Microstructure Of Copolymers Research Articles

Microstructure and mechanical properties of a statistical aromatic-aliphatic copolyester synthesized by catalytic transesterification

Copolymerising polyethylene terephthalate (PET) and polycaprolactone (PCL) could provide a cost-effective method to recycle PET waste into a compostable plastic. In this work we investigated the relationship between formulation, microstructure, and mechanical properties during catalytic transesterification. It was found that the wt.% PCL was most effective in reducing the average PET block length and determining the copolymer's microstructure at equilibrium. Catalytic transesterification is a random process and can only give a narrow distribution when the average homopolymer block length is less than three, as determined by 1H NMR spectroscopy. A statistical copolymer marks reaction equilibrium where the average PCL block length is greater than one, contradicting the theoretical limit of a single PCL block length. It was proposed that the number of PCL ester groups available for reaction diminishes as transesterification progresses, leading to a favouring of the more abundant PET ester groups to undergo neutral or reverse reactions, resulting in equilibrium. As a result of the imbalance in the availability of PET and PCL ester groups at equilibrium, secondary factors, such as increasing the catalyst amount, were ineffective in further propagating transesterification. Copolymers formed in this study were either amorphous or semi-crystalline. The mechanical properties had minimal correlation with crystallinity and instead was mainly influenced by the ratio between the “hard” (PET) and “soft” (PCL and copolymer) segments in the microstructure and the molecular mass. In this study it was demonstrated that the microstructure of aromatic-aliphatic copolymers, synthesized through catalytic transesterification, can be manipulated to tailor physical properties to meet application requirements.

Using Probability Models to Design the Microstructure of Linear Olefin Block Copolymers

Using Probability Models to Design the Microstructure of Linear Olefin Block Copolymers

Impact of Ionic Strength (Sodium Chloride Concentration) on Homopolymerization and Copolymerization Kinetics of Acrylamide and 2‐Acrylamido‐2‐Methylpropane Sulfonic Acid

AbstractAnionic polyelectrolytes can be used for a variety of applications, including flocculation and enhanced oil recovery. While it is widely recognized that polyelectrolyte synthesis is impacted by the pre‐polymer formulation and polymerization conditions, the specific relationships between these factors and the subsequent polymer properties are not well understood. Therefore, the current work intends to improve understanding of ionic strength (IS) effects during the copolymerization of 2‐acrylamido‐2‐methylpropane sulfonic acid (AMPS) and acrylamide (AAm). The aims of the study are i) to use in situ H1 NMR to study copolymerization kinetics, and ii) to determine how increasing IS impacts copolymerization kinetics (and, by extension copolymer microstructure). It is found that altering IS prior to copolymerization has significant impacts on the reactivity ratios, and therefore impacts the microstructure through multiple mechanisms. Increasing IS causes a crowding effect, where the propagating chain develops a random coil conformation and causes steric hindrance of the large AMPS monomer, decreasing the likelihood of AMPS propagation. When the IS is increased further, the ionic shielding effect is more impactful, increasing the likelihood of AMPS propagation. Ultimately, this work will make it possible to manipulate IS to synthesize AMPS/AAm copolymers with specific desirable properties for target applications.

Selective Transesterification to Control Copolymer Microstructure in the Ring-Opening Copolymerization of Lactide and ε-Caprolactone by Lanthanum Complexes.

A series of novel lanthanum amido complexes, supported by ligands designed around the salan framework (salan = N,N'-bis(o-hydroxy, m-di-tert-butylbenzyl)-1,2-diaminoethane) were synthesized and fully characterized in the solid and solution states. The ligands incorporate benzyl or 2-pyridyl substituents at each tertiary amine center. The complexes were investigated as catalysts in the ring-opening homopolymerization of lactide (LA) and ε-caprolactone (ε-CL) and copolymerization of equimolar amounts of LA and ε-CL at ambient temperature. Solvent (THF or toluene) and the number of 2-pyridyl groups in the complex were found to influence the reactivity of the catalysts in copolymerization reactions. In all cases, complete conversion of LA to PLA was observed. The use of THF, a coordinating solvent, suppressed ε-CL polymerization, while the presence of one or more 2-pyridyl groups promoted ε-CL polymerization. Each copolymer gave a monomodal trace in gel permeation chromatography-size-exclusion chromatography (GPC-SEC) experiments, indicative of copolymer formation over homopolymerization. Copolymer microstructure was found to be dependent on catalyst structure and reaction solvent, ranging from blocky to close to alternating. Experiments revealed rapid conversion of LA in the initial stages of the reaction, followed by incorporation of ε-CL into the copolymer by either transesterification or propagation reactions. Significantly, the mode of transesterification (TI or TII) that occurs is determined by the structure of the metal complex and the reaction solvent, leading to the possibility of controlling copolymer microstructure through catalyst design.

Synergistic effects of dry-brush compatibility and shear stress on rapid alignment of lamellar microstructures for block copolymer reflectors

Because of the high viscosity of severe chain entanglements, a time-consuming process of aligning microstructural orientation in high molecular-weight (Mw) block copolymer photonic crystal films imposed limitations on efficient mass production. In this study, the effective alignment of the block copolymer microstructures in the film state can be carried out within approximately a few minutes. This achievement was realized through the synergistic localized compatibility of dry brush and shear stress during the spin-casting process. The orientation and orderliness of the microphase-separated lamellar structure in as-spun poly(styrene)-block-poly(4-vinylpyridine) (PS-b-P4VP) films can be meticulously controlled by introducing blends with PS homopolymer (hPS) of varying Mws (Mw,hPS) and cholesteric liquid crystal mesogen (Chol). Within the ternary blended films of hPS/PS-b-P4VP(Chol), the wet-brush miscibility by blending low-Mw hPS with a small molecular weight ratio (α) of Mw,hPS to Mw,bPS (Mw of the PS block chain) of α <1 results in the formation of disoriented lamellar structures, whereas dry-brush localization by introducing high-Mw hPS with α∼0.9 yields highly parallel-aligned lamellar structures to the substrate after spin casting, even with a massive quantity of additive hPS (∼59 wt%). The dry-brush compatibility can be demonstrated by morphological observation in the ternary blended film after extraction of the hPS. As a result, without any further efforts, such as additional solvent or thermal annealing treatments, the as-spun ternary blended film can exhibit visible structural colorations with controlled wavelengths by alternating the quantity of hPS. This provides an accessible solution for rapidly producing flexible photonic crystals featuring tunable photonic band gaps.

Mechanism of Alternating Poly(lactic-co-glycolic acid) Formation by Polymerization of (S)- and (R)-3-Methyl Glycolide Using an Enantiopure Aluminum Complex.

The mechanism(s) of alternating PLGA synthesis by ring-opening polymerization of (S)- and (R)-3-methyl glycolide promoted by enantiopure aluminum complexes have been rationalized by density functional theory (DFT) calculations. The high regioselectivity of the (S)-MeG polymerization is obtained by repetitive ring opening at the glycolyl site by the (R)-catalyst whereas a lower regioselectivity is predicted by the ROP of (R)-MeG. The behavior of the two monomers is rationalized by unveiling the active site fluxionality of the enantiopure catalyst, identifying the rate-limiting steps that encode a preference at the glycolyl site versus the lactyl site, and revealing selection of the opposite monomer enantioface. The microstructure of the PLGA copolymers is predicted by considering the influence of the configuration of the last inserted unit. The identification of the preferred mechanistic paths may allow for a targeted catalyst design to enhance control of the polymer microstructures.

Synthesis of Deuterated and Sulfurated Polymers by Inverse Vulcanization: Engineering Infrared Transparency via Deuteration.

The synthesis of deuterated, sulfurated, proton-free, glassy polymers offers a route to optical polymers for infrared (IR) optics, specifically for midwave IR (MWIR) photonic devices. Deuterated polymers have been utilized to enhance neutron cross-sectional contrast with proteo polymers for morphological neutron scattering measurements but have found limited utility for other applications. We report the synthesis of perdeuterated d14-(1,3-diisopropenylbenzene) with over 99% levels of deuteration and the preparation of proton-free, perdeuterated poly(sulfur-random-d14-(1,3-diisopropenylbenzene)) (poly(S-r-d14-DIB)) via inverse vulcanization with elemental sulfur. Detailed structural analysis and quantum computational calculations of these reactions demonstrate significant kinetic isotope effects, which alter mechanistic pathways to form different copolymer microstructures for deutero vs proteo poly(S-r-DIB). This design also allows for molecular engineering of MWIR transparency by shifting C-H bond vibrations around 3.3 μm/3000 cm-1 observed in proteo poly(S-r-DIB) to 4.2 μm/2200 cm-1. Furthermore, the fabrication of thin-film MWIR optical gratings made from molding of deuterated-sulfurated, proton-free poly(S-r-d14-DIB) is demonstrated; operation of these gratings at 3.39 μm is achieved successfully, while the proteo poly(S-r-DIB) gratings are opaque at these wavelengths, highlighting the promise of MWIR sensors and compact spectrometers from these materials.

Copolymerization of ethylene and isoprene via silicon bridge metallocene [rac-Me2Si(2-Me-4-Ph-Ind)2ZrCl2] catalyst: A new way to control the composition and microstructure of copolymers

The copolymerization of ethylene (E) with isoprene (Ip) was performed catalyzed by a symmetrical catalyst exhibiting a silicon bridge [rac-Me2Si(2-Me-4-Ph-Ind)2ZrCl2 with the combination of borate/TIBA activator. The effect of cocatalyst, Ip concentration, and polymerization temperature on the activity, molecular weight (Mw), distribution (MWD), comonomer composition, chain structure (regio- and stereoselectivity), and resulting side reactions were logically addressed. Gel-permeation chromatography (GPC) was used to characterize the Mw and polydispersity, while nuclear magnetic resonance (NMR) was employed for the chain structure of the polymers. The catalytic activity was significantly lower by increasing the Ip concentration in the feed, and the isoprene content in resulting polymers was lower under the reaction condition, leading to higher activity. Insertion of isoprene units in polymer structure demonstrates the higher regioselectivity for the 3,4 connections than the 1,4 connections and is expected to be a high-resistance polymer against acids. The MWD presented monomodal even with a higher concentration (1.44 mol/L) and did not appear as low Mw peaks of Ip. The Mw was higher with a broader MWD when purely TIBA was used as a cocatalyst, and it significantly reduced and presented a narrowed MWD with TEA in the cocatalyst. The higher efficiency of the catalyst for the higher insertion of Ip (C=C double bond) effectively modifies the polymer backbone. It is expected to be a promising candidate for easily degradable and favorable solutions for solving environmental problems caused by PE. wastes.

Manipulating Cis-Trans Copolymer Chain Conformation to Simultaneously Improve Permittivity and DC Breakdown Strength in Polythiourea.

Polythioureas (PTUs) show great potentials for applications in the new generation of film capacitors due to their excellent dielectric properties. Herein, the cis-trans copolymer chain of PTU is successfully tailored by employing cis and trans cyclohexyl spacers. The relationship between the copolymer chain conformation, microstructure, and dielectric properties is carefully explored by a series of analysis. Compared with cis conformation, the trans with less steric hindrance can promote the formation of H-bonds. The enhanced H-bonding interactions not only reduce the molecular inter-chain spacing, but also drive the self-assembly of molecular chains to form cylindrical and droplet nano-morphologies. The phase separation between cis and trans PTUs is confirmed by combining the experimental results of TEM and DSC, and the CT64-PTU with the most two-phase interface thus obtains the highest permittivity of 5.5 (@10Hz). The reduced molecular inter-chain spacing is accompanied by a decreased hopping distance of charges, which improves breakdown strength by 17% from 498 MV/m to 580 MV/m. Therefore, the cis-trans copolymer chain conformation in PTU provides a simultaneous high permittivity and breakdown strength. This research offers a strategy to further design high-performance dielectrics via regulation of copolymer chain conformation.

New Insight into Nanoscale Identification of the Polar Axis Direction in Organic Ferroelectric Films.

Ferroelectric poly(vinylidene fluoride-co-trifluoroethylene) [P(VDF-co-TrFE)] thin films have been deposited by spin-coating onto the Bi0.5Na0.5TiO3(BNT)/LNO/SiO2/Si heterostructure. The copolymer microstructure investigated by using grazing-incidence wide-angle X-ray diffraction (GIWAXD) and deduced from the (200)/(110) reflections demonstrates that the b-axis in the P(VDF-co-TrFE) orthorhombic unit cell is either in the plane or out of the plane, depending on the face-on or on the two types of edge-on (called I and II) lamellar structures locally identified by atomic force microscopy (AFM). For edge-on I lamellae regions, the electroactivity (dzzeff ∼ -50.3 pm/V) is found to be twice as high as that measured for both edge-on II or face-on crystalline domains, as probed by piezoresponse force microscopy (PFM). This result is directly correlated to the direction of the ferroelectric polarization vector in the P(VDF-co-TrFE) orthorhombic cell: larger nanoscale piezoactivity is related to the b-axis which lies along the normal to the substrate plane in the case of the edge-on I domains. Here, the ability to thoroughly gain access to the as-grown polar axis direction within the edge-on crystal lamellae of the ferroelectric organic layers is evidenced by combining the nanometric resolution of the PFM technique with a statistical approach based on its spectroscopic tool. By the gathering of information at the nanoscale, two orientations for the polar b-axis are identified in edge-on lamellar structures. These findings contribute to a better understanding of the structure-property relationships in P(VDF-co-TrFE) films, which is a key issue for the design of future advanced organic electronic devices.

Investigation of monomer reactivity, polymer microstructure and solubility in the copolymerization of 1,5-dioxepan-2-one with alkyl substituted lactones

Ring Opening Polymerization of lactones is an excellent synthetic tool for the production of polyesters with tuned microstructure. In copolyesters, the polymer microstructure is an important feature that can greatly influence the properties. Therefore, it is desirable to investigate the copolymerization behaviour of monomers. In this work, the copolymerization of 1,5-dioxepan-2-one (DXP) with the potentially renewable alkyl substituted lactones δ-undecalactone (UDL) and β,δ-trimethyl-ε-caprolactone (TMCL) was investigated. The reactivity ratios were determined for both monomer pairs, and revealed that both substituted lactones react significantly different with DXP. Furthermore, the microstructure of copolymers from DXP and UDL with different monomer feed ratios was characterized by quantitative 13C NMR and MALDI-ToF MS analysis. The resulting copolymers exhibited a varying degree of randomness depending on the monomer feed ratio. The lactones in this study were selected for their different solubility properties. The Hansen solubility spheres were determined for the homo-and copolymers of DXP and UDL. Using this, we demonstrated that the polymer solubility properties can be tuned by copolymerization of polar and apolar monomers.

Controlled Radical Polymerization of Acrylates and Isocyanides Installs Degradable Functionality into Novel Copolymers.

Installing ketones into a polymer backbone is a known method for introducing photodegradability into polymers; however, most current methods are limited to ethylene-carbon monoxide copolymerization. Here we use isocyanides in place of carbon monoxide in a copolymerization strategy to access degradable nonalternating poly(ketones) that either maintain or enhance the thermal properties. A cobalt-mediated radical polymerization of acrylates and isocyanides synthesizes nonalternating poly(acrylate-co-isocyanide) copolymers with tunable incorporation using monomer feed ratios. The kinetic product of the polymerization is a dynamic β-imine ester that tautomerizes to the β-enamine ester. Hydrolysis of this copolymer affords a third copolymer microstructure─the elusive nonalternating poly(ketone)─from a single copolymerization strategy. Analysis of the copolymer properties demonstrates tunable thermal properties with the degree of incorporation. Finally, we show that poly(acrylate-co-isocyanide) and poly(acrylate-co-ketone) are photodegradable with 390 nm light, enabling chain cleavage.

Temperature Directs the Majority-Rules Principle in Supramolecular Copolymers Driven by Triazine-Benzene Interactions.

Supramolecular copolymers have typically been studied in the extreme cases, such as self-sorting or highly mixed copolymer systems, while the intermediate systems have been less understood. We have reported the temperature-dependent microstructure in copolymers of triazine- and benzene-derivatives based on charge-transfer interactions with a highly alternating microstructure at low temperatures. Here, we investigate the temperature-dependent copolymerization further and increase the complexity by combining triazine- and benzene-derivatives with opposite preferred helicities. In this case, intercalation of the benzene-derivative into the triazine-derivative assemblies causes a helical inversion. The inversion of the net helicity was rationalized by comparing the mismatch penalties of the individual monomers, which indicated that the benzene-derivative dictates the helical screw-sense of the supramolecular copolymers. Surprisingly, this was not reflected in further investigations of slightly modified triazine- and benzene-derivatives, thus highlighting that the outcome is a subtle balance between structural features, where small differences can be amplified due to the competitive nature of the interactions. Overall, these findings suggest that the temperature-dependent microstructure of triazine- and benzene-based supramolecular copolymers determines the copolymer helicity of the presented system in a similar way as the mixed majority-rules phenomenon.

Advance on nickel‐ and palladium‐catalyzed insertion copolymerization of ethylene and acrylate monomers

AbstractNickel‐ and palladium‐catalyzed insertion copolymerization of ethylene and acrylate comonomers for synthesis of ethylene‐acrylates copolymers have attracted much academic and industrial interests and remained highly challenging. This review provides an overview of the developments in nickel‐ and palladium‐catalyzed insertion copolymerization of ethylene and acrylate comonomers. Mechanistic interpretation of metal‐catalyzed insertion copolymerization of ethylene and acrylate comonomers is described. Late transition metal catalysts are divided to nickel‐based and palladium‐based catalysts with different chelate ligands. The effects of catalyst structure on copolymerization performance and copolymer microstructure are comprehensively discussed. This review aims to promote the design and development of nickel and palladium catalysts for ethylene/acrylate copolymerizations and synthesis of ethylene‐acrylates copolymers.

Microstructure similarity analysis between synthetic phase-separated block copolymers and natural spider silk

This papers primary purpose is to explore why the microstructure of synthetic block copolymers and natural spider silk is similar at the nanoscale. This paper analyses the main chain segments and secondary structures of natural spider silk, clarifies the aggregation order, and introduces the contribution of secondary systems to the properties of natural block copolymers. Secondly, combined with the synthesis mechanism of natural spider silk, this paper summarizes and analyzes the general process of the synthesized block copolymer. Finally, the conditions of self-assembly of artificial fragments to form the structure are analyzed by employing mean-field theory and a phase diagram. Natural and ideal synthetic spider silk block copolymers have high similarity in performance. To achieve this, scientists can only start from the primary segment to understand their arrangement order in the secondary structure. Then the influence of each block on the properties of the silk fiber is analyzed. At the same time, the size and shape of self-assembled block copolymers are controlled at the micro-scale, thereby changing their properties. The mechanism above shows that the synthesized spider silk block copolymer is similar to natural spider silk in microscopic morphology.

Biobased Copolymers via Cationic Ring-Opening Copolymerization of Levoglucosan Derivatives and ε-Caprolactone.

Simultaneous ring-opening copolymerization is a powerful strategy for the synthesis of highly functional copolymers from different types of cyclic monomers. Although copolymers are essential to the plastics industry, environmental concerns associated with current fossil-fuel-based synthetic polymers have led to an increasing interest in the use of renewable feedstock for polymer synthesis. Herein, we report a scalable synthetic platform to afford unique polysaccharides with different pendant functional groups from biomass-derived levoglucosan and ε-caprolactone via cationic ring-opening copolymerization (cROCOP). Biocompatible and recyclable bismuth triflate was identified as the optimal catalyst for cROCOP of levoglucosan. Copolymers from tribenzyl levoglucosan and ε-caprolactone, as well as from tribenzyl and triallyl levoglucosan, were successfully synthesized. The tribenzyl levoglucosan monomer composition ranged from 16% to 64% in the copolymers with ε-caprolactone and 22% to 79% in the copolymers with triallyl levoglucosan. The allylic levoglucosan copolymer can be utilized as a renewably derived scaffold to modify copolymer properties and create other polymer architectures via postpolymerization modification. Monomer reactivity ratios were determined to investigate the copolymer microstructure, indicating that levoglucosan-based copolymers have a gradient architecture. Additionally, we demonstrated that the copolymer glass transition temperature (Tg, ranging from -44.3 to 33.8 °C), thermal stability, and crystallization behavior could be tuned based on the copolymer composition. Overall, this work underscores the utility of levoglucosan as a bioderived feedstock for the development of functional sugar-based copolymers with applications ranging from sustainable materials to biomaterials.

Interrogation of PDD polymer and PDD-co-TFE copolymer microstructure by nuclear magnetic resonance spectroscopy

Teflon™ AF is a high temperature amorphous fluoropolymer manufactured by The Chemours Company composed of perfluoro-2,2-dimethyl-1,3-dioxole (PDD) and tetrafluoroethylene (TFE) exhibiting one of the lowest dielectric constants of any polymer. While physical properties are observed to change with the ratio of TFE to PDD incorporated in the polymer, interrogation of structure is limited due to its rigid structure, the amorphous nature of the material at higher PDD concentrations, and its limited solubility. Solution state 19F NMR of the dissolved polymer, however, allows the fine structure and stereochemistry of the polymer to be interrogated. Solid state NMR eliminates solubility as a concern, but line shapes are significantly broadened limiting resolution. In this study samples with different PDD: TFE molar ratios have been interrogated by solution and solid state NMR.

Amino acids induced modulations in linear PEO‐PPO‐PEO triblock copolymer microstructures and its exploration in prototypical drug solubilization

AbstractThis manuscript explains the effect of biologically important additives on the micellar behavior of an ethylene oxide‐propylene oxide (PEO101‐PPO56‐PEO101) based linear block copolymer, Poloxamer 407.The effect of common pharmaceutical excipients and three vital amino acids viz. alanine, glycine, and lysine (Ala, Gly, and Lys) is examined with the help of cloud point (CP), dynamic light scattering (DLS), and small angle neutron scattering (SANS) techniques. The drug solubilization ability for the copolymer was checked for two model drugs Quercetin (QCT) and Ibuprofen (IBU) with the help of high‐performance liquid chromatography (HPLC) in the presence/absence of additives such as Ala, Gly, and Lys. The observed results reveal that higher amino acid concentrations, favor the solubilization of drug which can potentially benefit the use of these biocompatible copolymers in pharmaceutical and biopharma industries.

Sequence-Enhanced Self-Healing in "Lock-and-Key" Copolymers.

Van der Waals-driven self-healing in copolymers with "lock-and-key" architecture has emerged as a concept to endow engineering-type polymers with the capacity to recover from structural damage. Complicating the realization of "lock-and-key"-enabled self-healing is the tendency of copolymers to form nonuniform sequence distributions during polymerization reactions. This limits favorable site interactions and renders the evaluation of van der Waals-driven healing difficult. Here, methods for the synthesis of lock-and-key copolymers with prescribed sequence were used to overcome this limitation and enable the deliberate synthesis of "lock-and-key" architectures most conducive to self-healing. The effect of molecular sequence on the material's recovery behavior was evaluated for the particular case of three poly(n-butyl acrylate/methyl methacrylate) [P(BA/MMA)] copolymers with similar molecular weights, dispersity, and overall composition but with different sequences: alternating (alt), statistical (stat), and gradient (grad). They were synthesized using atom transfer radical polymerization (ATRP). Copolymers with alt and stat sequence displayed a 10-fold increase of recovery rate compared to the grad copolymer variant despite a similar overall glass transition temperature. Investigation with small-angle neutron scattering (SANS) revealed that rapid property recovery is contingent on a uniform microstructure of copolymers in the solid state, thus avoiding the pinning of chains in glassy MMA-rich cluster regions. The results delineate strategies for the deliberate design and synthesis of engineering polymers that combine structural and thermal stability with the ability to recover from structural damage.

Copolymerization of butyl methacrylate with cyclopropyl styrene and its chlorinated derivatives

The radical copolymerization of butyl methacrylate with p-cyclopropyl styrene (I) and its monochlorine- (II), gemdichlorine-substituted derivatives (III) has been carried out and the basic regularities of formation of functionally substituted cyclopropyl styrene have been revealed. The composition and structure of the synthesized copolymers have been established. The copolymerization constants have been determined, the Alfrey–Price Q–e parameters and the microstructure of copolymers have been calculated. It has been established that the new copolymers are characterized by good optical indices (nD20 =1.640−1.650). For BMA + (I–III) copolymers in the range of 400−1100 nm, the base light transmission is 88−90%. It has been shown that the copolymers obtained from these monomers show excellent plasticity, due to which they can be used in making of small-sized injection molding products with improved exploitation properties. The characteristic viscosity of BMA + (I−III) copolymers is [η] = 0.90−1.02 dl/g. The copolymers based on BMA + chlorinated cyclopropyl styrene show incombustibility, whereas BMA-styrene copolymers are self-extinguishing. It has been found that the obtained copolymers show greater thermal stability than polystyrene itself. The copolymers obtained on the basis of chloro-substituted cyclopropane show optical transparency, which is an important characteristic for their application in optics.