Intrinsic High Refractive Index Polymers

By Emily K. Macdonald and Michael P. Shaver*

Keywords: High refractive index polymer, Intrinsic, Optical materials, Heteroatom

polymers, Metallopolymers

Abstract

As the ubiquity and complexity of optical devices grows, our technology becomes more

dependent on specialized functional materials. One area of continued interest is in high

refractive index polymers as lightweight, processable and inexpensive alternatives to silicon

and glass. In addition to a high refractive index, optical applications require these polymers

to be transparent and have a low dispersion. Both nanocomposite and intrinsic high

refractive index polymers offer particular advantages and disadvantages. While

nanocomposite high refractive index polymers have refractive indices above 1.80, the

nanoparticle type, content and size can negatively affect storage stability and processability.

Alternatively, intrinsic high refractive index polymers are prepared by introducing an atom

or substituent with a high molar refraction into a polymer chain; the resultant polymers are

easier to store, transport, tune and process. Polymers containing aromatic groups, halogens

(except fluorine), phosphorus, silicon, fullerenes and organometallic moieties have all

shown significant promise. Many factors can affect intrinsic high refractive index polymer

performance including molecular packing, molar volume, chain flexibility and substituent

content. This mini-review summarizes the principles behind and recent developments in

intrinsic high refractive index polymers.

1

Introduction

Continuing advances in optical devices are married to advances in high refractive index

materials.1, 2 The refractive index (RI) of a material is a measure of how light propagates

through that medium, as compared to a vacuum, and when light hits an interface between

two materials with different refractive indices, the light will change speed and direction. 3

Functional materials with higher refractive indices are better suited for use in modern

photonic devices because, with a higher RI, the material can be thinner (Figure 1). Polymers

are advantageous over other materials with high RIs (i.e. silicon and glass): they are light

weight, easy to process and have a high level of mechanical strength.4, 5 High refractive index

polymers (HRIPs) have a wide range of applications including lenses,5 antireflective

coatings,6 ophthalmic applications,7 encapsulates for organic light emitting diodes and image

sensors.8 Polymers typically have a refractive index in the range of 1.3-1.79 (see Table 1 for

refractive indices for commonly used materials). Optical dispersion is another key property

for HRIPs and measures how refractive index changes with wavelength of light in Abbe

numbers.3 The Abbe number is calculated using the refractive index at three different

wavelengths: the Fraunhofer lines. HRIPs need a low dispersion, correlating with higher

Abbe numbers; Abbe numbers are also provided for selected materials in Table 1. The two

main classes of HRIPs are intrinsic and nanocomposite. This mini-review will focus on the

development of intrinsic high-refractive index polymers, highlighting some key advances in

the field and giving a broad overview of the state-of-the art. It is intended to serve as a

guide for those new to the field rather than being a comprehensive review.

2

Figure 1: Representation of refractive index versus required lens thickness.

Table 1: Comparison of refractive indices and Abbe numbers for selected materials.

Material Refractive index, ɳ Abbe number, VD

Crystalline Silicon 3.49710 N/A

TiO2 (rutile) 2.57111 9.8711

Diamond 2.41710 55.3010

Sapphire 1.77112 72.2012

Polycarbonate 1.57913 27.5613

Polystyrene 1.57713 29.1213

Quartz 1.53714 69.6914

Display Glass 1.50810 50.7410

Pyrex 1.52410 65.4010

Poly(methyl methacrylate) 1.48413 52.6013

Water 1.32715 73.0015

Nanocomposite HRIPs

Nanocomposite HRIPs are inorganic/organic hybrid materials which comprise polymer

chains tethered to or intertwined with inorganic nanoparticles of high refractive index

(>1.8). The first reports of these materials appeared in the early 1990s16 and their

performance has improved dramatically alongside parallel advances in nanotechnology. The

refractive index of a material is additive of each component, taking into account volume

fraction. Titania is one of the most common nanoparticles used,17-25 with a refractive index

of 2.450 as anatase24 or 2.571 as rutile.11 While rutile would appear to be the better choice

3

for composites, it is challenging to synthesize the required small nanoparticles; particles

above 50 nm give undesirable scattering effects.26, 27 Increasing the TiO2 content can increase

the refractive index but may also induce cracks on the surface of the nanocomposite. 20, 28

Increasing the content of the inorganic nanoparticle also increases the rigidity and fragility

of the composite, however this can be counteracted by increasing the flexibility of the

polymer chains.29 Recently, graphene has been used as the nanoparticle in nanocomposite

HRIPs, resulting in a promising refractive index of 2.058.30 ZnS has also become a popular

choice as the inorganic component31, 32 and a range of polymer chains have been attached to

the nanoparticle surface, including polyimides,18, 19, 23 methacrylates22 and sulfur-containing

materials.33 High performing nanocomposites contain polymers with high refractive indices

and low molar volumes, combined with the optimal content level of small nanoparticles.

However, these nanocomposite materials can lead to aggregation, which results in poor

stability and processability.34 All nanocomposites suffer from this same limitation in

processability: if lenses or devices are to be fabricated using high temperature extrusion or

injection moulding, nanocomposites are not ideal. While intrinsic HRIPs do not, and will not,

meet the RI performance of these nanocomposites, they offer significant advantages in

tunability, stability and processability.

Intrinsic HRIPs

4

Intrinsic HRIPs incorporate an atom or functional group with a high refractive index directly

into the polymer chain. The Lorentz-Lorenz equation (Eq. 1) can be used to predict the

refractive index of a substituent:35

n2−1n2+2

= RMx MV

=RMV M

(1)

where R is the molecular refraction, M the molecular weight and V the molecular volume of

the repeat unit. R/M can also be represented as molar refraction (Rm) and M/V as the

reciprocal of molar volume (Vm). Accordingly, a substituent with a high molar refraction and

low molar volume will increase the refractive index of a polymer. Some common functional

groups with their molar refractions are shown in Table 2.

Table 2: Comparison of molar refraction of selected substituents.

Substituent Rm /(cm3mol-1) Substituent Rm /(cm3mol-1)

H 1.100 C≡C 2.398

C 2.418 C=C 1.733

O (in OH) 1.524 4-membered ring 0.400

O (in C=O) 2.211 Phenyl 25.463

O (in ether) 1.643 Naphthyl 43.000

Cl 5.967 S (S-H) 7.691

Br 8.865 S (S-S) 8.112

I 13.900 PH3 9.104

From Table 2, aromatic groups, sulfur and the higher halogens all possess a high molar

refractivity. Molar refraction is related to the polarizability and density of the material, with

5

higher molar refractivity values obtained with more polarizable, higher density

atoms/moieties. As a beam of light enters a medium, it causes a disruption of electron

density, slowing the electromagnetic wave. More polarizable materials slow the wave more,

hence increasing the RI. Aside from the selected groups in Table 2, metallic and π-

conjugated systems are also effective at increasing the RI of the polymer.

Most intrinsic HRIPs are synthesized by either step growth polymerizations, via Michael

polyaddition or polycondensation reactions, or by radical polymerizations. A Michael

addition is the attack of a nucleophile on an α,β-unsaturated carbonyl compound; in this

case the Michael donor is a bis-nucleophile and the α,β-unsaturated carbonyl compound is a

Michael acceptor, resulting in polymerization. Scheme 1 shows one of the more recent

examples of such a polymer: a polyimidothioether synthesized by successive Michael

additions, with the high RI of 1.665 derived from the many key aromatic and sulfur

functionalities.8

Scheme 1: A polyimidothioether prepared via Michael addition from commercially available

monomers.

Polycondensations, whereby a small neutral molecule is eliminated from a bi-functional

monomer, are also a popular synthetic strategy in the synthesis of intrinsic HRIPs. The

6

example shown in Scheme 2 is of an unusual polymer with a fullerene-substituted side-chain

which benefits from the very high molar refractivities of the polyaromatic fullerene units

and possesses one of the highest reported RIs for an intrinsic HRIP (RI = 1.793).36

Scheme 2: Polycondensation of click-derived fullerene monomer to prepare an intrinsic HRIP.

A radical polymerization is a chain polymerization where the chain propagator is a reactive

radical, with polymer formation occurring through addition of this free radical to an

unsaturated monomer unit, extending the chain and forming a new radical moiety. A

carbazole phenyoxy-based methacrylate homopolymer was synthesized by McGrath et al.

by radical polymerization.37 As illustrated in Scheme 3, this free radical polymerization can

be initiated either thermally or photochemically, yielding a polymer with an RI of 1.631.

7

Scheme 3: Free radical or UV photo-polymerization of a functionalized methacrylate

monomer to afford a HRIP with RI of 1.631.

Halogen-rich HRIPs

Halogens are effective in increasing the RI of polymers, with the exception of

electronegative fluorine which is not polarizable and thus decreases the RI. Guadiana et al.

were one of the first to systematically investigate halogen-functionalized polymers,

reporting the polymerization of a series of unsaturated monomers with pendant

halogenated carbazole substituents to produce HRIPs.38 Free radical polymerization of the

substituted (meth)acrylates afforded the desired HRIPs, as depicted in Scheme 4. The

polymerization can be carried out in the melt with reaction times from minutes to hours.

8

Scheme 4: Synthesis of halogen-substituted poly(meth)acrylates by radical polymerization,

showing linker group Z, where X1, X2 and X3 are chlorine, bromine or iodine. Y1, Y2, Y3, Y4 and

Y5 are hydrogen, chlorine, bromine or iodine and R is hydrogen or methyl.

The RI of the resultant polymer varied depending on the halogen incorporated (I > Br > Cl),

correlating with their polarizability. In this specific example, the RIs ranged from 1.67-1.77, 38

with the highest RI obtained with the periodated carbazoles. Tuning could be quite precise

by controlling the number and type of halogens present to obtain specific polymer

properties. The linker group can also affect melting and glass transition temperatures, as

well as RI, with longer linker groups resulting in a decrease in RI, melting temperature (Tm)

and glass transition temperature (Tg). Lower temperatures and linker flexibility can help in

the manufacture and processing of these polymers.

Sulfur-rich HRIPs

Sulfur-containing polymers are the most extensively investigated intrinsic HRIPs and have

incorporated various moieties including thioethers,39 thianthrenes,40 sulfones,41 and many

9

other functionalities. Highlights include the work of Ueda et al. who synthesized and

characterized a number of sulfur-containing aromatic polyimides by a two-step reaction.

The process involved a polycondensation reaction followed by a thermal imidization from

the parent dianhydrides and diamines39-44 and their results confirmed that polymers with the

highest sulfur content per repeat unit had the highest RIs. However, they also noted a

significant contribution from molecular packing, tuned by controlling the steric bulk present

in the polymer backbone. Chain flexibility was also investigated through the synthesis of a

series of aromatic polyimides containing either meta or para linkages, with the meta

substituted polymers giving HRIPs with better optical transparency, as there are less chain-

chain electronic interactions.39, 41 One study highlighted the importance of low molar

volume, with replacement of a sulfonyl (O=S=O) substituent by a thioether (-S-) resulting in

an increase in RI by 0.015; the oxygen increases the molar volume and reduces the

polarisability of the sulfur atom.41 Bent structures using thianthrene rings and flexible

thioether linkages gave HRIPs with high transparency and low birefringence (high Abbe

number).40 Furthermore, it was reported that fluorene bridges increased transparency by

preventing molecular packing, but incorporating more than one fluorene group could

reduce the RI due to the considerable increase in molar volume.44 Table 3 illustrates some of

the best performing sulfur-rich polymers and their refractive indices, using the general

structure shown in Figure 2:

Figure 2: General structure of the sulfur-rich polyimides presented in Table 3.

10

Table 3: Structure and refractive index of best-performing sulfur-rich polyimides.

R1 R2 ɳ

1.735

1.719

1.746

1.740

1.716

1.760

1.755

1.737

1.769

1.742

11

1.721

1.737

1.695

1.726

1.702

1.726

More recently Ueda et al. have also synthesized poly(thioether sulfones) HRIPs by Michael

polyaddition,45 producing polymers with an RI of 1.686 and a high Abbe number. In addition

to homopolymers, copolymers have also been produced via Michael polyadditions, including

co-poly(thioether sulfone)s, with a top RI of 1.651 and high Abbe numbers.46 Yang et al.

combined the effects of flexible thioether linkers and highly conjugated rings to produce

polymers with ultra-high refractive indices of up to 1.796.47 Recently, polyamides featuring

thioether and sulfone substituents have been reported with RIs up to 1.725, with the

12

heterocycle and thioether units also imparting improved solubility in polar aprotic

solvents.48

Phosphorus-Rich HRIPs

Phosphorus has a high polarizability due to its electronic structure, with the polarizability

comparison to nitrogen remaining one of the classic components of undergraduate

inorganic curricula. Figure 3 shows atomic energy levels: the 3s-3d promotional energy for

phosphorus is 17 eV compared to 23 eV for nitrogen.49 The contribution of higher energy

levels (4s, 4p, 5s) to stabilize electronic distortions is greater in phosphorus because the

energy gap is smaller, leading to greater polarizability and hence a higher RI. This energy gap

is even smaller in, for example, metallic chromium: this is why transition metal

nanoparticles have such success in nanocomposite HRIPs. Phosphorus-containing

functionalities also tend to have good transmission in the visible region of the

electromagnetic spectrum, making them a good choice to incorporate into HRIPs.

Figure 3: Atomic energy levels of nitrogen, phosphorus and chromium.

McGrath et al. synthesized aromatic polyphosphonates through polycondensation

reactions,50 using the organocatalysts N-methyl imidazole and 4-(dimethylamino)pyridine.

13

The RI of polyphosphonates is higher than the analogous polycarbonate systems by 0.02. RI

can also be increased 0.04 by conjugating rings in a biphenol system, compared to a

bisphenol-A system. In addition to these modest RI increases, the phosphorus-rich polymers

absorb at a much lower wavelength than the polycarbonate systems, a beneficial property

for optical applications. Scheme 5 shows the top-performing polyphosphonate thus far

reported, with an RI of 1.61.

Scheme 5: Polycondensation synthesis of poly(phenylbiphenylphosphonate).

Allcock et al. reported a series of polyphosphazenes with high RIs synthesized via ring

opening polymerization (Scheme 6).51, 52 The phosphazene backbone gives the polymer a

high RI and is optically transparent in the visible region. With pendant naphthyl

functionalities, the polymers showed a shorter cut off point in the UV, limiting their utility.

However, biphenyl systems showed refractive indices as high as 1.755, and several also had

14

low optical dispersion, making them promising HRIP targets.52 The RIs for the

polyphosphazenes are given in Table 4, using the general formula in Scheme 6.

Scheme 6: Ring-opening polymerization of phosphazenes to prepare polyphosphazene

HRIPs substituted by various R groups (Table 4).

Table 4: Refractive indices of substituted polyphosphazenes.

R X = H Br I1.618-1.620 1.644-1.646 1.710-1.715

1.662-1.664 1.686-1.688 1.750-1.755

1.632-1.634 1.646-1.648 1.682-1.684

1.650-1.652 1.660-1.662 1.664-1.666

Allcock’s group also investigated the ring-opening polymerization of sulfur-substituted cyclic

phosphazenes,53 with an RI as high as 1.616 with an ethylthio substituent. Scheme 7 shows

the range of cyclic phosphazenes prepared.

15

Scheme 7: Preparation of substituted cyclotriphosphazenes.

Silicon-Rich HRIPs

Recently, intrinsic HRIPs have been extended to those containing silicon and heavier main

group compounds.54, 55 Polymers containing these highly polarizable main group elements,

including silicon, germanium, tin and sulfur, can be synthesized by a slow reaction between

a main group vinyl or allyl compound and a multi-functional thiol. As an example, the

reaction shown in Scheme 8 is the thiol-ene coupling reaction between tetravinylgermane

and 1,2-ethanedithiol. The reaction can use virtually any vinyl or allyl substituted main

group monomer and a dithiol monomer, with selected examples shown in Figure 4.

Scheme 8: Preparation of branched HRIP from the poly(thiol-ene) reaction of

tetravinylgermane and 1,2-ethanedithiol.

16

Figure 4: Vinyl, allyl and dithiol monomers used in thiol-ene coupling reactions.

The resulting polymers were highly cross-linked, improving their mechanical strength. High

refractive indices were obtained from the incorporation of the polarizable main group

elements and the absence of highly electronegative, low-polarizability atoms such as

nitrogen or oxygen, common in many other high RI polymers. The refractive indices varied

significantly over the range of 1.590-1.703.55 Copolymers incorporating silicon have also

been synthesized via hydrosilylation, as shown in Scheme 9, obtaining a maximum RI of

1.605.56

17

Scheme 9: Hydrosilation of poly(siloxane) macromonomers to prepare branched HRIPs.

Silicon-based HRIPs offer exceptional stability, finding particular application in light emitting

diodes. This is especially true when the polymer is cross-linked where composition pot lives

reach upwards of 24 hours.46

Organometallic HRIPs

As with nanocomposite HRIPs, metal incorporation into the polymer gives excellent RIs. To

overcome difficulties with solubility and processability, recent research has focused on

polymers of organometallic coordination compounds, building the metals into the polymer

chain. Organometallic species combine the highly refractive metal and the macromolecular

nature of an intrinsic HRIP. Manners et al.47 synthesized a range of polyferrocenes with both

high refractive indices and high Abbe numbers, possessing very low optical dispersions. The

18

polymers were easily synthesized by ring opening polymerization of the strained cyclic

monomer and contained main group spacers to further boost the RI, incorporating

phosphorus, silicon, germanium and tin alongside a range of R groups, as shown in Table 5.

Table 5: Refractive indices of polyferrrocenes.

Repeat unit E R/R1 ɳ

Si

R = CH3; R1 = CH2CH2CF3 1.60R = CH3; R1 = CH2CH3 1.66

R = R1 = CH3 1.68R = CH3; R1 = C6H5 1.68

Ge R = R1 = CH3 1.69

SnR = R1 = tBu 1.64

R = R1 = Mes 1.66R = R1 = Nap 1.82

P

R = C6H5; X = absent 1.74R = C6H5; X=S 1.72

Tang et al.48 produced a remarkable organocobalt polymer that had an RI of 1.813, with low

optical dispersion and high optical transparency. This polymer cannot be injection moulded,

but is readily spin-coated, making it an ideal candidate for optical coatings if the synthesis

can be scaled. The basic structure of the polymer is shown in Figure 5.

19

Figure

Conclusions

In this mini-review, we have introduced the field of intrinsic HRIPs. Offering advantages of

stability and easy processing compared to nanocomposite HRIPs, these polymers can be

precisely tuned by controlling the functional group, relative position, steric bulk and

flexibility in the polymer chain. A high molar refraction and low molar volume are the main

considerations for substituent choice when designing an intrinsic HRIP. Most intrinsic HRIPs

are produced by Michael polyaddition or polycondensation reactions, thus straightforward

to manufacture on a large scale. Several simple trends give guidance to future HRIP design:

a higher percent of the moiety of choice increases RI; limiting steric bulk in the polymer

improves molecular packing and increases RI; and flexibility in the chain makes the polymer

easier to process.

Early research focused on halogen-rich HRIPs, before a considerable effort was made in the

development of sulfur-rich polymers. Recently, new intrinsic HRIPs have emerged using

phosphorus and silicon building blocks. These new systems are complemented by rare

examples of heavier, even more polarizable, main group elements that have been exploited

in these systems. Organometallic HRIPs also give high refractive indices along with low

optical dispersion and, while challenging to injection mould, are suitable for spin-coating. Of

course, the key driver in the search for new intrinsic HRIPs is in the ever expanding range of

applications: from encapsulants for LEDs, thin lenses such as those found in mobile devices,

fibre optic communications materials with minimal or zero birefringence and advanced

sensors and functional coatings. On the more fundamental side, we expect that the upper

20

limit of intrinsic polymer refractive indices has yet to be reached. In particular, phosphorus,

silicon and organometallic components remain understudied, as do the interfacial areas

combining two or more of these high molar refractivity functionalities. Due to the ever

present demand for improved polymer properties for use in next-generation optical devices,

research will continue to push the limits of intrinsic HRIPs, targeting performance polymers

that remain easy to manufacture, process and store.

Acknowledgements

We would like to thank the University of Edinburgh, EaStCHEM and the Marie Curie Actions

Program (FP7-PEOPLE-2013-CIG-618372) for funding. We would also like to thank Dr Laura

Allan for helpful discussions.

References

1. Ma H, Jen AKY, Dalton LR, Adv Mater. 14: 1339-65 (2002)

2. A. Nakamura HF, N. Juni, N. Tsutsumi, Optical Review. 13: 104-10 (206)

3. M. Born EW, Principles of Optics, 7th ed, Cambridge University Press, Cambridge, 1999

4. Gao C, Yang B, Shen J, J Appl Polym Sci. 75: 1474-9 (2000)

5. Matsuda T, Funae Y, Yoshida M, Yamamoto T, Takaya T, J Appl Polym Sci. 76: 50-4 (2000)

6. Krogman KC, Druffel T, Sunkara MK, Nanotechnology. 16: S338-43 (2005)

7. K. Mentak SR, High refractive index polymers for ophthalmic applications, US patent US

7,354,980 B1, 2008

21

8. Yen H-J, Liou G-S, J Mater Chem. 20: 4080 (2010)

9. Biron M, Optical Applications. 49-53 (2010)

10. Bass M, Lakshinarayanana V, Li G, MacDonald C, Mahajan VN, Decusatis CM, et al.,

Handbook of Optics, Volume IV, 3rd ed, McGraw-Hill, Unites States, 2009

11. Devore JR, J Opt Soc Am. 41: 416-7 (1951)

12. Harman AK, Ninomiya S, Adachi S, J Appl Phys. 76: 8032-6 (1994)

13. Kasarova SN, Sultanova NG, Ivanov CD, Nikolov ID, Optical Materials. 29: 1481-90 (2007)

14. Ghosh G, Opt Commun. 163: 95-102 (1999)

15. Hale GM, Querry MR, Appl Opt. 12: 555-63 (1973)

16. Novak B, Adv Mater. 5: (1993)

17. Chang C-C, Chen W-C, J Polym Sci, Part A: Polym Chem. 39: 3419-27 (2001)

18. Chang C-M, Chang C-L, Chang C-C, Macromol Mater Eng. 291: 1521-8 (2006)

19. Su H-W, Chen W-C, J Mater Chem. 18: 1139 (2008)

20. Chau JLH, Tung C-T, Lin Y-M, Li A-K, Materials Letters. 62: 3416-8 (2008)

21. Oda S, Uchiyama H, Kozuka H, J Sol-Gel Sci Technol. 61: 484-93 (2012)

22. Tao P, Li Y, Rungta A, Viswanath A, Gao J, Benicewicz BC, et al., J Mater Chem. 21: 18623

(2011)

23. J. Liu YN, T. Ogura, Y. Shibusaki, S. Ando, M. Ueda, Chem Mater. 20: 273-81 (2008)

24. Yuwono AH, Liu B, Xue J, Wang J, Elim HI, Ji W, et al., J Mater Chem. 14: 2978 (2004)

25. R. Nussbumer WC, P. Smith, T. Tervoort, Macromol Mater Eng. 288: 44-9 (2003)

26. Tsai C-M, Hsu S-H, Ho C-C, Tu Y-C, Tsai H-C, Wang C-A, et al., J Mater Chem C. 2: 2251 (2014)

27. Imai Y, Terahara A, Hakuta Y, Matsui K, Hayashi H, Ueno N, Polym J. 42: 179-84 (2009)

28. Y. Kurata OS, T. Kaino, K. Komatsu, N. Kambe, J Opt Soc Am B. 26: (2009)

29. E. Nicol DD, T. Nicolai, Macromolecules. 34: 59-65 (2001)

30. Zhang G, Zhang H, Zhang X, Zhu S, Zhang L, Meng Q, et al., J Mater Chem. 22: 21218 (2012)

31. Liu L, Zheng Z, Wang X, J Appl Polym Sci. 117: 1978-83 (2010)

22

32. Lu C, Cui Z, Wang Y, Li Z, Guan C, Yang B, et al., J Mater Chem. 13: 2189 (2003)

33. Lin Z, Cheng Y, Lü H, Zhang L, Yang B, Polymer. 51: 5424-31 (2010)

34. Liu J-g, Ueda M, J Mater Chem. 19: 8907 (2009)

35. Dislich H, Angew Chem Int Ed Engl. 18: 49-59 (1979)

36. Yan H, Chen S, Lu M, Zhu X, Li Y, Wu D, et al., Materials Horizons. 1: 247-50 (2014)

37. McGrath JE, Rasmussen L, Shultz AR, Shobha HK, Sankarapandian M, Glass T, et al., Polymer.

47: 4042-57 (2006)

38. Gaudiana RA, Minns RA, Rogers HG, High refractive index polymers, US patent US 5,132,430,

1992

39. Liu J-G, Nakamura Y, Shibasaki Y, Ando S, Ueda M, J Polym Sci, Part A: Polym Chem. 45: 5606-

17 (2007)

40. Liu J-g, Nakamura Y, Shibasaki Y, Ando S, Ueda M, Macromolecules. 40: 4614-20 (2007)

41. Liu J-g, Nakamura Y, Suzuki Y, Shibasaki Y, Ando S, Ueda M, Macromolecules. 40: 7902-9

(2007)

42. N. You YS, D., Yorifuji SA, M. Ueda, Macromolecules. 41: 6361-6 (2008)

43. You N-H, Suzuki Y, Higashihara T, Ando S, Ueda M, Polymer. 50: 789-95 (2009)

44. Terraza CA, Liu J-G, Nakamura Y, Shibasaki Y, Ando S, Ueda M, J Polym Sci, Part A: Polym

Chem. 46: 1510-20 (2008)

45. R. Okutsu YS, S. Ando, M. Ueda, Macromolecules. 41: 6165-8 (2008)

46. Suzuki Y, Higashihara T, Ando S, Ueda M, Euro Polym J. 46: 34-41 (2010)

47. Li C, Li Z, Liu J-g, Zhao X-j, Yang H-x, Yang S-y, Polymer. 51: 3851-8 (2010)

48. Li Z-m, Zhang G, Li D-s, Yang J, Chin J Polym Sci. 32: 292-304 (2014)

49. Hudson RF, Structure and Mechanism in organo-phosphorus chemistry, ed, Academic Press,

London, 1965

50. Shobha HK, Sekharipuram V, McGrath JE, Bhatnagar A, High refractive index thermoplastic

polyphosphonates, US patent 6,288,210 B1, 2001

23

51. Olshavsky M, Allcock HR, Macromolecules. 30: 4179-83 (1997)

52. Olshavsky MA, Allcock HR, Macromolecules. 28: 6188-97 (1995)

53. Fushimi T, Allcock HR, Dalton Trans. 2477-81 (2009)

54. Stiegman A, High refractive index polymers, US patent 2011/0054136 A1, 2011

55. Bhagat SD, Chatterjee J, Chen B, Stiegman AE, Macromolecules. 45: 1174-81 (2012)

56. Mosley DW, Khanarian G, Conner DM, Thorsen DL, Zhang T, Wills M, J Appl Polym Sci. 131:

(2014)

24