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Abstract

The objective of the article is to explore the fabrication of dental restorative composite materials and the ranking order using the preference selection index (PSI) as a multi criteria decision making (MCDM) technique under a set of conflict performance defining criteria (PDCs). The polymer matrix of the dental restorative composite was prepared using bisphenol a-glycidyl methacrylate (55 wt.%), triethylene glycol dimethacrylate (44 wt.%), camphorquinone (0.3 wt.%), and ethyl 4-(dimethylamino) benzoate (0.7 wt.%). Five different dental restorative composite material compositions were fabricated using hybrid nSiO₂-TiO₂ particulates with a variation of nSiO₂ (0, 2, 4, 6, 8 wt.%) while TiO₂ is constant (15 wt.%). The results revealed that an increasing trend has been found in compressive strength, flexural strength, Vickers hardness, etc., while a decreasing trend has been shown in depth of cure, polymerization shrinkage, degree of conversion etc. The performance analysis of five dental composite formulations via the PSI method shows the following ranking order: nS4 > nS6 > nS2 > nS0 > nS8. The obtained experimental results are associated with the ranking order of the different sets of dental composite formulations. Hence, the preference selection index approach is one of the best techniques among MCDM techniques for ranking under different PDCs.

Keywords

Dental restorative composite materials Bis-GMA Performance defining criteria’s (PDCs)Multi criteria decision making (MCDM )

Introduction

Due to their aesthetic properties, dental resin composite materials have been widely employed instead of dental amalgam materials.¹ Dental resin composites have good physical, mechanical, chemical, optical, thermal, and tribological (wear) properties with great aesthetic nature than old and amalgam-filled materials.² Composite materials have superior properties to the plain polymer matrix. Resin matrix (organic) and ceramic (inorganic) fillers are two major constituents of dental restorative composite materials.³ The resin matrix’s main elements are monomers,⁴ diluents,⁵ photo initiators,⁶ accelerators,⁷ and coupling agents.⁸ The hybrid filling technique has been widely employed for dental restorative composite materials. In recent years, nano particles and nano fibers are typically employed as novel fillers due to their excellent aesthetic, bioactivity, and biocompatibility properties.⁹

Different composites have been fabricated by adding together polymers and reinforcements with multiple factors and multi-levels. Therefore, it is not very easy to choose the optimal solution from the set of criteria. The optimal performance selection may be found by multi attribute decision making (MADM) or multi criteria decision making (MCDM). MCDM/MADM is a powerful optimization technique employed to select/choose one or more materials from a set of alternatives and also gives a definite configuration for material selection/choice based on the assessment of different conflict criteria. Goh et al.¹⁰ approved the combination of AHP (analytic hierarchy process) and TOPSIS (the technique for order of preference by similarity to ideal solution) for a large pump mill electrical system. It deals with the electric loads ranking order according to the levels of the system and extracts a needless electric load from the system. A study was also investigated about implementing the MCDM (hybrid AHP-TOPSIS) technique for electronic industries to overcome its barriers.¹¹ Chen and Yang¹² proposed multiple attribute group decision making (MAGDM) for robust rank selection in the fields of economy, environment, and management suppliers. Boran et al.¹³ proposed the Fuzzy with TOPSIS technique to provide the right time, right quality, and the right price for the supplier selection problem in the group decision making environment. The Hybrid FAHP-FTOPSIS technique has been widely used in different applications for weight criterion and ranking.^14–17 Maniya and Bhatt¹⁸ suggested the application of the preference selection index (PSI) approach for the selection of materials from a set of mechanical results. A study has been investigated into the PSI approach used in the parameter settings on the lesser cutting machine for quality and productivity.¹⁹ Attri and Grover²⁰ applied the PSI technique to the decision making during the life cycle of the production system. The PSI approach has been applied to give the rank among a set of conflict criteria in alloy composite materials.

Based on the above literature, this paper investigates the design, fabrication, and evaluation of mechanical, physical, and chemical properties, and finally, the use of the hybrid PSI technique to predict the optimal formulation and ranking of the alternatives for dental restorative composite materials.

Experimental details and methodology

The polymeric matrix was fabricated by bisphenol a-glycidyl methacrylate (Bis-GMA) (Sigma Aldrich, US), triethylene glycol dimethacrylate (TEGDMA) (TCI, Japan), camphorquinone (CQ) (Spectrochem Pvt. Ltd, Mumbai, India), and ethyl 4-(dimethylamino) benzoate (EDMAB) (Sigma Aldrich, US). Nano silica (nSiO₂) (average particle size of 20–80 nm; Sigma Aldrich, US) and titanium oxide (TiO₂) (average particle size of 10–25 μm; Sigma Aldrich, US) were used as fillers. Five different formulations (nS0, nS2, nS4, nS6, and nS8) were designed with 15 wt.% as a constant fraction of titanium oxide, while 0–8 wt.% of nSiO₂ with a step of 2 wt.% and the rest of the resinous matrix. The fabrication procedure followed as (i) at first, the resinous matrix composed of Bis-GMA (55 wt.%), TEGDMA (44 wt.%), CQ (0.3 wt.%), and EDMAB (0.7 wt.%) was prepared. (ii) Thereafter, γ-MPS (3-(trimethoxysilyl) propyl methacrylate) (TCI, Japan) silane treated²¹ nSiO₂ particles were mixed with the resinous matrix in the required proportion along with TiO₂ particles. (iii) The mixture was then filled into the glass drum tubes of different specimen sizes. It was cured using a light activation unit (LED light cure GX-240, Ahmedabad, India) for 40 s on each side (with light wavelength 420–480 nm, light intensity 1200–2000 mW/cm²). After that, specimens were extracted from the glass molds for further characterization and experimentation of dental composites. The dental composite designations are shown in Table 1. The compressive strength of the dental composite specimens (Ø 5 × 6 mm) as per ASTM D695-08 standard²² and the flexural strength and modulus of dental composite specimens (25 mm × 2 mm × 2 mm) as per ISO 4049 standard²³ were performed on the universal testing machine (UTM, INSTRON-5967). The Vickers micro-hardness (Walter UHL, Germany) of dental composite specimens (Ø 8 × 6 mm) was measured as per ASTM E384-11 × 10¹.²⁴ The experimental density of the dental composite was calculated by Archimedes Principle,²⁵ while the theoretical density was determined by the rule of mixture. The experiments were repeated four times for each dental composite specimen and the average value was taken for the analysis. Depth of cure as determined by measuring the height of cured dental composite specimens (Ø4 × 8 mm) using a digital caliper (least count = 0.01 mm), water sorption (W_SP) and water solubility (W_SL) as determined with cylindrical glass mold (Ø4 × 8 mm) were calculated as per ISO 4049 standard. The polymerization shrinkage of the fabricated dental samples (Ø4 × 8 mm) was determined by the Archimedes Principle. The degree of conversion⁹ is evaluated by the ratio of absorbance intensities of the aliphatic peak at 1634 cm⁻¹ and the aromatic peak at 1608 cm⁻¹ of cured/uncured dental composite samples.

Table 1.

Details of dental composites designation and composition structure.

Composition (wt.%)	nS0	nS2	nS4	nS6	nS8
Resinous matrix	85	83	81	79	77
nSiO₂	0	2	4	6	8
TiO₂	15	15	15	15	15

Preference selection index method algorithm^{18,20,26–30}

The PSI technique comprises the following steps:

Step 1

Determine the objective of the given problem and identify the relevant selection criteria for the evaluation of the set of alternatives. As per previous literature, the hierarchy structure of the complex decision making problem clarifies the problem. The decisive objective must be at the upper portion, evaluating criteria at the middle part and alternatives/options lie at the lower portion of the hierarchy structure (Figure 1).

Figure 1.

The hierarchy structure of investigated problem.

Step 2

Formulate the initial decision matrix, A

A = {[a_{i j}]}_{m \times n} = [\begin{matrix} \begin{matrix} a_{11} & a_{12} \dots \dots & a_{1 n} \\ a_{21} & a_{22} \dots \dots & a_{2 n} \\ a_{31} & a_{32} \dots \dots & a_{3 n} \end{matrix} \end{matrix}]

(1)

where A_ij is the appraisal value of i^th alternative in respect to j^th criterion, m is the number of alternatives, and n is the number of criteria

Step 3

Discover the normalized decision matrix (B_ij) in which the data of the given matrix are expressed using the following equations:

• for larger-the-better (beneficial) criteria

B_{i j} = \frac{a_{i j}}{a_{i j}^{m a x}}; where i = 1, 2, 3, \dots, m .

(2a)

• for smaller-the-better (non-beneficial) criteria

B_{i j} = \frac{a_{i j}^{m i n}}{a_{i j}}; where i = 1, 2, 3, \dots, m .

(2b)

Step 4

Calculate the mean values of normalized performance for each criterion using the following equation

R j_{j} = \frac{1}{n} \sum_{i = 1}^{m} B_{i j}

(3)

Step 5

Compute the preference variation value for each criterion using the following equation

ϕ_{j} = \sum_{i = 1}^{m} {(B_{i j} - R j_{j})}^{2}

(4)

Step 6

Calculate the deviations value of the preference for each criterion using the following equation

ψ_{j} = 1 - \sum φ_{j}

(5)

For uniformity, the summation of overall preference value for all the criteria should be unity, that is, Σ ρ_j = 1.

Step 7

Compute the criteria weights using the following equation

ρ_{i} = \frac{ψ_{j}}{\sum_{j = 1}^{n} ψ_{j}}

(6)

Step 8

Express the preference selection index of alternatives using the following equation

I_{i} = \sum_{j = 1}^{n} (B_{ij} \times ρ_{j})

(7)

Step 9

According to the preference selection index values of the set of alternatives, compute the ranking of alternatives. The alternative which has the highest preference selection index indicates the best ranked alternative.

Results and discussion

Physical, chemical, and mechanical characterization

The various characteristics of hybrid fillers (nSiO₂-TiO₂) based dental restorative composite materials are shown and listed in Table 2 (Figures 2–4). The increasing trend was found in Vickers micro-hardness (69, 77, 84, 86, and 99 HV) and compressive strength (152, 161, 179, 201, and 205 MPa) of respective dental composites. The hardness and compressive strength of a dental restorative composite material were directly dependent on the reinforcement percentage. Noushad et al.³¹ evaluated that Vickers hardness and compressive strength increased as the filler particle percentage was added to the resin composite. The strength of dental composite material against three point bending loading in the transverse direction, that is, flexural strength (79, 82, 96, 109, and 108 MPa) and corresponding flexural modulus (1.2, 2.1, 3.2, 3.3, and 3.1 GPa) recorded to show increasing order of respective dental composites except nS8 dental composite. The flexural strength and modulus effects on regenerating stress applied during the mastication process of the mouth. According to ISO 4049, flexural strength should be more than 50 MPa (anterior restorations) for any dental composite material’s suitability.³¹ The theoretical density (1.268, 1.284, 1.307, 1.319, and 1.337 g/cc) of the different dental composites has gradually increased with increasing nSiO₂ in the resinous matrix. It depends on the uniform presence of filler particles and the increasing proportion of nSiO₂ particulates in the resin matrix. An increasing trend has been found in the void content (1.365, 1.359, 1.299, 1.216, and 1.237%) except nS8 dental composite. It may be due to improper mixing of the polymer matrix, filler particles, and improper fabrication method of the dental composite. An increasing trend was found in both water sorption (13.98, 15.23, 16.92, 18.83, and 20.34 μg/mm³) as well as water solubility (1.23, 1.56, 1.90, 2.61, and 3.05 μg/mm³) of different nSiO₂ filled dental composites. This may be due to the extraction of un-reacted components from the resinous matrix, monomer shrinkage, loss of weight, and reduction in mechanical properties.³² Higher filler filled dental composites show high water sorption and water solubility. It may be due to missing filler particles in the oral environment during mastication (saliva in the mouth). As per ISO 4049 standard, water sorption and water solubility should be less than 40 μg/mm³ and 7 μg/mm³, respectively, for any suitable dental composite materials.³³ The depth of cure (7.71, 6.91, 6.76, 6.42, and 5.81 mm) of the different dental composites decreases with increasing nSiO₂ filler particles in the resinous matrix. As per ISO 4049 standard,²³ the depth of cure should be more than 5 mm for the sustainability of the dental composite. The decreasing trend in the depth of cure could be due to the decreasing permeability of LED blue light in the different dental composites.⁹ A decreasing trend was observed in the polymerization shrinkage (2.58, 2.21, 1.96, 1.62, and 1.33%) of the dental composites with increasing nSiO₂ filler particles in the resinous matrix. It was investigated that polymerization shrinkage depends upon the curing time and curing intensity of LED blue light and it also partially depends on monomer conversions.⁹ A decreasing trend was observed in the degree of conversion (77, 74, 70, 67, and 65%) of the respective dental composites. The decreasing trend of the degree of conversion depends on the permeability of LED blue light in the dental composite and the mobility of the molecules' in the resin matrix.⁹ A similar study has been carried out by Yadav and Kumar³³ on nano-hydroxyapatite and zinc oxide reinforced dental restorative composite materials.

Table 2.

Results of different dental composite restorative composite materials for decision matrix.

PDCs ↓	Material alternatives →	nS0	nS2	nS4	nS6	nS8
PDCs ↓	PDC ↓	nS0	nS2	nS4	nS6	nS8
PDC-1	Compressive strength	152	161	179	201	205
PDC-2	Flexural strength	79	82	96	109	108
PDC-3	Flexural modulus	1.2	2.1	3.2	3.3	3.1
PDC-4	Vickers hardness	69	77	84	86	99
PDC-5	Depth of cure	7.71	6.91	6.76	6.42	5.81
PDC-6	Polymerization shrinkage	2.58	2.21	1.96	1.62	1.33
PDC-7	Density	1.268	1.284	1.307	1.319	1.337
PDC-8	Void content	1.365	1.359	1.299	1.216	1.237
PDC-9	Water sorption	13.98	15.23	16.92	18.83	20.34
PDC-10	Water solubility	1.23	1.56	1.9	2.61	3.05
PDC-11	Degree of conversion	77	74	70	67	65

Figure 2.

The variation in compressive strength, Vickers hardness, flexural strength, and flexural modulus of different dental restorative composite materials.

Figure 3.

The variation in the density, void content, water sorption, and water solubility of dental restorative composite materials.

Figure 4.

The variation in depth of cure, polymerization, and degree of conversion of different dental restorative composite materials.

Determinations of PIS method

In this article, the PIS method is applied to the decisive matrix (D), having performance criteria discussed in Table 3, with five dental composite formulations as alternatives (nS0, nS2, nS4, nS6, and nS8). The hierarchy structure of dental restorative composite materials is illustrated in Figure 5. The formulation of the initial decision matrix was calculated by equation (1). The normalized decision matrix (Bij) was calculated by equations (2a) and (2b) for larger-the-better and smaller-the-better. The mean values of normalized performance were determined by equation (3). The preference variation value, deviation value, and criteria weights were expressed by equations (4)–(6), respectively. Preference variation value, deviation value, and criteria weights for different PDCs are shown in Table 4. Finally, the preference selection index of alternatives was obtained by equation (7). Computation of Preference Selection Index (Ii) Ranking of alternatives is shown in Table 5. The performance analysis of five dental composite formulations via the PSI method shows a ranking order of nS4 > nS6 > nS2 > nS0 > nS8 under investigation (shown in Table 5). This verifies the consistency of dental resin composites in-line with an objective evaluation of performance (shown in Table 3). Hence, the PSI method could be employed for ranking orders from a set of alternatives based on performance; this could be a tool in the hands of material scientists in decision making due to the conflicting nature of the different sets of materials.

Table 3.

Descriptions of the performance defining criteria (PDCs) applied in this case study.

PDC-no.: PDC; implications on performance	Description of PDC
PDC-1: Compressive strength (CS) (MPa); (higher-the-better)	The strength that resists any material deformation along the axis, when subjected to externally applied compressive load under compression test
PDC-2: Flexural strength (FS) (MPa); (higher-the-better)	The strength that resists any material deformation against externally applied lateral load in flexure test
PDC-3: Flexural modulus (FM) (GPa); (higher-the-better)	It is the tendency for a material to resist bending forces
PDC-4: Vickers hardness (HV) (higher-the-better)	Its material resistance against plastic deformation usually by penetration/scratch. Higher hardness improves wear resistance
PDC-5: Depth of cure (DC) (mm); (higher-the-better)	It is the curing depth of the dental composite by LED curing unit
PDC-6: Polymerization shrinkage (PS) (%); (higher-the-better)	It is measured by the gap between restorative material and cavity wall after polymerization of dental resin composite
PDC-7: Density (DE) (g/cc) (lower-the-better)	It is the ratio of mass per unit volume of the material
PDC-8: Void content (VC) (%) (lower-the-better)	The amount of voids or pores in a material that may result due to fabrication error
PDC-9: Water sorption (WS) (μg/mm³); (lower-the-better)	It is defined as amount of water absorbed by the material at room temperature
PDC-10: Water solubility (WSL) (μg/mm³); (lower-the-better)	It is defined as amount of material that gets dissolved in the water at room temperature
PDC-11: Degree of conversion (DOC) (%); (higher-the-better)	It is determined from the ratio of absorbance intensities of aliphatic (C-C) peak and aromatic peak (C=C) peak

Figure 5.

The hierarchy structure of dental restorative composite materials (case study).

Table 4.

Preference variation value, deviation value, and criteria weights for different PDCs.

Materialalternatives →	nS0	nS2	nS4	nS6	nS8	SUM(Ø_j)	ψ_j	ρ_j
PDCs ↓	nS0	nS2	nS4	nS6	nS8	SUM(Ø_j)	ψ_j	ρ_j
PDC-1	0.02	0.01	0.00	0.01	0.02	0.0526	0.9474	0.1141
PDC-2	0.02	0.01	0.00	0.02	0.01	0.0666	0.9334	0.1125
PDC-3	0.17	0.02	0.04	0.05	0.02	0.3038	0.6962	0.0839
PDC-4	0.02	0.00	0.00	0.00	0.03	0.0508	0.9492	0.1144
PDC-5	0.02	0.00	0.00	0.00	0.01	0.0326	0.9674	0.1166
PDC-6	0.23	0.04	0.00	0.06	0.21	0.5412	0.4588	0.0553
PDC-7	0.00	0.00	0.00	0.00	0.00	0.0019	0.9981	0.1203
PDC-8	0.00	0.00	0.00	0.00	0.00	0.0126	0.9874	0.1190
PDC-9	0.05	0.02	0.00	0.02	0.06	0.1369	0.8631	0.1040
PDC-10	0.47	0.17	0.02	0.19	0.63	1.4850	−0.4850	−0.0584
PDC-11	0.01	0.00	0.00	0.00	0.01	0.0164	0.9836	0.1185

Table 5.

Computation of preference selection index (I_i) ranking of alternatives.

PDCs ↓	Material alternatives →	nS0	nS2	nS4	nS6	nS8
PDCs ↓	PDC ↓	nS0	nS2	nS4	nS6	nS8
PDC-1	Compressive strength	0.0846	0.0896	0.0997	0.1119	0.1141
PDC-2	Flexural strength	0.0815	0.0846	0.0991	0.1125	0.1114
PDC-3	Flexural modulus	0.0305	0.0534	0.0813	0.0839	0.0788
PDC-4	Vickers hardness	0.0797	0.0889	0.0970	0.0993	0.1144
PDC-5	Depth of cure	0.1166	0.1045	0.1022	0.0971	0.0878
PDC-6	Polymerization shrinkage	0.1072	0.0918	0.0815	0.0673	0.0553
PDC-7	Density	0.1203	0.1218	0.1240	0.1251	0.1268
PDC-8	Void content	0.1335	0.1330	0.1271	0.1190	0.1210
PDC-9	Water sorption	0.1040	0.1133	0.1259	0.1401	0.1513
PDC-10	Water solubility	−0.0584	−0.0741	−0.0903	−0.1240	−0.1449
PDC-11	Degree of conversion	0.1185	0.1139	0.1077	0.1031	0.1000
Overall preference index (I_i)		0.92	0.92	0.96	0.94	0.92
Preference ranking		4	3	1	2	5

Conclusion

The designed, fabricated, and experimental evaluation of physical, mechanical, and chemical characteristics of hybrid ceramic particulate (nSiO₂-TiO₂) reinforced dental restorative composites are analyzed using the PSI MCDM technique that leads to the following specific conclusions: The formulations have a well disbursement of ceramic particles in the resinous matrix that show superior characteristics like higher compressive strength, lower void content, lower water sorption, a higher degree of conversion etc. The results revealed that an increasing trend has been found in compressive strength, flexural strength, Vickers hardness, etc., while a decreasing trend has been shown in depth of cure, polymerization shrinkage, degree of conversion etc. The performance analysis of five dental composite formulations via the PSI method shows the following ranking order: nS4 > nS6 > nS2 > nS0 > nS8. The PSI method could be employed for ranking orders from a set of alternatives based on performance. This could be a tool in the hands of material scientists in decision making due to the conflicting nature of the different sets of materials. The sensitivity analysis reveals a stable ranking order as PDC weights change from 10% to 30%. Thus, it aids material scientists to validate their subjective ranking of materials with quantity analysis. Hence, it serves as an important tool in decision making.

Footnotes

Declaration of Conflicting Interests

We confirm that no conflict of interest while documenting this manuscript.

Funding

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

Ethical approval

We declare that no ethical approval is required for documenting this manuscript.

ORCID iD

Ramkumar Yadav

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Fabrication,characterization,and optimization selection of ceramic particulate reinforced dental restorative composite materials

Abstract

Keywords

Introduction

Experimental details and methodology

Preference selection index method algorithm18,20,26–30

Results and discussion

Physical, chemical, and mechanical characterization

Determinations of PIS method

Conclusion

Footnotes

Declaration of Conflicting Interests

Funding

Ethical approval

ORCID iD

References

Preference selection index method algorithm^{18,20,26–30}