Copolymerization Reactivity Ratios Research Articles

In-Situ NMR Measurement of Reactivity Ratios for Copolymerization of Methyl Methacrylate and Diallyl Dimethylammonium Chloride

The present work examines an in-situ NMR technique for the copolymerization of methyl methacrylate (MMA) and diallyl dimethylammonium chloride (DADMAC). The copolymer poly(MMA-co-DADMAC) contains monomers of significantly different polarities, making it challenging to measure DADMAC incorporation. The conventional technique for accurate measurement of monomer reactivity ratios in copolymers is time consuming, requiring a large number of experiments, in addition to being challenging for isolation/analysis of formed copolymers from this heterogeneous polymerization. The results show that the reactivity ratios were insensitive to temperatures between 60 and 80 °C, while the reactivity ratios of MMA were found to be much higher than that of DADMAC. The results were comparable to those obtained by the conventional technique. Due to the heterogeneous nature, the measured reactivity ratios are considered as apparent reactivity ratios but important for modifying poly(methyl methacrylate) with DADMAC by copolymeri...

Estimation of Reactivity Ratios in the RAFT Copolymerization of Styrene and Glycidyl Methacrylate

AbstractThe bulk reversible addition‐fragmentation chain transfer (RAFT) copolymerization of glycidyl methacrylate (GMA) and styrene (S) at several GMA molar feed fractions in the presence of 2‐cyano isopropyl dodecyl trithiocarbonate as RAFT agent and 1,10‐azobis(cyclohexane carbonitrile) as initiator is reported. The reaction conditions are similar to those used in the industrial production of crystal and high‐impact polystyrene by free radical polymerization with the purpose of synthesizing well‐defined copolymers in current industrial processes with only minor changes. Reactivity ratios calculated with linear Kelen–Tüdos, extended Kelen–Tüdos, and nonlinear regression (error in all variables) methods are reported. The results obtained suggest that the RAFT process modifies copolymer composition development. Increased preference for the monomer with the higher reactivity ratio is observed.

Endo/Exo Reactivity Ratios in Living Vinyl Addition Polymerization of Substituted Norbornenes

AbstractSubstituted norbornenes may be enchained by vinyl addition polymerization (VAP), through the norbornene double bond. Such monomers are generally prepared by Diels–Alder cycloaddition of cyclopentadiene and the corresponding olefin, which leads to a mixture of endo and exo stereoisomers with potentially very different reactivity, but these differences have not previously been quantified (e.g., as copolymerization reactivity ratios rendo and rexo). A living Pd‐based VAP initiator is employed and the consumption of endo and exo monomers to high conversions is measured to determine rendo and rexo; since the polymerization is living, the products are gradient copolymers. For norbornenes bearing n‐butyl, norbornyl, or methylhexafluoroisopropanol substituents, rexo = 1–4, and rexo rendo = 0.2–0.8, indicating only moderate deviations from ideal copolymerization behavior. By contrast, for norbornene bearing a pentamethyldisiloxane substituent, rendo is indistinguishable from zero, indicating that the endo isomer is effectively incapable of homopropagation. However, since the polymerization is living, propagation resumes (and chain extension proceeds) when additional exo monomer is charged.

Asetil Benzofuran Metakrilat Kopolimerlerinin Termal Özelliklerinin ve Reaktivite Oranlarının İncelenmesi

2-asetil benzofuril metilmetakrilat (ABM) ve akrilonitril (AN), baslatici olarak benzoil peroksit kullanilarak 60°C'de 1,4-dioksan cozucusunde serbest radikal polimerizasyonu ile hazirlanmistir. Kopolimer karakterizasyonu icin 1H-NMR spektrofotometresi kullanilmistir. Kopolimerdeki monomer kompozisyonlari elementel analiz ile belirlenmis ve reaktivite oranlari (r1 ve r2) Finemann-Ross (FR) ve Kelen-Tuds (KT) olmak uzere cesitli dogrusal yontemler kullanilarak hesaplanmistir. ABM (1) ve AN (2)’nin reaktivite oranlari sirasiyla 6,67 ve 0,17 olarak tespit edilmistir. Molekul agirligi jel permasyon kromatografisi (GPC) ile belirlenmis, heterojendik indeksi (Mw/Mn) 1,13 olarak bulunmustur. Polimerlerin camsi gecis sicakligi Shimadzu DSC-50 ile incelenmis olup, camsi gecis sicakliklarinin (Tg), kopolimerdeki polar monomer (ABM) konsantrasyonu arttikca arttigi gozlenmistir. Polimerlerin termal analizi, Shimadzu TG-50 ile incelenmis ve kopolimerlerin yuksek sicakliga dayanikli olmadigi gorulmustur.

Computational Package for Copolymerization Reactivity Ratio Estimation: Improved Access to the Error-in-Variables-Model

The error-in-variables-model (EVM) is the most statistically correct non-linear parameter estimation technique for reactivity ratio estimation. However, many polymer researchers are unaware of the advantages of EVM and therefore still choose to use rather erroneous or approximate methods. The procedure is straightforward but it is often avoided because it is seen as mathematically and computationally intensive. Therefore, the goal of this work is to make EVM more accessible to all researchers through a series of focused case studies. All analyses employ a MATLAB-based computational package for copolymerization reactivity ratio estimation. The basis of the package is previous work in our group over many years. This version is an improvement, as it ensures wider compatibility and enhanced flexibility with respect to copolymerization parameter estimation scenarios that can be considered.

Effect of Scandium Triflate on the RAFT Copolymerization of Methyl Acrylate and Vinyl Acetate Controlled by an Acid/Base “Switchable” Chain Transfer Agent

Modulation of the activity of an acid/base switchable dithiocarbamate RAFT agent, cyanomethyl (4-fluorophenyl)(pyridin-4-yl)carbamodithioate, with the Lewis acid scandium triflate (Sc(OTf)3) was investigated to examine the ability to deliver improved control over RAFT copolymerizations involving both more-activated and less-activated monomers—specifically the copolymerization of methyl acrylate (MA) and vinyl acetate (VAc). The introduction of either 0.5 or 1 mol equiv of Sc(OTf)3, with respect to RAFT agent, into a RAFT copolymerization of MA and VAc provides substantially improved control resulting in significantly reduced molar mass dispersities (Đ) (∼1.1–1.3) than achieved in its absence (Đ ∼ 1.3–1.4). Furthermore, similar introduction of Sc(OTf)3 into MA homopolymerization mediated by the same RAFT agent also delivered polymers of very low Đ (∼1.15). Sc(OTf)3 was also found to lower the rate of polymerization and alter the copolymerization reactivity ratios for MA and VAc. Increasing the Lewis acid concentration provides enhanced incorporation of the less active monomer, VAc, into the copolymers ([Sc(OTf)3]/[RAFT] = 0, rMA = 4.04, rVAc = 0.032; [Sc(OTf)3]/[RAFT] = 0.5, rMA = 3.08, rVAc = 0.17; [Sc(OTf)3]/[RAFT] = 1, rMA = 2.68, rVAc = 0.62). Carbon nuclear magnetic resonance (13C NMR) and differential scanning calorimetry (DSC) analysis of preparative samples confirm the enhanced VAc incorporation with increased levels of Sc(OTf)3. Importantly the inclusion of Sc(OTf)3 does not deleteriously affect the thiocarbonylthio end-groups of the RAFT polymers, with high end-group fidelity being observed in all copolymerizations.

Encapsulation of multi-walled carbon nanotubes with copolymer to disperse in aqueous media

An emulsion-like polymerization technique called admicellar polymerization (AP) was used to encapsulate a thin film of copolymer on the surface of multi-walled carbon nanotubes (MWCNTs). A water-soluble component sodium acrylate and a non-water soluble component methyl methacrylate were used to form thin films of copolymer on multi-walled carbon nanotubes. Various ratios of polymer combinations were formulated on MWCNT’s to understand the stability of polymer composition and surface heterogeneity on MWCNT’s. Encapsulated MWCNTs were characterized using SEM, energy dispersive spectroscopy (EDS), thermal analysis and FT-IR. Analytical studies indicate the formation of copolymer on MWCNTs. Monomer conversion rate and copolymer reactivity ratios were analyzed using high performance liquid chromatography (HPLC) by Fineman-Ross and Kelen-Tudos methods. The copolymer combination showed an alternating tendency and azeotropic composition at 0.6 acrylate monomer. The encapsulated MWCNTs were stable in aqueous media with onset of aggregate formation beginning at 40 days for the copolymer.

Designing catechol‐end functionalized poly(DMAm‐co‐NIPAM) by RAFT with tunable LCSTs

ABSTRACTProviding catechol‐end functionality to controlled structure lower critical solution temperature (LCST) copolymers is attractive, given the versatility of catechol chemistry for tethering to nanostructures. Controlled polymer chain lengths with catechol RAFT end groups are of interest to provide tunable LCST behavior to nanoparticles, although these polymerizations are relatively unexplored. Herein, the reactivity ratios for the RAFT copolymerization of N,N‐dimethylacrylamide (DMAm) and N‐isopropylacrylamide (NIPAM) pairs based on catechol‐end RAFT agents using an in situ NMR technique were first determined. Several catechol‐end poly(DMAm‐co‐NIPAM) samples were then prepared using the RAFT agent to provide copolymer. The reactivity ratios for the DMAm‐NIPAM pair were rDMAm = 1.28–1.31 and rNIPAM = 0.48–0.51. All the poly(DMAm‐co‐NIPAM) samples were found to have Mn values ≤ 26 kDa and Ð < 1.08 with LCST values ranging from 31 to 92°C, while maintaining a short range of glass transition temperature (Tg = 118–137°C). The difference in LCST values for the catechol functionalized poly(DMAm‐co‐NIPAM) based on 0.5 wt% aqueous buffered solutions at pH 5.5 and 8.5 was found to be <3.0°C. These conditions are suitable for subsequent catechol‐induced coordination and nucleophilic addition chemistry for covalent and noncovalent linkages during subsequent post‐modification. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017, 55, 4062–4070

Synthesis of β-Myrcene-Based Polymers and Styrene Block and Statistical Copolymers by SG1 Nitroxide-Mediated Controlled Radical Polymerization

Nitroxide-mediated polymerization (NMP) of β-myrcene (My) at 120 °C in bulk using unimolecular SG1-based succinimidyl ester-functionalized BlocBuilder (BB) alkoxyamine resulted in low dispersity (Đ = 1.1–1.4) poly(myrcene)s P(My)s with high SG1 chain-end fidelity. The polymerizations also showed the number-average molecular weights (Mn) increased almost linearly with conversion. SG1-terminated P(My) macroinitiators were cleanly chain-extended with styrene (S) and the S-rich P(My-b-S) diblock copolymers exhibited two distinct glass transition temperatures (Tgs), indicative of microphase separation. P(My-b-S) diblocks showed brittle stress–strain behavior, plausibly due to relatively low Mn. My/S mixtures with initial S molar feed compositions fS,0 = 0.10–0.94 were also statistically copolymerized (Mn = 8.2–19.8 kg mol–1, Đ ≤ 1.37, and monomodal distributions). Copolymer reactivity ratios were rS = 0.25 ± 0.04/0.34 ± 0.19 and rMy = 1.88 ± 0.12/2.19 ± 0.07 using Fineman–Ross and Kelen–Tudos methods. The stat...

Phosphorus‐Containing Gradient (Block) Copolymers via RAFT Polymerization and Postpolymerization Modification

Reversible addition‐fragmentation chain transfer (RAFT) copolymerization of styrene (St) and 4‐(diphenylphosphino)styrene (DPPS) is explored to establish the statistical distribution of the phosphine‐functional monomer within the copolymer. RAFT copolymerization of St and DPPS at a variety of feed ratios provides phosphine‐functional copolymers of low dispersity at moderate monomer conversion (Ð < 1.2 at conv. >60%). In all cases, the fraction of DPPS in the resulting polymers is greater than that in the monomer feed. Estimation of copolymerization reactivity ratios indicates DPPS has a strong tendency to homopolymerize while St preferentially copolymerizes with DPPS (rDPPS = 4.4; rSt = 0.31). The utility of the copolymers as macro‐RAFT agents in block copolymer synthesis is demonstrated via chain extension with hydrophilic acrylamide (N,N‐dimethylacrylamide (DMAm)) and acrylate (poly(ethylene glycol) methyl ether acrylate (mPEGA), and di(ethylene glycol) ethyl ether acrylate (EDEGA)) monomers. Finally, access to polymers containing phosphine oxide and phosphonium salt functionalities is shown through postpolymerization modification of the phosphine‐containing copolymers. image

Tulips: A Renewable Source of Monomer for Superabsorbent Hydrogels

A new class of superabsorbent hydrogels was synthesized by copolymerization of acrylamide with sodium 4-hydroxy-2-methylenebutanoate (SHMB). SHMB is obtained by saponification of α-methylene-γ-butyrolactone (MBL) which is a renewable monomer from tulips. Radical polymerization of SHMB was studied for the first time. The extent of side products through the ring closure depended on the pH used during the polymerization. Reactivity ratios for copolymerization of SHMB with acrylamide were estimated. Prepared hydrogels with various composition were investigated for their swelling, mechanical and thermal properties, and morphology as well as cytotoxicity. The achieved degree of swelling of the hydrogels was up to 82 000% and significantly exceeds the capacity of classical superabsorbent hydrogels made of acrylamide and salts of acrylic acid. The degree of swelling as well as mechanical and thermal properties of the hydrogels could be tuned by SHMB content.

Polycarboxylate superplasticizers of acrylic acid–isobutylene polyethylene glycol copolymers: monomer reactivity ratios, copolymerization behavior and performance

Acrylic acid–isobutylene polyethylene glycol (AA-TPEG) copolymers are typical of polycarboxylate superplasticizers (PCEs). AA-TPEG copolymers are prepared via free-radical polymerization with potassium persulfate as the initiator. The obtained copolymers were characterized by gel permeation chromatography (GPC) and infrared spectra (FTIR). The GPC method can break through the former limitations of the instruments and receive instantaneous unreacted and instantaneous monomer concentrations and not the initial monomer feeds. Since TPEG monomer is highly bulky, the common calculation methods for determining monomer reactivity ratios in copolymerization based on terminal copolymerization equation are not suitable. However, this study created non-linear least squares curve fitting of terminal copolymerization equation (NLLSQ-T) and penultimate copolymerization equation (NLLSQ-P) methods, which used Python’s NumPy, SciPy, and SymPy libraries to generate code and did numerical computations, bringing greater accuracy of monomer reactivity ratios. The monomer reactivity ratios were calculated with Fineman–Ross, Kelen–Tudos, YBR, NLLSQ-T, and NLLSQ-P methods and found to be r AA = 10.888, r′ AA = 1.131, r TPEG = 0.012, and r′ TPEG = 0.042 for AA-TPEG copolymers. Moreover, this study also explored specific copolymerization behavior of similar structure of copolymers with steric hindrance under penultimate copolymerization equation, such as dependence of the mole fractions in the copolymer on the mole fractions of unreacted monomers in solution, variation of copolymer compositions with conversion and sequence length distribution. The fluidity and flow loss of pastes containing PCEs were investigated, and the appropriate PCEs dosages resulted in a better workability of cement pastes.

Determination of Reactivity Ratios of Copolymerization of Acrylamide (Am) and Methacryloxyethyltrimethyl Ammonium Chloride (Dmc) with Ultraviolet Initiation, and Their Sequence Length Distribution

The copolymer P(AM-DMC), one kind of cationic polyacrylamide, was synthesized by using acrylamide (AM) and methacryloxyethyltrimethyl ammonium chloride (DMC) as monomers with ultraviolet initiation. The copolymer was characterized by Fourier transform infrared spectroscopy. The composition of the copolymer was determined from the chlorine content by silver nitrate titration. The effects of monomer feed ratio and conversion on the composition of copolymer were discussed. Reactivity ratios were determined by the Fineman-Ross, Kelen-Tudos and Yezrielev-Brokhina-Roskin methods, indicating that their positive order calculation results were very different with those of reverse order, when the reactivity ratios were determined by Fineman-Ross. However, their positive order and reverse order calculation results were similar when the reactivity ratios were determined by the Kelen-Tudos and Yezrielev-Brokhina-Roskin methods. Therefore, the reactivity ratios were determined using the average results of the Kelen-Tudos and Yezrielev-Brokhina-Roskin methods. The reactivity ratios of AM and DMC were 2.3398 and 0.2285, respectively. This result showed that the copolymerization of AM and DMC was a non-ideal random copolymerization. Furthermore, the content of AM segments decreased with the increase of AM feed content, but the content of DMC segments increased. Moreover, the sequence length distribution was irregular and narrow, because AM was prone to homopolymerization.

Reactivity ratios and properties of copolymers of 2-ethoxyethyl methacrylate with dodecyl methacrylate or styrene

The copolymerization reactivity ratios for 2-ethoxyethyl methacrylate (EOEMA) with dodecyl methacrylate (DDMA) or styrene (ST) were estimated. Polymerization was performed by using tert-butyl peroxy-2-ethylhexanoate (0.01 mol dm−3) as initiator, isothermally (70 °C) to low conversions (< 10 wt.%) in a wide range of copolymer compositions (every 10 mol-% steps). For the DDMA/EOEMA copolymerization both monomers prefer to react with EOEMA: r (DDMA) = 0.82 and r (EOEMA) = 1.26 with r (DDMA) × r (EOEMA) = 1, which results in the random copolymerization. For the ST/EOEMA copolymerization reactivity ratios are r (ST) = 0.59 and r (EOEMA) = 0.49 indicating a higher reactivity with opposite monomer, while the alternation tendency is not highly pronounced. The probabilities for formations of dyad and triad monomer sequences in dependence on monomer compositions were calculated from the obtained reactivity ratios. With the share increase of ST or DDMA in copolymers surface properties changed from hydrophilic to hydrophobic. Glass transition temperature of copolymer increased with the increase of ST and decrease of DDMA. The molar mass distribution and thermal degradation of synthesized copolymers were also determined and discussed. The reactivity ratios enable optimization of copolymer properties for a given application as polyelectrolytes, drug delivery systems and multifunctional additives for improvement of rheological properties of lubricating oils.

Effects of polar additives on the anionic polymerization of 1,3-butadiene and styrene

The homopolymerization of butadiene and copolymerization of styrene with butadiene were performed using n-butyllithium as the initiator, cyclohexane as a solvent and some new ethers (σ-ligands) as active centers modifiers. The modifiers were synthesized using an elegant synthetic route starting from a commercial precursor, and high yields were obtained. Their addition in the homopolymerization of butadiene strongly influences the vinyl content and reduces the polydispersity of the obtained polymer. The modifiers are also able to change the reactivity ratios in the styrene-butadiene copolymerization, leading to an appreciable randomizing effect. The modifiers also show a high activity, since their addition in a very low amount is able to strongly modify the progress in the reaction of anionic polymerization.

Synthesis and Free Radical Copolymerization of a Vinyl Monomer from Soybean Oil

A one-step method that converts soybean oil into (acryloylamino)ethyl soyate, a new vinyl monomer of free radical polymerization, was developed. The synthesized monomer combines a vinyl double bond (acryloyl functional group) and nonconjugated (isolated) double bonds of fatty acids. The double bond of the acryloyl group is reactive in a free radical chain polymerization that yields linear macromolecules containing isolated double bonds in side chains. Monomer reactivity ratios (r1, r2) in copolymerization of the new soybean oil-based acrylic monomer (SBA) with styrene, methyl methacrylate, and vinyl acetate, as well as the Q–e parameters of the SBA, were determined. The obtained results indicate that copolymerization can be described with the classical Mayo–Lewis equation. In terms of polymerizability, the SBA can be classified as an acrylic monomer. The double bonds of the fatty acid chains remain mainly unaffected during the free radical polymerization. The remaining unsaturated fragments in the side ch...

Reactivity ratios and copolymer properties of 2‐(diisopropylamino)ethyl methacrylate with methyl methacrylate and styrene

AbstractFree radical copolymerization kinetics of 2‐(diisopropylamino)ethyl methacrylate (DPA) with styrene (ST) or methyl methacrylate (MMA) was investigated and the corresponding copolymers obtained were characterized. Polymerization was performed using tert‐butylperoxy‐2‐ethylhexanoate (0.01 mol dm−3) as initiator, isothermally (70 °C) to low conversions (&lt;10 wt%) in a wide range of copolymer compositions (10 mol% steps). The reactivity ratios of the monomers were calculated using linear Kelen–Tüdős (KT) and nonlinear Tidwell–Mortimer (TM) methods. The reactivity ratios for MMA/DPA were found to be r1 = 0.99 and r2 = 1.00 (KT), r1 = 0.99 and r2 = 1.03 (TM); for the ST/DPA system r1 = 2.74, r2 = 0.54 (KT) and r1 = 2.48, r2 = 0.49 (TM). It can be concluded that copolymerization of MMA with DPA is ideal while copolymerization of ST with DPA has a small but noticeable tendency for block copolymer building. The probabilities for formations of dyad and triad monomer sequences dependent on monomer compositions were calculated from the obtained reactivity ratios. The molar mass distribution, thermal stability and glass transition temperatures of synthesized copolymers were determined. Hydrophobicity of copolymers depending on the composition was determined using contact angle measurements, decreasing from hydrophobic polystyrene and poly(methyl methacrylate) to hydrophilic DPA. Copolymerization reactivity ratios are crucial for the control of copolymer structural properties and conversion heterogeneity that greatly influence the applications of copolymers as rheology modifiers of lubricating oils or in drug delivery systems. © 2015 Society of Chemical Industry

Terpolymerization of Styrenic Photoresist Polymers: Effect of RAFT Polymerization on the Compositional Heterogeneity

The heterogeneity of the chemical structure of photoresist polymers, both within and between the polymer chains, is believed to contribute to the phenomenon of line edge roughness in high-resolution lithography. The copolymerization and terpolymerization of three important photoresist monomers—4-acetoxystyrene (AOST), styrene (Sty), and tert-butyl acrylate (tBA)—are examined in detail in this work. In particular, the effect of the use of a reversible addition–fragmentation chain transfer (RAFT) agent in these reactions is reported. The pairwise copolymerization reactivity ratios for the RAFT polymerizations are close to but different from those measured under the same conditions but in the absence of the RAFT agent. The differences are suggested to be related to the effect of the RAFT agent on the environment of the locus of polymerization. The course of the terpolymerization reactions can be well predicted from the copolymer reactivity ratios and the classical Alfrey–Goldfinger expression, indicating that the reactions in this system conform to terminal model of reactivity. Calculations of the expected sequence distributions as a function of composition and conversion clearly demonstrate that the polymers prepared under RAFT conditions are significantly more homogeneous than their counterparts prepared using conventional free radical polymerization. The significance of these results for the performance of the RAFT terpolymers in photoresist formulations is highlighted.

Syntheses and properties of amphiphilic poly (diethyl vinylphosphonate-co-2-chloroethyl methacrylate) copolymers

Poly (diethyl vinylphosphonate-co-2-chloroethyl methacrylate) (P(DEVP-co-CEMA)) copolymers are synthesized by free radical copolymerization initiated by benzoyl peroxide. The reactivity ratios for the free radical copolymerization of CEMA (M1) and DEVP (M2) are r1 = 19.45 and r2 = 0.11, respectively. The desired amphiphilic copolymers with relatively low polydispersity index (PDI) and different DEVP contents are isolated and purified from the reaction mixtures through precipitation fractionation. The structures and molecular characteristics of the obtained products are characterized by 1H NMR, FTIR, and SEC analysis. All of these fractionated copolymers have a unimodal distribution and moderate PDI. The thermal properties of the P(DEVP-co-CEMA) copolymers are investigated by TGA and differential scanning calorimetry (DSC) measurements. Single glass transition temperature (Tg) appears in the DSC profiles differing from the existence of two Tgs in the blend of poly (diethyl vinylphosphonate) and poly (2-chloroethyl methacrylate), which indicates the random structure of the copolymers. The MALDI–ToF mass analysis further reveals that DEVP and CEMA units are randomly distributed in the copolymer chains. The self-assembly behavior of the P(DEVP-co-CEMA) copolymers in aqueous solution is preliminarily investigated.

Copolymerization of Limonene with n‐Butyl Acrylate

The bulk free radical copolymerization of d‐limonene (Lim) with n‐butyl acrylate (BA) was carried out at 80 °C using benzoyl peroxide as initiator. Low conversion experiments were run to estimate the copolymer reactivity ratios as rBA = 6.07 and rLim = 0.0067. High conversion experiments were then conducted to validate the reactivity ratios for prediction of cumulative copolymer composition. The presence of allylic hydrogen in d‐limonene caused a notable degradative chain transfer reaction which greatly impeded polymerization. Increasing d‐limonene fractions in the copolymer resulted in a decrease in final conversion and molecular weight, and an increase in glass transition temperature.