Structure, electronic, optical and thermodynamic behavior on the polymerization of PMMA: A DFT investigation

Accepted Manuscript Title: Structure, Electronic, Optical and Thermodynamic behavior on the Polymerization of PMMA: A DFT Investigation Authors: Esha V. Shah, Chetna M. Patel, Debesh R. Roy PII: DOI: Reference:

S1476-9271(17)30415-2 https://doi.org/10.1016/j.compbiolchem.2017.10.013 CBAC 6750

To appear in:

Computational Biology and Chemistry

Received date: Revised date: Accepted date:

19-6-2017 23-9-2017 31-10-2017

Please cite this article as: Shah, Esha V., Patel, Chetna M., Roy, Debesh R., Structure, Electronic, Optical and Thermodynamic behavior on the Polymerization of PMMA: A DFT Investigation.Computational Biology and Chemistry https://doi.org/10.1016/j.compbiolchem.2017.10.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Structure, Electronic, Optical and Thermodynamic behavior on the Polymerization of PMMA: A DFT Investigation

Esha V. Shah, Chetna M. Patel and Debesh R. Roy*

Department of Applied Physics, S. V. National Institute of Technology, Surat 395007, INDIA

Graphical abstract

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Highlights  DFT investigation on structural and physicochemical aspects of PMMA is performed.  The PMMA units belong in UV-C region with a sequential red shift during growth.  The thermodynamic aspects also noticed to be in favor the polymerization process.  FMOs analysis provides incisive insight on the stability during polymerization.  NLO property for PMMA is understood through polarizability and hyperpolarizability.

ABSTRACT A density functional theory based scrutiny is implemented on the structure, electronic, optical and thermodynamic properties of the Poly (Methyl MethAcrylate) polymers (PMMA or nMMA; n = 1 to 5). The quantum chemical descriptors e.g., HOMO-LUMO gap, ionization potential, chemical hardness, binding energies etc. of the PMMA polymers provides the measure for the structural and electronic properties. The parameters polarizability (α) and hyperpolarizability (β) provides information for the non-linear optical (NLO) properties of the polymers. The absorption range of the PMMA polymer in the electromagnetic radiation spectrum during its growth is assessed by the UltraViolet-Visible (UV-Vis) optical absorption spectra. To gain further insight on the origin of stability during the polymerization process, we have simulated frontier molecular orbitals (FMOs) and various thermodynamic properties, viz., entropy (S), enthalpy (H) and Gibbs free energy (G).

Keywords: Density Functional Theory (DFT), Non Linear Optics (NLO), UV-Vis, PMMA polymers.

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*E-mail: [email protected] ,

Tel: +91 (261) 2204184 (O), Fax: +91 (261) 2227334

I. INTRODUCTION PMMA polymer acquires very wide range of applications in diverse fields like organic sensors, polymer electrolytes, molecular separators, biomedical, solar cells, nanotechnology, non-volatile memory, organic electronic devices and many more [1]. Recently the amount of research in the field of non-volatile memory utilizing PMMA polymer is found to be noteworthy. It is noticed that the introduction of insulating PMMA interlayer at the hetero-interface of CuSCN-nanopyramids/ ZnO-nanorods hetero-junction can be used as next-generation nonvolatile memory storage material [2]. It was studied that on mixing ZnS/ CdSe core-shell nanoparticles in PMMA, and using this mixture in pentacene based devices shows the effect of retention of performance in non-volatile floating gate memory devices [3]. PMMA anodes along with copper and aluminum are studied for showing resistive switching behavior of conductingbridge random-access memory (CBRAM) devices [4]. A nanocomposite formed from the blending of PMMA and 2-(4-tert-butylphenyl)-5-(4-biphenylyl)-1,3,4-oxadiazole (also known as PBD) shows the phenomena of bistable resistive switching which is important for organic nonvolatile memory devices [5]. A type of PMMA known as syndiotactic poly (methyl methacrylate) can encapsulate the fullerenes in its helical structure cavity which forms a processable complex with a macromolecular helicity memory [6]. P. S. Hariharan and coworkers [7] experimentally showed that ZnS nanoparticles show strong fluorescence in transparent PMMA matrix. Photoluminescence is observed when nanocrystals are embedded in PMMA matrix [8]. The doping of C60 in PMMA makes nanocomposite thin film which has application in organic memory devices [9]. PMMA is also noticed to be useful as good optical materials. Neodymium acetylacetonate hydrate (NAH) dopped PMMA form a potential Near

3

InfraRed (NIR) optical material which can find applications in optical fibers and thin films as observed by Y. Du and co-workers [10]. A severe experimental study conducted by Y. Kalachyova and co-workers [11] showing that porphyrin-doped PMMA can be employed as long-term stable active optical materials. PMMA can show electrical conductivity when used with conducting filler/dopants. An intensive study of conductivity across graphene/PMMA nanocomposite employing Landauer-Buttiker approach was carried out by Z. Zabihi and H. Araghi [12]. According to Al-Kadhemy and Saeed [13], on increasing the concentration of filler LiF in LiF-PMMA composites increases the D.C. electrical conductivity of the composites. A study conducted by J. Cao and co-workers [14] implied single layer of ITO/PMMA/Al as a variable resistance organic device. PMMA is also known to show important thermal properties, e.g., polystyrene and PMMA are studied as copolymers for their thermal conductivity [15]. It was observed experimentally and computationally by H. Mortazavian and co-workers [16] that PMMA Poly (methyl methacrylate) show stronger surface bonding to glass substrate compared to PVAc Poly(vinyl acetate). S. Jiang and co-workers [17] have showed through experimental investigation

that

monomer

DOPO-AA

(6-oxido-6H-dibenzo[c,e][1,2]oxaphosphinin-6-

yl)methyl acrylate when introduced into PMMA matrix to form new PMMA/DOPO-AA copolymer, maintains high transparency and improved thermal stability. I. Al-Saidi and F. Sadik [18] showed by an experimental investigation that phenol red dye doped PMMA thin films can be used in photonic devices like solar cells and optical sensors. S. Hung and co-workers [19] showed that aminoanthraquinones doped PMMA polymers are capable of displaying the mechanism of reversible photodegradation. Recently, T.J. Holmquist and co-workers [20] have studied on the mechanical properties of PMMA and concluded that it is a highly compressible material. Although a number of studies on the application of PMMA is carried out, none of the

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study has been performed on the fundamental aspects of PMMA in terms of structure, electronic, optical and thermodynamic properties of PMMA during its polymerization process. The objective of the present study is to employ density functional theory [21-23] to probe the structure, electronic, non-linear optical (NLO) and thermochemical properties of poly methyl methacrylate (nMMA; n=1-5) polymers. The stability and electronic properties of nMMA are analyzed by HOMO-LUMO energy gap (HLG), ionization potential (I.P.), chemical hardness (η), electron affinity (E.A.) and binding energies (BE) etc. during the growth of PMMA. The polarizability (α) and hyperpolarizability (β) are predicted to analyze the NLO properties. The nature of electromagnetic absorption during the growth of PMMA polymer is evaluated by the (UV-Vis) optical absorption spectra. To obtain the profound reason for the stability and/or instability of the different polymers we have scrutinized simulated frontier molecular orbitals (FMOs). To gain further insight into the thermodynamic behaviour of PMMA during its growth, we have calculated enthalpy (H), entropy (S) and Gibbs free energy (G).

II. THEORY AND COMPUTATION The electronic, optical and thermochemical properties of all the PMMA polymer units (n=1-5), viz., mono-, di-, tri-, tetra- and penta-methyl methacrylates are calculated within the framework of density functional theory (DFT) [21-23] utilizing gradient corrected approximation. The electronic structure of the polymers is probed by a linear combination of atomic orbitals (LCAO) approach. B3LYP (Becke’s three parameter exchange with Lee-YangParr correlation) functional [24], a widely used and known to be one of the most reliable hybrid functional, determines the exchange and correlation contribution in the present study. The basis

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sets employed for all the polymer units under account is an all-electron 6-31+G(d,p). The actual calculations are performed by utilizing the series of codes as implemented in GAUSSIAN 09 program [25]. According to Koopmans’ approximation, highest occupied (ЄHOMO) molecular orbital can be approximated to the ionization potential (IP) and lowest unoccupied (ЄLUMO) molecular orbital to the electron affinity (EA) [23] as: IP ≈ – ЄHOMO

; EA ≈ – ЄLUMO

(1)

Chemical hardness (η) is the measure for stability of a compound or molecule [26], and is defined as the second derivative of energy with respect to N, for an N-electron system 

considering external potential v (r ) to be fixed: 1  2E    2 2  N v ( r )

(2)

Using a finite difference approach chemical hardness (η) can also be represented in terms of ЄHOMO and ЄLUMO [23], as follows: 

IP  EA Є LUMO  Є HOMO  2 2

(3)

The electronegativity (χ) is defined as [23], E         v ( r )

(4)



where E and v (r ) are the total energy and external potential respectively. Also, a finite difference approximation, can express χ as:



IP  EA 2

6

(5)

Parr et al. [27] defined electrophilicity index (ω) as:



2 2  2 2

(6)

which measures the stabilization in energy when the system acquires an additional electronic charge ∆N from the environment. The binding energy (BE) for a single MMA molecule toward forming PMMA (or nMMA) polymer, where n = 1 to 5, is calculated as: BE = [ EMMA + E(n-1)MMA ] - EnMMA

(7)

The electric dipole polarizability (α) is defined as the second order variation in energy (E) with respect to the applied electric field (F):  2E   a ,b     ;  Fa Fb 

a , b  x, y , z

(8)

The polarizability (α) can be calculated as [23, 29]:



 xx   yy   zz 3

(9)

The polarizability is usually inversely varies with the hardness (η) of a system. A larger (more polarizable) chemical system is usually less chemically harder and vice-versa. The minimum polarizability principle (MPP) [30] states that “The natural direction of evolution of any system is towards a state of minimum polarizability”. The MPP provides a correlation between the cube root of α (  1/3 ) and inverse of ionization potential (IP-1) as follows:

 1/3  IP 1

7

(10)

The hyperpolarizibility (β) is the second order polarizability of a molecule or a system [29] and is defined as:



1 2 p 2 F 2

(11)

β can be calculated as [29, 31]:

tot 

 

2

xxx

2

  xyy   xzz     yyy   yzz   yxx     zzz   zxx   zyy 

2



(12)

III. RESULTS AND DISCUSSION The optimized geometries along with the representative bond lengths of all the nMMA polymer units are presented in Fig. 1, where n shows the number of MMA monomers as considered in PMMA polymer. It may be noted that on addition of monomer units, the lowest energy configuration of the polymers attains isotacticity (i.e., the ester groups on the same side of the plane of the polymer). < Fig. 1 > Table 1 presents various electronic parameters, viz., HOMO-LUMO energy gap (HLG), ionization potential (IP), electron affinity (EA), chemical hardness (η), electronegativity (χ), electrophilicity (ω) and binding energy (BE) for methyl methacrylate and its polymers. < Table 1 > It may be noted that all the computed properties show a particular trend towards the polymerization of MMA units (nMMA) except for n=1 (i.e. for MMA molecule) which may be expected from its de-polymerized state/effect. The HLG and η decreases toward growth direction

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indicating that polymerization makes the system softer. The large IP (>7 eV) for all the systems justifies the required stability in the polymerization process. On the other hand increase of EA and χ (except for n=1) during the growth of PMMA implies that MMA units are in favor for combining with more and more homologous molecules which is essentially required for the polymerization process. The reactivity of PMMA increases with size (except for MMA) as indicated by electrophilicity index (ω) values. The BE calculation for the MMA units by how strongly they are bound to the previous system during their growth to form PMMA reveals that MMA units are weakly bounds as their reactivity increases. < Fig. 2 > The Fig. 2 shows the profile of two important non-linear optical (NLO) parameters, viz., polarizability (α) and hyperpolarizability (β) with increase in the units of MMA in the PMMA molecules. It can be observed that both α and β values enhance almost linearly with increase of the number of MMA units. The actual values for α and β for n=1-5 in nMMA (or PMMA) is presented in Table 2. The linear increase of NLO parameters (α and β) toward the growth of PMMA polymer clearly identifies PMMA as an important NLO material which is evidenced with recent experimental studies [32, 33]. < Table 2 > Fig. 3 shows the profile of cube root of polarizability (  1/3 ) with the inverse of ionization potential

for nMMA (n=1-5) polymer. The linear relation between  1/3 and IP-1 obeys the

minimum polarizability principle (MPP) [30]. Also, such linear relation may be utilized for prediction of α or IP (if one is known) for any arbitrary dimension of PMMA polymer.

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< Fig. 3 > To gain insight into the stability of the MMA polymerization towards forming PMMA, we have generated frontier molecular orbitals (FMOs). Fig. 4 represents some important FMOs for nMMA (n=1-5). A large delocalization in the occupied states may be noticed for all nMMA towards their growth, e.g., n=1 (HOMO-1), n=2 (HOMO), n=3(HOMO-1), n=4 (HOMO-1) and n=5 (HOMO-2). These delocalizations may be understood as the source of electronic stability for assembling of MMA units towards their polymerization. < Fig. 4 > Motivated with the linear increase of the NLO parameters (α and β) during the polymerization of MMA units, we have simulated UV-Vis spectra for all nMMA (n=1-5) to understand their energy absorbance range and trends in the electromagnetic domain, as shown in Fig. 5. It is very encouraging to perceive that all the polymers belong to Ultraviolet C (i.e. 100nm - 280 nm) region of the electromagnetic spectra. This trait of the PMMA polymers gives them high potential for finding applications as strong disinfectant material in air and water refinement systems. Also, for all nMMAs, two major absorption peaks (except for n=1 which has four distinct peaks) are observed. Interestingly, in both the lower and higher peak region for nMMA, a red shift is noticed during the polymerization, viz., for lower range: 128.6 nm (n=1) to 180.3 nm (n=5) and for higher range: 211.4 nm (n=1) to 216.6 nm (n=5). This trend of red shifting clearly indicates the possibility of PMMA (with large no. of MMA units) to be active in the visible electromagnetic region. < Fig. 5 > < Table 3 > 10

Table 3 shows thermochemical parameters, viz., total entropy (S), total enthalpy (H) and total free energy (G) for methyl methacrylate and its polymers. Fig. 6 represents the profile of S, H and G with increase of MMA units towards polymerization and the actual values are shown in Table 3. The linear decrease of all the considered thermodynamic variables clearly justifies the thermodynamic stability in the polymerization of MMA to form PMMA. < Fig. 6 >

IV. CONCLUDING REMARKS In summary, structure, electronic, optical and thermodynamic properties during the growth/polymerization of methyl methacrylate (MMA) to form PMMA is investigated in detail with the aid of density functional theory. The decrease in HLG, IP and η and also increase in EA, χ and ω in general except for n=1 in nMMA (due to depolymerization effect) clearly favors the polymerization process. The linear increase of NLO parameters, viz., α and β during polymerization process motivated us to look into their optical absorption spectra. Accordingly, these nMMA units for n=1-5 are noticed to belong in UV-C region with major absorption peak range between 100 - 280 nm. Also, a sequential red shift in the spectra during the growth of the polymer addresses the suitability of visible active nature of PMMA at larger dimension as reported in recent experimental studies. The linear response of (  1/3 ) with the inverse of IP indicates that PMMA polymerization obeys the minimum polarizability principle. The thermodynamic properties, viz., S, H and G also favor the polymerization process. The present investigation will definitely provide some basic/fundamental aspect on the growth/

11

polymerization of PMMA which may be extremely useful for its application in air and water purification systems as intense disinfectants as well as in optoelectronic industries.

ACKNOWLEDGEMENTS

DRR is thankful to the SERB, New Delhi, Govt. of India, for financial support by awarding FAST Track project grant (D.O. SR/FTP/PS-199/2011). EVS is thankful to SVNIT, Surat for institute research fellowship.

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O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian 09, Revision E.01, Gaussian, Inc., Wallingford CT, (2009). [26] R.G. Parr and R.G. Pearson, J. Am. Chem. Soc. 105 (1983) 7512. [27] R.G. Parr and L.v. Szentpaly, J. Am. Chem. Soc. 121 (1999) 1922. [28] B.E.A. Saleh and M.C. Teich, Fundamentals of Photonics, 2nd Ed., WILEY, 2013. [29] G.C. Baldwin, An Introduction to Nonlinear Optics, Plenum Publishing Corporation, 1974. [30] P. K. Chattaraj and S. Sengupta, J. Phys. Chem. 100 (1996) 16126. [31] J.W. Ochterski, Thermochemistry in Gaussian (Gaussian Inc. 2000). [32] Y. Du, B. Chen, K. Liu, X. Zhao, Z. Wang, H. Lin, Opt. Eng. 53 (2014) 057102. [33] Q. M. Ali Hassan, J. Nat. Sci. Res. 4 (2014) 97.

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Table 1 HOMO-LUMO energy gap (HLG), ionization potential (IP), electron affinity (EA), chemical hardness (η), electronegativity (χ), electrophilicity (ω) and binding energy (BE) for poly methyl methacrylate (nMMA; n=1-5) polymers. n

HLG (eV)

IP (eV)

EA (eV)

η (eV)

χ (eV)

ω (eV)

BE (eV)

1

6.010

7.489

1.479

3.005

4.484

3.345

-

2

7.402

7.421

0.019

3.701

3.720

1.869

34.033

3

7.327

7.393

0.065

3.664

3.730

1.898

0.313

4

7.257

7.365

0.108

3.629

3.737

1.924

0.280

5

7.199

7.351

0.152

3.599

3.752

1.955

0.279

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Table 2 Polarizability (α) and hyperpolarizability (β) values for PMMA (nMMA, n=1-5) n

α

β

(a.u.)

(a.u.)

1

66.46

92.96

2

128.44

134.92

3

190.52

181.27

4

253.22

227.30

5

324.06

283.86

17

Table 3 Total Entropy (S), enthalpy (H) and free energy (G) for methyl methacrylate and its polymers (nMMA, n=1-5) Entropy

Enthalpy

Free Energy

(S, eV)

(H, eV)

(G, eV)

1

0.0038

-9406.446

-9407.578

2

0.0057

-18846.163

-18847.868

3

0.0074

-28252.807

-28255.021

4

0.0091

-37659.419

-37662.120

5

0.0106

-47064.612

-47067.776

n

18

FIGURE CAPTIONS Fig. 1 The optimized geometries of poly methyl methacrylate (nMMA; n=1-5) polymers. Fig. 2 Profile of polarizability (α) and hyperpolarizability (β) for PMMA (nMMA; n=1-5). Fig. 3 Profile of  1/3 with IP -1 for nMMA (n=1-5). Fig. 4 Frontier molecular orbitals of nMMA (n=1-5) Fig. 5 Optical absorption spectra of nMMA (n=1-5). Fig. 6 Profile of total Entropy (S), enthalpy (H) and free energy (G) for methyl methacrylate and its polymers (nMMA; n=1-5).

19

Fig. 1 The optimized geometries of poly methyl methacrylate (nMMA; n=1-5) polymers.

20

Fig. 2 Profile of polarizability (α) and hyperpolarizability (β) for PMMA (nMMA; n=1-5).

21

Fig. 3 Profile of  1/3 with IP-1 for nMMA (n=1-5).

22

Fig. 4 Frontier molecular orbitals of nMMA (n=1-5)

23

Fig. 5 Optical absorption spectra of nMMA (n=1-5).

24

Fig. 6 Profile of total Entropy (S), enthalpy (H) and free energy (G) for methyl methacrylate and its polymers (nMMA, n=1-5).

25