption procedure (due to increasing porosity) or sudden reduction in moisture content (because of losing mass) of a polymeric material demonstrates that material is hygrothermally degraded. All in all, there are three mechanisms by which the moisture can penetrate into a nanocomposite.¹⁶ The most common is “diffusion” that may happen through the matrix or, in some cases, in fillers. Several models have been introduced to describe moisture diffusion behavior.¹⁷ Meanwhile, “Fickian” model has been widely used due to its simplicity and adaptation with various types of polymeric nanocomposites. For one-dimensional diffusion through an infinite plate of thickness h, Fick’s model is summarized as¹⁶

\frac{\partial C}{\partial t} = D (\frac{\partial^{2} C}{\partial x^{2}})

(2)

where C (

k g . m^{- 3}

) is the moisture concentration, t (

s

) is the time, and D (

m^{2} . s^{- 1}

) is the diffusion coefficient through the thickness of the material.

Moisture diffusion rate in nanocomposites is quantified by specifying the diffusion coefficient ( $D$ ). The moisture diffusivity of nanocomposites under certain temperatures and humidity is evinced by¹⁶

\frac{M_{t}}{M_{\infty}} = 1 - \sum_{n = 1}^{\infty} \frac{8}{{[(2 n + 1) π]}^{2}} e x p [\frac{- D {(2 n + 1)}^{2} π^{2} t}{h^{2}}]

(3)

where

M_{\infty}

is the saturated weight of moisture in specimens and h is the thickness of dry specimens. By simplifying equation (3) for a short period of time, different models have been approached to determine the diffusion coefficient ¹⁸ in which the following model provides more precise results than others due to taking into account the slope of the initial stage of absorption curves

D = π {(\frac{k h}{4 M_{\infty}})}^{2}

(4)

where k is the initial slope of absorption curves.

In the initial stage of the absorption curves up to approximately half of the saturation ( $M_{\infty} / M_{t} ≅ 0.5$ ), there is a linear relationship between mass increment versus the square root of time. In this phase, the diffusion profiles (as long as they do not overlap) have the same mass flux of moisture on different sides of the specimens.¹⁹

Coefficient of Hygrothermal Expansion (CHE)

Substantially, the expansion behavior becomes more important when the used materials are in contact with other components, and the coefficient expansion of one member should be matched with others.²⁰ More specifically, the simultaneous effect of moisture and temperature creates a new form of swelling that is known as “hygrothermal expansion” and is described as a linear relation between swelling strain and moisture content of the material that mathematically is defined as²¹

ε_{Hygrothermal} = \frac{Δ L}{L} = β Δ m

(5)

where

Δ L

is the elongation of a considered tin bar of a given material with

L

initial length,

β

is the coefficient of hygrothermal expansion as a constant factor, and

Δ m

is the absorbed moisture content for nanocomposite.

Principally, nanocomposites are nonhomogeneous materials, but as an exception, for particulate nanocomposites (not having directionally dependent behavior) with the quite small scale of reinforcement, nanocomposite can often be considered macroscopically isotropic.²² By assuming a linear relationship between stress and strain for an orthotropic nanocomposite that is subjected to mechanical and hygrothermal actions, the general three-dimensional Hooke’s law is written as below²²

{\begin{matrix} ε_{1} \\ ε_{2} \\ ε_{3} \\ γ_{23} \\ γ_{31} \\ γ_{12} \end{matrix}} = [\begin{matrix} 1 / E_{1} & ϑ_{21} / E_{2} & ϑ_{31} / E_{3} & 0 & 0 & 0 \\ ϑ_{12} / E_{1} & 1 / E_{2} & ϑ_{32} / E_{3} & 0 & 0 & 0 \\ ϑ_{13} / E_{1} & ϑ_{23} / E_{2} & 1 / E_{3} & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 / G_{23} & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 / G_{31} & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 / G_{12} \end{matrix}] {\begin{matrix} σ_{1} \\ σ_{2} \\ σ_{3} \\ τ_{23} \\ τ_{31} \\ τ_{12} \end{matrix}} + {\begin{matrix} β_{1} \\ β_{2} \\ β_{3} \\ 0 \\ 0 \\ 0 \end{matrix}} Δ m

(6)

where

$E_{1} . E_{2} . E_{3} =$ Elastic modulus in the 1, 2, and 3 directions.

$ε_{1} . ε_{2} . ε_{3} =$ Total strain in the 1, 2, and 3 directions.

$G_{23} . G_{12} . G_{31} =$ Shear modulus.

$σ_{1} . σ_{2} . σ_{3} =$ Normal stresses.

$τ_{23} . τ_{12} . τ_{31} =$ Shear stresses.

$ϑ_{12} . ϑ_{21} . ϑ_{23} . ϑ_{32} . ϑ_{31} . ϑ_{13} =$ Poisson’s ratios.

Concerning the symmetry of elastic arrays and regarding the fact that the hygrothermal expansion does not affect the shear strains or stresses,²¹ the thermoelastic constitutive relation is simplified as equation (7)

{ε_{i j}} = {ε_{M e c h a n i c a l}} + {ε_{H y g r o t h e r m a l}} = [S_{i j}] [S_{i j}] {σ_{j}} + {β_{i}} Δ C . (i . j = 1. \dots . 6)

(7)

where

S_{i j}

is compliance coefficients and related to the traditional elastic.

Multi-Criteria Decision Making (MCDM) method

According to the literature review, the addition of nanoparticles in various content and types would have complex and multiple effects on nanocomposite properties. Regarding other authors’ suggestions ²³ and suitable adaption of MCDM methods in solving polymeric nanocomposite selection problems,^24,25 the combination of analytic hierarchy process (AHP) and technique for order of preference by similarity to ideal solution (TOPSIS) has been used to rank the nanocomposites.

In the MCDM method, a problem can be depicted by a $m \times n$ matrix (M) in which each element ( $X_{i j}$ ) identifies the scale value of ith alternative on jth criterion as

M = [\begin{matrix} X_{11} & X_{12} & \dots & \dots & X_{1 n} \\ X_{21} & X_{22} & \dots & \dots & X_{2 n} \\ \dots & \dots & \dots & \dots & \dots \\ \dots & \dots & \dots & \dots & \dots \\ X_{m 1} & X_{m 2} & \dots & \dots & X_{m n} \end{matrix}]

(8)

AHP method

The AHP method was first designed by Saaty in 1980 ²⁶ and originally follows four steps. As the first step, by applying it to a complex multi-criteria problem, it will be partitioned into three main levels as goal, criteria, and alternative. Then, the relative importance of each criterion must be assigned by pairwise comparison; the result is ordered in a

n \times n

matrix (C) that its elements are computed by

a_{i j} = \frac{1}{a_{j i}}

(9)

The comparative judgment values between the two criteria are shown in Table 3.

Table 3.

Scale of relative importance.

Scale of importance	Description
1	Equal importance
3	Moderate importance
5	Strong importance
7	Very strong importance
9	Absolute importance
2, 4, 6, 8	Intermediate values

Lastly, in order to check the consistency of the consumed matrix, after weighting criteria by averaging the normalized pairwise comparison matrix (W), three parameters must be calculated:²⁷

• Estimating the maximum eigenvalue (λ_max) by calculating the average of matrix E

[C'] = [C] \times {[W]}^{T} \cdot [E] = [C'] \times {[W]}^{T}

(10)

• Computing the consistency index (CI) of pairwise comparison matrix

CI = \frac{λ_{m a x} - n}{n - 1}

(11)

where

n

is the number of criteria.

• Determining the trustworthy and consistency of the pairwise comparison matrix by consistency ratio (CR)

C R = \frac{C I}{R I}

(12)

where RI is the random consistency index, and its values depend on the number of criteria (n). CR values must be less than 0.1; for greater values of CR = 0.1, the pairwise comparison matrix must be revised. The relevant values of RI for the specific number of criteria are shown in Table 4.

Table 4.

Random index (RI) values in order to n criteria.

n	1	2	3	4	5	6	7	8	9	10
RI	0	0	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.51

TOPSIS method

TOPSIS is another famous MCDM technique that was first introduced by Hwang and Yoon,²⁸ which is also used for ranking and selection of nanocomposite materials.²⁹ By applying the TOPSIS method, the optimum chosen material must have the shortest and farthest Euclidean distance from ideal solution ( $S_{i}^{+})$ and negative ideal solution ( $S_{i}^{-})$ , respectively. Generally, the TOPSIS ranking method involves the following six steps²⁷:

Step 1

It is necessary to transform the decision matrix scales to non-dimensional values to have comparable attributes; the normalized decision matrix ( ${\bar{X}}_{i j}$ ) is calculated by

{\bar{X}}_{i j} = \frac{X_{i j}}{\sqrt{\sum_{i = 1}^{m} X_{i j}^{2}}}

(13)

where

m

is the number of alternatives. In this step, each attribute would get a value between 0 to 1.

Step 2

The weighted-normalized decision matrix is determined by

V_{i j} = {\bar{X}}_{i j} \times W_{j}

(14)

where

W = [W_{1}, W_{2}, W_{3}, \dots, W_{j}, \dots, W_{n}], \sum_{j = 1}^{n} W_{j} = 1

Step 3

Next, the concept of the ideal solution ( $V^{+}$ ) and the negative-ideal solution ( $V^{-}$ ) are found out by

V^{+} = [(\max ν_{i j} | j ϵ I^{'}) . (\min ν_{i j} | j ϵ I^{′′}), i = 1. 2. 3. \dots . m] = [ν_{1}^{+} . ν_{2}^{+} . \dots . v_{n}^{+}]

(15)

V^{-} = [(\min ν_{i j} | j ϵ I^{'}) . (\max ν_{i j} | j ϵ I^{′′}), i = 1. 2. 3. \dots . m] = [ν_{1}^{-} . ν_{2}^{-} . \dots . v_{n}^{-}]

(16)

where

$I$ = [ $j = 1. 2. 3. \dots . n$ and $j$ is related to beneficial criteria],

$I^{'}$ = [ $j = 1. 2. 3. \dots . n$ and $j$ is related to non-beneficial criteria].

Step 4

In this step, the separation measure of each alternative from the ideal ( $S_{i}^{+}$ ) and negative-ideal ( $S_{i}^{-}$ ) solution is computed by

S_{i}^{+} = {[\sum_{j = 1}^{m} {(V_{i j} - V_{j}^{+})}^{2}]}^{0.5}

(17)

S_{i}^{-} = {[\sum_{j = 1}^{m} {(V_{i j} - V_{j}^{-})}^{2}]}^{0.5}

(18)

Step 5

The relative closeness of each alternative to the ideal solution is determined by

P_{i} = \frac{S_{i}^{-}}{S_{i}^{+} + S_{i}^{-}}

(19)

where

0 < P_{i} < 1

and

i = 1. 2. 3. \dots . m .

Step 6

Finally, the alternatives are ranked based on the highest values of $P_{i}$ .

Results

SEM analysis

Homogeneity is a critical challenge among the various preparation methods of particle-reinforced nanocomposites since the interaction between nano-filler and matrix is the most urgent factor in controlling the properties of nanocomposites.^30,31 The microstructure of produced nanocomposites is illustrated in Figures 2(a)–(d). The evaluation of the SEM images in different magnifications indicated that there is no crucial agglomeration region, and nanoparticles have been distributed appropriately in the polymeric matrix.

Figure 2.

SEM micrographs of fractured surfaces for a) pure PMMA and PMMA nanocomposites containing b) 2 wt% TiO₂, c) 2 wt% SiO₂, and d) 1 wt% Al₂O₃.

Effect of nanoparticles on structural durability

Figure 3 represents experimental results of the moisture absorption process of neat PMMA and nanocomposites versus square root of exposure time. The aging process lasted for 90 days (2160 h) until the moisture equilibrant was achieved. It can be seen that the kinetics of nanocomposite absorption curves are similar to pure PMMA. The curves generally show two phases of diffusion: A high moisture uptake rate up to half of the saturation (first 340 h) that is gradually followed by a slow absorption thereafter. According to Figure 3, the applied typical Fickian curve by using the least square method,^14,18 shows an acceptable curve-fitting to the experimental data (R²=0.9944).

Figure 3.

Experimental data of moisture uptake (M_t) of pure PMMA and its nanocomposites with TiO₂ (a), SiO₂ (b), and Al₂O₃ (c) nanoparticles versus square root of exposure time.

Effect of nanoparticles on moisture absorption

After moisture saturation of all specimens, the final moisture content (M_∞) was measured as Figure 4. Results illustrated that the addition of nanoparticles generally increased the moisture content of nanocomposites compared to neat PMMA. However, the most resistance to moisture absorption was observed for 0.5 wt% of nanoparticles, particularly for PMMA containing 0.5 wt% TiO₂, which its absorbed moisture amount was found out almost similar to pure PMMA (just 0.08% reduction). Results also indicate a continuous increasing trend in moisture content only by TiO₂ nanoparticles, which is accordingly the highest moisture content (1.917 wt%) found for nanocomposite containing 2 wt% TiO₂.

Figure 4.

Final moisture content (M_∞) values of PMMA nanocomposites immersed in distilled water at 36°C for 90 days.

Effect of nanoparticles on Diffusion coefficient

The diffusion coefficient for PMMA nanocomposites was calculated, according to the data points of moisture absorption curves (Figure 3), and its value is presented in Figure 5. Results indicated that contrary to the influence of nanoparticles on the ultimate moisture content of nanocomposites (Figure 4), the diffusivity decreased by the presence of nanoparticles. This reduction is more prominent for samples with lower nanoparticles content in which the maximum reduction was achieved for samples with 0.5 wt% TiO₂ by 8% compared to neat PMMA. Figure 5 also demonstrated that for most nanocomposites (except 2 wt% TiO₂), the diffusivity significantly increased by enhancing the nanoparticles weight fraction.

Figure 5.

Diffusion coefficient (m²/s) of moisture in first 360 h of aging time.

Mechanical properties

Fracture behavior

The tensile stress–strain curves of nano-filled PMMA compared to pure specimen are shown in Figure 6. Results indicated that the addition of nanoparticles caused more brittle fracture behavior for nanocomposites compared to unfilled PMMA by hygrothermal condition. According to the fracture points, the elongation at break for all nanocomposites was also dramatically decreased, which accordingly, the least and the most reduction were obtained for PMMAs containing 0.5 wt% TiO₂ (38.1%) and 2 wt% SiO₂ (58.5%), respectively. The fractured specimens and their elongation under the universal tensile test are presented in Figure 7. Similarly, the ultimate tensile strength (UTS) values of nanocomposites were decreased by increasing the wt% of nanoparticles, as shown in Figure 8. Generally, the best and the worst performance in UTS were done by PMMAs containing 0.5 wt% TiO₂ (19.7% reduction) and 1 wt% Al₂O₃ (35.3% reduction), respectively. Figure 9 represents the elastic modulus of hygrothermal aged nanocomposites. It can be seen that the presence of nanoparticles did not have a remarkable effect on modulus compared to pure PMMA. Overall, only a reduction was observed for 0.5 wt% of nanoparticles, just up to 3%.

Figure 6.

Stress–strain curves obtained by the universal tensile test of PMMA nanocomposites filled with 0.5 wt% (a), 1 wt% (b), and 2 wt% (c) nanoparticles compared to pure specimen.

Figure 7.

Fractured specimens of standard tensile test and their elongation (%) at fracture point compared to pure PMMA.

Figure 8.

Ultimate tensile strength of PMMA nanocomposites.

Figure 9.

Elastic modulus of PMMA nanocomposites.

Impact strength

The result of Charpy impact test (Figure 10) shows that the impact strength of PMMA was improved by adding 0.5 wt% of nanoparticles in the wet environment, especially for 0.5 wt% SiO₂. It is also well seen in Figure 10 that for samples containing more than 0.5 wt% of nanoparticles, the impact strength grew linearly only for the higher content of TiO₂ that indeed the maximum value of impact strength reached 99 $k J / m^{2}$ for 2 wt% TiO₂. Figure 11 shows notched standard impact test specimens before and after the operation of the test.

Figure 10.

Charpy impact strength of PMMA nanocomposites.

Figure 11.

V-notched PMMA-1 wt% Al₂O₃ before (a) and after (b) performing Charpy impact test.

Hardness

The results of the Rockwell hardness-M test are plotted in Figure 12. As it is clear, the addition of nanoparticles did not have a substantial effect on wet PMMA hardness, and just a slight increment has been seen for 0.5 wt% of nanoparticles, particularly for 0.5 wt% TiO₂ that led to 2.3% as a maximum improvement.

Figure 12.

Rockwell hardness-M of PMMA nanocomposites.

Swelling

According to the macro-mechanical approach CHE values were calculated, by assuming an isotropic and homogeneous microscopic structure for produced specimens. To determining the hygrothermal strain, the total and mechanical strain values were measured by analyzing the universal tensile tests results for both wet and dry conditions, respectively. All measured strain values are reported in Table 5. In Figure 13, the CHE (

β

) values of PMMA nanocomposites are plotted against pure PMMA. Results illustrated that specimens with higher content of nanoparticles (1 and 2 wt%) indicated significant changes in CHE compared to pure PMMA, but for nanocomposites with low content of nanoparticles (as 0.5 wt%), the CHE was observed almost similar to pure PMMA. According to Figure 13, the PMMA containing 1 wt% Al₂O₃ showed the best performance by a 24.3% reduction in the CHE of pure PMMA.

Table 5.

Strain measured values (for 1400 N tensile load).

Sample	$ε_{T o t a l}$	$ε_{M e c h a n i c a l}$	$ε_{H y g r o t h e r m a l}$
Pure PMMA	0.017739	0.011939	0.005800
PMMA-0.5% TiO₂	0.017353	0.011536	0.005817
PMMA-1% TiO₂	0.017598	0.011569	0.006030
PMMA-2% TiO₂	0.017006	0.010459	0.006547
PMMA-0.5% SiO₂	0.017654	0.011989	0.005664
PMMA-1% SiO₂	0.017538	0.012395	0.005143
PMMA-2% SiO₂	0.017315	0.011581	0.005735
PMMA-0.5% Al₂O₃	0.017467	0.011565	0.005902
PMMA-1% Al₂O₃	0.017613	0.013208	0.004404

Figure 13.

CHE values of PMMA nanocomposites, immersed in water for 90 days.

Optimization

The hierarchy process diagram was purposed as Figure 14, according to the medical applications of the material. According to diagram, six criteria such as impact strength, CHE, hardness, diffusion coefficient, elastic modulus, and cost were considered for nine alternatives. The pairwise comparison matrix of criteria based on the knowledge of authors was composed as Table 6. Table 7 shows the results of criteria weighting by the AHP method. The CR was also obtained as 0.004 (<0.1), which verified that the considered matrix (Table 6) was reliable. All the data of hygrothermal aged specimens for each criteria are summarized as a decision matrix in Table 8. For ranking the alternatives by the TOPSIS method, the normalized decision matrix was considered as Table 9. Then, the normalized decision matrix is multiplied with the criteria weighting matrix, as shown in Table 10. According to Table 11, the ideal and negative ideal solution values were specified for each criteria. Similarly, the separation measure was calculated for each alternative, as Table 12. Lastly, based on the highest values of relative closeness, the alternatives were ranked according to Table 13.

Figure 14.

Purposed hierarchy structure.

Table 6.

Pairwise comparison of criteria matrix (fractional values).

	IS	CHE	RM	D	E	C
IS	1	1	2	2	3	4
CHE	1	1	2	2	3	4
RM	1/2	1/2	1	1	1	2
D	1/2	1/2	1	1	1	2
E	1/3	1/3	1	1	1	2
C	1/4	1/4	1/2	1/2	1/2	1

$λ_{m a x}$ = 6.03, $C I$ = 0.01, $R I$ = 1.24 (for $n$ = 6), $C R$ = 0.004. IS impact strength; CHE, coefficient of hygrothermal expansion; RM, Rockwell hardness-M; D, diffusion coefficient; E, elastic modulus; C, cost.

Table 7.

Average weights of criteria.

Criteria	Weight
Impact strength	0.28
Coefficient of hygrothermal expansion	0.28
Hardness	0.13
Diffusion coefficient	0.13
Elastic modulus	0.12
Cost	0.07

Table 8.

Decision matrix.

No	Alternatives	Criteria
No	Alternatives	Impact strength ( $kJ / m^{2})$	CHE ×10⁻³	Hardness (RM)	Diffusion coefficient×10⁻⁹ (m²/s)	Elastic modulus (MPa)	Cost (US $/kg)
A1	Pure PMMA	74.90	3.093	86.68	4.709	2078.40	3.46
A2	PMMA-0.5% TiO₂	83.50	3.104	88.66	4.335	2016.06	8.92
A3	PMMA-1% TiO₂	88.54	3.178	86.82	4.565	2032.30	14.38
A4	PMMA-2% TiO₂	98.96	3.414	85.43	4.377	2040.05	25.31
A5	PMMA-0.5% SiO₂	95.56	3.010	87.95	4.366	1995.80	5.46
A6	PMMA-1% SiO₂	69.95	2.718	86.80	4.496	2051.66	7.46
A7	PMMA-2% SiO₂	68.75	3.038	87.38	4.854	2073.33	11.46
A8	PMMA-0.5% Al₂O₃	86.09	3.144	87.30	4.441	2013.11	8.92
A9	PMMA-1% Al₂O₃	69.37	2.341	85.92	4.643	2061.33	14.38

Table 9.

Normalized decision matrix.

Alternatives	Criteria
Alternatives	IS	CHE	RM	D	E	C
Pure PMMA	0.3028	0.3416	0.3321	0.3462	0.3395	0.0911
PMMA-0.5% TiO₂	0.3376	0.3428	0.3397	0.3187	0.3294	0.2349
PMMA-1% TiO₂	0.3579	0.3510	0.3327	0.3356	0.3320	0.3787
PMMA-2% TiO₂	0.4001	0.3770	0.3273	0.3217	0.3333	0.6665
PMMA-0.5% SiO₂	0.3863	0.3324	0.3370	0.3209	0.3260	0.1438
PMMA-1% SiO₂	0.2828	0.3002	0.3326	0.3305	0.3352	0.1964
PMMA-2% SiO₂	0.2779	0.3355	0.3348	0.3568	0.3387	0.3018
PMMA-0.5% Al₂O₃	0.3480	0.3472	0.3345	0.3264	0.3289	0.2349
PMMA-1% Al₂O₃	0.2804	0.2585	0.3292	0.3413	0.3368	0.3787

Table 10.

Weighted-normalized decision matrix.

Alternatives	Criteria
Alternatives	IS	CHE	RM	D	E	C
Pure PMMA	0.0845	0.0953	0.0434	0.0453	0.0391	0.0060
PMMA-0.5% TiO₂	0.0942	0.0956	0.0444	0.0417	0.0379	0.0154
PMMA-1% TiO₂	0.0999	0.0979	0.0435	0.0439	0.0383	0.0248
PMMA-2% TiO₂	0.1116	0.1052	0.0428	0.0421	0.0384	0.0436
PMMA-0.5% SiO₂	0.1078	0.0927	0.0441	0.0419	0.0376	0.0094
PMMA-1% SiO₂	0.0789	0.0837	0.0435	0.0432	0.0386	0.0128
PMMA-2% SiO₂	0.0775	0.0936	0.0438	0.0466	0.0390	0.0197
PMMA-0.5% Al₂O₃	0.0971	0.0969	0.0437	0.0427	0.0379	0.0154
PMMA-1% Al₂O₃	0.0782	0.0721	0.0430	0.0446	0.0388	0.0248

Table 11.

Ideal and negative-ideal solution values.

Solutions	Criteria
Solutions	IS	CHE	RM	D	E	C
V ⁺	0.112	0.072	0.044	0.042	0.039	0.006
V ⁻	0.078	0.105	0.043	0.047	0.038	0.044

Table 12.

The separation measure of decision matrix.

Alternatives	Criteria
Alternatives	$S_{i}^{+}$	$S_{i}^{-}$
Pure PMMA	0.0359	0.0396
PMMA-0.5% TiO₂	0.0308	0.0345
PMMA-1% TiO₂	0.0341	0.0302
PMMA-2% TiO₂	0.0501	0.0344
PMMA-0.5% SiO₂	0.0213	0.0475
PMMA-1% SiO₂	0.0354	0.0377
PMMA-2% SiO₂	0.0429	0.0266
PMMA-0.5% Al₂O₃	0.0302	0.0356
PMMA-1% Al₂O₃	0.0384	0.0381

Table 13.

Optimized rank of alternatives by TOPSIS method.

Ranking	P _i	Alternatives	No
1	0.6905	PMMA-0.5% SiO₂	A5
2	0.5404	PMMA-0.5% Al₂O₃	A8
3	0.5288	PMMA-0.5% TiO₂	A2
4	0.5244	Pure PMMA	A1
5	0.5152	PMMA-1% SiO₂	A6
6	0.4979	PMMA-1% Al₂O₃	A9
7	0.4699	PMMA-1% TiO₂	A3
8	0.4070	PMMA-2% TiO₂	A4
9	0.3826	PMMA-2% SiO₂	A7

To sum up, the PMMA containing 0.5 wt% SiO₂ was selected as the most suitable material for the hygrothermal environment, and continuously, the PMMA with 0.5 wt% TiO₂ and Al₂O₃ were placed at second and third places, respectively.

Discussion

The moisture absorption curves revealed that all the specimens would preserve their long-term structural durability by reaching a stable condition of moisture content¹⁴ under hygrothermal aging conditions with or without the presence of nanoparticles. Generally, the large surface area to volume ratio in nanoparticles caused the increment of moisture uptake of nanocomposites.³²

Related to the diffusion coefficient values, some researches^8,11 certified that due to the growing agglomerates, voids, and cracks by increasing the nanoparticles content, the diffusion tendency in nanocomposites would increase compared to samples with low concentration of nanoparticles.

Moreover, by comparing the moisture content (Figure 4) and diffusion coefficient (Figure 5) values, a remarkable result was obtained for samples with high wt% of nanoparticles. It can be found that PMMA containing 1 wt% Al₂O₃ showed the highest diffusion coefficient in the early days of immersion, but at last, it absorbed a low level of moisture by saturation. Similar behavior was also observed in contrast for 2 wt% TiO₂ samples. In brief, It seems that the absorption behavior of specimens for short-term aging times could be considerably different from long-term hygrothermal aging. In other words, for selecting an appropriate nanocomposite for an application, alternatives could be modified with respect to the duration of exposure. Besides, the obtained results revealed that ISO-62 and ASTM D570-98 standard test methods of plastic material are not appropriate for estimating the moisture absorption behavior for long-term immersion (more than 24 h). These methods also might give the impression that the nanocomposite would absorb less moisture due to the presence of nano-filler, while the obtained results indicate quite the opposite.

The moisture absorption behavior of nanocomposites such as their absorption curve, final moisture content, and diffusivity are complex, and related to the differences in temperature of aging,³³ hygrophobicity of nano-fillers regarded to the hygrophilic behavior of matrix,³⁴ agglomeration, aspect ratio, morphology,³² and penetration of nano-fillers.⁷

A noticeable result can be observed by comparing the results of ultimate moisture content and UTS of specimens, that although the nano-filled specimens absorbed more moisture compared to pure PMMA, but this did not cause a ductile fracture behavior by them. Related to this behavior, Valsveld et al. ¹⁰ prove that the fracture behavior of nanocomposites is not only related to moisture content, but also directly depends on the nano-fillers type and nature, wt% of nano-fillers, and the duration of aging.

The evaluation of impact test results showed two main phenomena that influenced the toughness of nanocomposites. First, the improvement in the impact strength for PMMAs with low content of nanoparticles (0.5 wt%) and moisture is related to the toughness increment caused by microplastic deformation creating around the nanoparticles.³⁵ Second, in addition to the first mentioned effect, for samples with higher moisture content, more ductile behavior was also expected due to the plasticization effect of water molecules and the increased chain mobility of the polymer matrix.⁶ However, only for samples with higher content of SiO₂ and Al₂O₃ nanoparticles a different behavior was obtained.

Related to the CHE of nanocomposites, Jahan et al. ³⁶ demonstrated that the addition of nanoparticles to some polymeric matrix would increase the crystallinity, and indeed, it could reduce the swelling caused by moisture absorption. Nevertheless, for PMMA nanocomposites, such behavior did not conclude the same result.

The comparison of mechanical test results of wet specimens with our previous study in dry condition³⁷ indicates the potential effects of the hygrothermal aging process on nanocomposites. The evaluation reveals that the mean modulus of dry specimens has reduced up to 30.8% by the aging process. Besides, the addition of nanoparticles was also inefficacious on modulus in the dry environment similar to wet condition, nevertheless, a very partial increase (up to 6%) was obtained. The negative effect of moisture on nanocomposite can be discussed by softening role of water molecules in changing the nanocomposite behavior from elastic to plastic state, which would decrease the stiffness of material.

Analysis of the impact test data demonstrates a significant increase (733%) for all specimens by wet condition. Also, a notable result indicated decreasing impact strength (8.21%) values of PMMA containing 2 wt% SiO₂ compared to pure PMMA by hygrothermal aging, whereas in the dry condition, it eventuated to 62% improvement.

In contrast to the wet condition, the addition of nanoparticles improved the hardness of dry PMMA up to 8% (for 2 wt% SiO₂). Moreover, the data illustrated an appealing result that all hygrothermal aged specimens indicated about 70% enhancement in hardness for dry specimens, which is in conflict with softening effect of moisture. Related to this phenomenon, Karimzadeh et al.³⁸ reported the same result for resin-based nanocomposite contained SiO₂ and zirconia nano-fillers as a dental restorative material. In their survey, by storing both thermocycled and non-thermocycled samples in distilled water, the increment in hardness by using nano-indention test were observed as 60.52% and 23.6%, respectively, compared to ambient condition. They suggested that creation of hygrothermal stresses in nanocomposite components generated during the aging process is another factor that affects the mechanical properties of specimens.

A deeper review in previous studies ^{6,12,36,39–42} and the obtained results of this research reveals that the effect of moisture on the mechanical properties of nanocomposites does not follow a specific law and the lack of suitable macro-mechanical and micro-mechanical models for predicting these behaviors makes it essential to proceed further experiments to find it out.

The evaluation of Table 13 demonstrated that the concentration of nanoparticles has more paramount effects than material type on the properties of nanocomposites. Somehow, the samples with lower content of nanoparticles achieved the higher rank. The results also revealed that adding more than 0.5 wt%-nanoparticles is not appropriate for improving the properties of PMMA under hygrothermal conditions. However, the comparison of optimization data showed a considerable point that nanocomposites with higher content of nanoparticles indicated better performance in dry conditions in contrast to wet environments; the sample with 2 wt% TiO₂ is the optimum mixer in dry condition.

Conclusion

In this study, the properties of PMMA nanocomposites under the hygrothermal aging condition of human body were investigated. The moisture absorption curves followed Fickian model and acknowledged that the nanocomposites would retain their structural stability. The presence of nanoparticles decreased the diffusion coefficient, especially by 0.5 wt%-nanoparticles. However, at saturation time, by increasing the nano-fillers wt%, the final absorbed moisture amounts were found to increase. The addition of nanoparticles significantly reduced the tensile strength and increased the brittleness. The embedded nanoparticles in PMMA were almost ineffectual on elastic modulus and hardness. The presence of 0.5 wt%-nanoparticles was also found as an effective and reliable way to enhance the impact strength. The paramount influence of nanoparticles on CHE was obtained for samples containing 1 wt%-nanoparticles that decreased it up to 24.3%. Results of selecting the optimum combination for medical applications indicated that the addition of 0.5 wt%-nanoparticles is the best mixture for improving the properties of PMMA, particularly by using SiO₂.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Shervin Jodatnia

Samrand Rash-Ahmadi

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	IS	CHE	RM	D	E	C
IS	1	1	2	2	3	4
CHE	1	1	2	2	3	4
RM	1/2	1/2	1	1	1	2
D	1/2	1/2	1	1	1	2
E	1/3	1/3	1	1	1	2
C	1/4	1/4	1/2	1/2	1/2	1

	IS	CHE	RM	D	E	C
IS	1	1	2	2	3	4
CHE	1	1	2	2	3	4
RM	1/2	1/2	1	1	1	2
D	1/2	1/2	1	1	1	2
E	1/3	1/3	1	1	1	2
C	1/4	1/4	1/2	1/2	1/2	1

	IS	CHE	RM	D	E	C
IS	1	1	2	2	3	4
CHE	1	1	2	2	3	4
RM	1/2	1/2	1	1	1	2
D	1/2	1/2	1	1	1	2
E	1/3	1/3	1	1	1	2
C	1/4	1/4	1/2	1/2	1/2	1