Penultimate Model Research Articles

135 It’s about time for exercise: the Exercise Participation Explained in Relation to Time (EXPERT) Model

Abstract Background ‘Lack of time’ is consistently the most commonly reported barrier to regular exercise participation. However, this term insufficiently captures the complex and multidimensional nature of time. Recognizing the need for a more comprehensive analysis of ‘lack of time’ as a barrier to exercise, in this presentation the authors introduce the Exercise Participation Explained in Relation to Time (EXPERT) model. Purpose To present the temporal (time-related) factors relevant to exercise via the Exercise Participation Explained in Relation to Time (EXPERT) model. Methods To develop the EXPERT model, the authors used a rigorous sequential process that comprised the following steps. First, an umbrella literature review of time as barrier, determinant, and correlate of exercise was conducted. Second, a targeted review of existing temporal models was completed. Third, the lead author developed a first draft of the EXPERT model, led a series of focused discussions with members of the authorship team to refine the model, and then conducted a Delphi process to solicit pointed feedback and produce the penultimate model. Finally, this penultimate model was shared with a convenience sample of end-users and experts who informed revisions to make the final EXPERT model. Results The final EXPERT model factors includes four categories of factors: (1) Temporal needs and preferences for exercise (an individual’s preferences in relation to when they exercise); (2) Temporal autonomy for exercise (an individual’s autonomy in scheduling their free time); (3) Temporal conditions for exercise (an individual’s actual available time for exercise); and, (4) Temporal dimensions of exercise (an individual’s actual use of time for exercise). These four categories include multiple factors which collectively represent an individual’s preferences for, autonomy over, conditions for, and actual use of time for exercise. Conclusions The EXPERT model provides a framework that comprehensively explains the temporal factors that relate to exercise participation. This framework can help guide more nuanced assessments of time as a barrier to exercise and help inform novel approaches to mitigate this pervasive and potent barrier to regular exercise engagement.

Umpolung Isomerization in Radical Copolymerization of Benzyl Vinyl Ether with Pentafluorophenylacrylate Leading to Degradable AAB Periodic Copolymers

AbstractThis study revealed that benzyl vinyl ether (BnVE) shows a peculiar isomerization propagation in its radical copolymerization with an electron‐deficient acrylate carrying a pentafluorophenyl group (PFA). The co‐monomer pair inherently exhibits the cross‐over propagation feature due to the large difference in the electron density. However, the radical species of PFA was found to undergo a backward isomerization to the penultimate BnVE pendant giving a benzyl radical species prior to propagation with BnVE. The isomerization brings a drastic change in the character of the growing radical species from electrophilic to nucleophilic, and thus the isomerized benzyl radial species propagates with PFA. Consequently, the two monomers were consumed in the order AAB (A: PFA; B: BnVE) and the unique periodic consumption was confirmed by the pseudo‐reactivity ratios calculated by the penultimate model: r11=0.174 and r21=6600 for PFA (M1) with BnVE (M2). The pentafluorophenyl ester groups of the resulting copolymers are transformed into ester and amide groups by post‐polymerization alcoholysis and aminolysis modifications. The unique isomerization in the AAB sequence allowed the periodic introduction of a benzyl ether structure in the backbone leading to efficient degradation under acid conditions.

Umpolung Isomerization in Radical Copolymerization of Benzyl Vinyl Ether with Pentafluorophenylacrylate Leading to Degradable AAB Periodic Copolymers.

This study revealed that benzyl vinyl ether (BnVE) shows a peculiar isomerization propagation in its radical copolymerization with an electron-deficient acrylate carrying a pentafluorophenyl group (PFA). The co-monomer pair inherently exhibits the cross-over propagation feature due to the large difference in the electron density. However, the radical species of PFA was found to undergo a backward isomerization to the penultimate BnVE pendant giving a benzyl radical species prior to propagation with BnVE. The isomerization brings a drastic change in the character of the growing radical species from electrophilic to nucleophilic, and thus the isomerized benzyl radial species propagates with PFA. Consequently, the two monomers were consumed in the order AAB (A: PFA; B: BnVE) and the unique periodic consumption was confirmed by the pseudo-reactivity ratios calculated by the penultimate model: r11 =0.174 and r21 =6600 for PFA (M1 ) with BnVE (M2 ). The pentafluorophenyl ester groups of the resulting copolymers are transformed into ester and amide groups by post-polymerization alcoholysis and aminolysis modifications. The unique isomerization in the AAB sequence allowed the periodic introduction of a benzyl ether structure in the backbone leading to efficient degradation under acid conditions.

Random and block architectures of N-arylitaconimide monomers with methyl methacrylate

Abstract “Itaconimide” is the members of imide (–CO–NH–CO–) family with reactive exocyclic double bond and it is easily obtained from the renewable resource i.e. D-glucose. The polymerization of various N-arylitaconimide (NAI) monomers with methyl methacrylate (MMA) have been reported to improve the glass transition temperature (T g) and thermal stability of poly(methyl methacrylate) (PMMA). In literature, these studies have been done mostly using conventional free radical polymerization methods, which restricts the architecture of copolymers to “random” only. The block copolymers of NAI and MMA are an important due to the combination of glassy PMMA and thermally stable poly(NAI), which offers its applications for higher temperature service. The architectural control of polymers in provisions of its topology, composition, and various functionalities is possibly obtained using reversible-deactivation radical polymerizations (RDRPs). In RDRPs, the concentration of free radical is controlled in such a way that the termination reactions are minimized (normally in range of 1–10 mol%), and not allowed to obstruct with the desired architecture. However, this is possible by achieving (or by establishing) a rapid dynamic equilibrium between propagating radical and dormant species (i.e. R–X). Among all RDRPs, the atom transfer radical polymerization (ATRP) is very popular and adaptable method for the synthesis of polymers with specifically controlled architecture. Two different architectures of NAI and MMA copolymers are reported using ATRP process. The effect of various pedant groups on the rate constants of propagation (k p) and thermal properties NAI and MMA copolymers is studied. The poly(NAI-ran-MMA)-b-poly(MMA) are stable up to 200 °C and degraded in three steps. Whereas, the poly(NAI-ran-MMA)-b-poly(NAI) are stable up to 330 °C and degraded in two steps. The density functional theory methods are used for calculation of equilibrium constants (K ATRP) for the ATRP process for the series of laboratory synthesized alkyl halides. A good agreement was observed between the experimentally determined and theoretically calculated K ATRP values. The mechanistic studies are carried for poly(NAI-ran-MMA) copolymer system using statistical model discrimination method along with 1H decoupled 13C NMR spectroscopy. For studying the mechanism of copolymerization of NAI and MMA via ATRP methods, “trimer model or penultimate model” will be more accurate than “dimer model or terminal model”.

Mechanistic aspect for the atom transfer radical polymerization of itaconimide monomers with methyl methacrylate: a computational study

Abstract Atom transfer radical polymerization (ATRP) is a versatile & famous technique for the synthesis of well defined molecular architectures. In ATRP, there is a dynamic equilibrium exists between active & dormant species. Therefore, ATRP progress through a sequence of activation & deactivation cycles, ending upon complete monomer consumption & termination reactions are minimized. This paper presents a systematic computational study on kinetics & thermodynamics associates in the ATRP of itaconimide monomers & methyl methacrylate (MMA). For this, the copolymerization system is modeled as a unimer, dimer & trimer of various itaconimides & MMA monomer. The density functional theory with B3LYP functional & 6–31 + G(d)/LanL2DZ basis sets is used in the prediction of geometries & energetics associated with the dissociation of terminal R–X bond present in the unimer, dimer & trimer. The relative equilibrium constant (K ATRP) for the ATRP activation/deactivation steps is calculated from the free energy values associated with dissociation of R–X bond. The relative K ATRP values of dimer & trimer of selected monomers is compared with their respective unimer. From the transition state geometries of the dimeric propagating radical, activation energy is calculated. The gas phase rate coefficients for propagation (k p) (of itaconimides & MMA copolymerization) are calculated using the standard transition state theory. The effect of system parameters such as solvent, temperature & substituent on K ATRP & k p values of dimer is investigated systematically. The change in the initiating system & temperature has significant effect on k p values as compared to solvent & various substituent. The K ATRP values of dimer & trimer dormant species are higher as compared to their respective monomeric species. The neighboring monomer & penultimate monomer plays vital role in kinetics & thermodynamics associated with copolymerization. The obtained initial results show that the mechanism of copolymerization of itaconimide monomers & MMA follows penultimate model.

Refining Reactivity Ratios in the Copolymerization of Styrene and Methyl Methacrylate by EasySpin/MATLAB Simulations and Electron Paramagnetic Resonance Spectroscopy

AbstractElectron paramagnetic resonance (EPR) spectra of the ensemble of growing macroradicals are recorded during the radical copolymerization of styrene‐d8 and methyl methacrylate (MMA) for various comonomer compositions and subsequently modeled by MATLAB in combination with EasySpin simulations. Fully deuterated styrene‐d8 is used to simplify the EPR spectra and to allow a clear assignment of the EPR‐signals to the two different terminal units. By that approach, the macroradical fraction having styrene‐d8 as terminal unit, Φs, could directly be determined from the copolymerization spectra without concentration calibration. The so‐obtained Φs values could not be described by the penultimate model using the literature‐reported set of reactivity ratios. Consequently, Φs, the copolymer composition, and the overall propagation rate coefficient are adjusted in small steps simultaneously using Excel arriving at a new and more reliable set of reactivity ratios for the copolymerization of styrene and MMA.

Feature Estimations Based Correlation Distillation for Incremental Image Retrieval

Deep learning for fine-grained image retrieval in an incremental context is less investigated. In this paper, we explore this task to realize the model’s continuous retrieval ability. That means, the model enables to perform well on new incoming data and reduce forgetting of the knowledge learned on preceding old tasks. For this purpose, we distill semantic correlations knowledge among the representations extracted from the new data only so as to regularize the parameters updates using the teacher-student framework. In particular, for the case of learning multiple tasks sequentially, aside from the correlations distilled from the penultimate model, we estimate the representations for all prior models and further their semantic correlations by using the representations extracted from the new data. To this end, the estimated correlations are used as an additional regularization and further prevent catastrophic forgetting over all previous tasks, and it is unnecessary to save the stream of models trained on these tasks. Extensive experiments demonstrate that the proposed method performs favorably for retaining performance on the already-trained old tasks and achieving good accuracy on the current task when new data are added at once or sequentially.

Kinetic analysis of continuous reaction data for RAFT and free radical copolymerization with acrylic and styrenic monomers

Free radical (FR) and Reversible Addition Fragmentation Chain Transfer (RAFT) copolymerization rates for styrenic monomers in bulk and aqueous reactions were accelerated by acrylic comonomers, whose own rates were both delayed and decreased. The effect was found with styrenics as low as 0.6% by mole, and is directly observable from Automatic Continuous Online Monitoring of Polymerization reactions (ACOMP) data. Rapid radical transfer from acrylic to styrenic comonomer, through lower energy radical resonance stabilization in styrenics, was the suspected cause. FR and RAFT rates were equal, suggesting that FR termination controlled radical concentrations and rates. Despite strongly changing concentrations of initiator and comonomer radicals during reactions, the Quasi-Steady-State Approximation was demonstrated to hold. While rates were identical, molecular weights showed the characteristic increase with conversion for RAFT and decrease for FR. A new, generalized method for reactivity ratio determination was found and acceleration/deceleration behavior was consistently interpreted within a penultimate model.

Statistical Copolymers of N-Vinylpyrrolidone and Isobornyl Methacrylate via Free Radical and RAFT Polymerization: Monomer Reactivity Ratios, Thermal Properties, and Kinetics of Thermal Decomposition.

The synthesis of statistical copolymers of N-vinylpyrrolidone (NVP) with isobornyl methacrylate (IBMA) was conducted by free radical and reversible addition-fragmentation chain transfer (RAFT) polymerization. The reactivity ratios were estimated using the Finemann-Ross, inverted Fineman-Ross, Kelen-Tüdos, extended Kelen-Tüdos and Barson-Fenn graphical methods, along with the computer program COPOINT, modified to both the terminal and the penultimate models. According to COPOINT the reactivity ratios were found to be equal to 0.292 for NVP and 2.673 for IBMA for conventional radical polymerization, whereas for RAFT polymerization and for the penultimate model the following reactivity ratios were obtained: r11 = 4.466, r22 = 0, r21 = 14.830, and r12 = 0 (1 stands for NVP and 2 for IBMA). In all cases, the NVP reactivity ratio was significantly lower than that of IBMA. Structural parameters of the copolymers were obtained by calculating the dyad sequence fractions and the mean sequence length. The thermal properties of the copolymers were studied by differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and differential thermogravimetry (DTG). The results were compared with those of the respective homopolymers.

Statistical copolymerization of N-vinyl-pyrrolidone and alkyl methacrylates via RAFT: reactivity ratios and thermal analysis

The synthesis of statistical copolymers of N-vinylpyrrolidone (NVP) with the alkyl methacrylates: hexyl methacrylate (HMA) and stearyl methacrylate (SMA), is conducted by reversible addition-fragmentation chain transfer polymerization (RAFT), employing [(O-ethylxanthyl) methyl]benzene and [1-(O-ethylxanthyl) ethyl]benzene as the RAFT agents. The reactivity ratios are estimated using the Fineman-Ross, inverted Fineman-Ross, Kelen-Tudos and Barson-Fenn graphical methods as well as the computer program COPOINT, modified to both the terminal and the penultimate model. In all cases, the NVP reactivity ratio is significantly lower than that of the methacrylates. Structural parameters of the copolymers are obtained by calculating the dyad and triad sequence fractions and the mean sequence length. The thermal properties of the copolymers are studied by Differential Scanning Calorimetry and Thermogravimetric Analysis, and the results are compared with those of the respective homopolymers. In spite of the relatively small amount of NVP in the copolymers, copolymer thermal properties are influenced by both monomers.

Valencene as a naturally occurring sesquiterpene monomer for radical copolymerization with maleimide to induce concurrent 1:1 and 1:2 propagation

Valencene, a naturally occurring sesquiterpene that can be obtained from various citrus fruits, was copolymerized as an unconjugated 1,1-disubstituted bulky vinyl monomer by radical copolymerization with conjugated monomers possessing electron-withdrawing substituents, such as maleimides, acrylates, methacrylates, acrylonitrile, and methacrylonitrile, in toluene and PhC(CF3)2OH. The fluorinated alcohol increased the copolymerizability, as in the radical copolymerization of other unconjugated non-polar olefins with those electron-acceptor comonomers. In particular, the copolymerization of valencene and N-phenylmaleimide in PhC(CF3)2OH proceeded via concurrently occurring 1:1 and 1:2 propagation, in which the monomer reactivity ratio of maleimide and valencene to the maleimide radical with the penultimate valencene unit was close to 1 according to a kinetic analysis of the copolymerization based on the penultimate model. Therefore, the copolymerizability of valencene was higher than that of limonene, which is a similar unconjugated 1,1-disubstituted vinyl monomer with a smaller cyclohexenyl substituent that undergoes selective 1:2 radical copolymerization with maleimide derivatives under the same conditions. Reversible addition-fragmentation chain transfer RAFT copolymerization using a trithiocarbonate resulted in copolymers with controlled molecular weights and chain-end groups. The biobased copolymers of valencene and N-phenylmaleimide showed relatively high glass transition temperatures (Tg) of approximately 220–240 °C and relatively high thermal stability with 5% decomposition temperatures (Td5) of approximately 330–340 °C due to their rigid main-chain structures.

Practical Prediction of Heteropolymer Composition and Drift.

Composition drift in batch polymerizations is a well-known phenomenon and can lead to composition gradients in polymers synthesized using controlled polymerization methodologies. With known reactivity ratios of monomers, the drift, and thus resultant gradient copolymer, can be designed by adjusting reagent ratios and targeted conversions. Although such prediction is straightforward, it is seldom done, likely due to the perceived difficulty and unfamiliarity for nonspecialists. We seek to remedy this by providing the communities using copolymerswith an easy-to-use program called Compositional Driftwhich isbased on the Mayo-Lewis model and the penultimate model of monomer addition, using Monte Carlo methodology. This tool can also be applied to predict composition in nondrifting polymerizations.Herein we supply this tool to the community, showcasing two recent examples of use to guide experimental design and understanding of heteropolymers (RHP).

Determination of the Radical Reactivity Ratios of 2-(N-Ethylperfluorooctanesulfonamido)ethyl Acrylate and Methacrylate in Copolymerizations with N,N-Dimethylacrylamide by in Situ 1H NMR Analysis As Established for Styrene–Methyl Methacrylate Copolymerizations

A model system of styrene (St) and methyl methacrylate (MMA) was copolymerized in an NMR tube at 60 °C using 2,2′-azobis(isobutyronitrile) as the initiator and pyridazine as an internal standard to optimize an in situ 1H NMR spectroscopic method for determining reactivity ratios by generating data at hundreds of instantaneous comonomer compositions (244 data points from 8 to 91 mol % St) starting with only nine initial comonomer compositions. The radical reactivity ratios of styrene (rSt = 0.697 ± 0.010) and methyl methacrylate (rMMA = 0.491 ± 0.007) were determined by nonlinear least-squares fitting of a Mayo–Lewis plot of the instantaneous copolymer composition as a function of the comonomer feed composition using the terminal model and MINITAB statistical software, in which the copolymer composition was calculated by assuming that all comonomer consumed was converted to copolymer without side reactions; the results were similar to accepted literature values for the terminal and implicit penultimate models. After correcting for changes in the “lock” value at the initial stages of the copolymerization (because of solids formed in the sealed NMR tube), the same technique was used to determine the reactivity ratios of 2-(N-ethylperfluorooctanesulfonamido)ethyl acrylate (FOSA; rFOSA = 1.624 ± 0.048) and 2-(N-ethylperfluorooctanesulfonamido)ethyl methacrylate (FOSM; rFOSM = 2.876 ± 0.083) in their radical copolymerizations with N,N-dimethylacrylamide (DMA; rDMA = 1.126 ± 0.031 with FOSA; rDMA = 0.859 ± 0.026 with FOSM).

Propagation Kinetics of Isoprene-Glycidyl Methacrylate Copolymerizations Investigated via PLP-SEC.

Pulsed-laser polymerization combined with polymer analysis by NMR and size-exclusion chromatography is used to study the radical copolymerization kinetics of isoprene (IP) with glycidyl methacrylate (GMA). The copolymer is characterized by a close-to-alternating microstructure, with the addition of IP leading to a significant decrease in the composition-averaged propagation rate coefficient. A rigorous fitting strategy is developed to fit a mixed penultimate model to the data, with the selectivity of the IP, but not the GMA, macroradical dependent on the penultimate unit.

Kinetics on the copolymerization of acrylonitrile with itaconic acid or methyl acrylate in dimethylsulfoxide by NMR spectroscopy

The free radical solution polymerization of acrylonitrile (AN) with itaconic acid (IA) or methyl acrylate (MA) was carried out in dimethylsulfoxide (DMSO) using 2 2'-azobisisobutyronitrile (AIBN) as the initiator. Based on the monomer conversion versus time data, the copolymerization rate was retarded by IA but promoted by MA. The monomer sequence distribution was characterized by 13C NMR to explain the significant difference in the copolymerization kinetics of the ANIA and AN-MA copolymers. The results of the copolymer composition curves and 13C NMR spectral analysis illustrated that the penultimate model was suitable for describing the copolymerization behavior of AN-IA, and the terminal and penultimate models were adequate for AN-MA. The penultimate reactivity ratios, rMA, were ~2 times higher than rIA, indicating that the reactivity of AN-terminated radical having MA as the preceding group was higher than that with IA. Then, the corresponding content of triads sequence AN-AN-AN (AAA) in the AN-MA copolymers was higher than those in the AN-IA copolymers. The appearance of new resonance signals of the quaternary and methyl carbon indicated a higher content of IA in copolymers. The higher IA concentrations the lower viscosity-average molecular weight of the polymers. The decrease in the molecular weight was correlated to the formation of the oligomers.

Theoretical Consideration of Phase Behavior of the Products of Free‐Radical Copolymerization Described by the Penultimate Model

The penultimate model of copolymerization taking into account the dependence of the reactivity of a macroradical on the type of the unit preceding the ultimate one is well‐known in polymer chemistry. All types of chemical structure of multiblock copolymers capable to form during copolymerization processes described by such a model are revealed in the present work. Phase diagrams of copolymers of all these types specifying the regions of thermodynamic stability of spatially periodic mesophases differing in morphology are constructed in the framework of the weak segregation theory. Besides, the periods and amplitudes of the variation of different type densities of units in mesophases as well as volume fractions of these latter within the regions of their coexistence are calculated.

A general theory of kinetics and thermodynamics of steady-state copolymerization

Kinetics of steady-state copolymerization has been investigated since the 1940s. Irreversible terminal and penultimate models were successfully applied to a number of comonomer systems, but failed for systems where depropagation is significant. Although a general mathematical treatment of the terminal model with depropagation was established in the 1980s, a penultimate model and higher-order terminal models with depropagation have not been systematically studied, since depropagation leads to hierarchically-coupled and unclosed kinetic equations which are hard to solve analytically. In this work, we propose a truncation method to solve the steady-state kinetic equations of any-order terminal models with depropagation in a unified way, by reducing them into closed steady-state equations which give the exact solution of the original kinetic equations. Based on the steady-state equations, we also derive a general thermodynamic equality in which the Shannon entropy of the copolymer sequence is explicitly introduced as part of the free energy dissipation of the whole copolymerization system.

Improved threshold diagnostic plots for extreme value analyses

A crucial aspect of threshold-based extreme value analyses is the level at which the threshold is set. For a suitably high threshold asymptotic theory suggests that threshold excesses may be modelled by a generalized Pareto distribution. A common threshold diagnostic is a plot of estimates of the generalized Pareto shape parameter over a range of thresholds. The aim is to select the lowest threshold above which the estimates are judged to be approximately constant, taking into account sampling variability summarized by pointwise confidence intervals. This approach doesn’t test directly the hypothesis that the underlying shape parameter is constant above a given threshold, but requires the user subjectively to combine information from many dependent estimates and confidence intervals. We develop tests of this hypothesis based on a multiple-threshold penultimate model that generalizes a two-threshold model proposed recently. One variant uses only the model fits from the traditional parameter stability plot. This is particularly beneficial when many datasets are analysed and enables assessment of the properties of the test on simulated data. We assess and illustrate these tests on river flow rate data and 72 series of significant wave heights.

Periodically Functionalized and Grafted Copolymers via 1:2-Sequence-Regulated Radical Copolymerization of Naturally Occurring Functional Limonene and Maleimide Derivatives

Naturally occurring hydroxy-functionalized limonene analogues, i.e., monoterpene alcohols such as perillyl alcohol and carveol, were radically copolymerized with cyclohexylmaleimide (CyMI) in PhC(CF3)2OH via 1:2-sequence-regulated propagation to obtain periodically functionalized bio-based copolymers possessing one hydroxyl group in every three-monomer unit. Alternatively, a combination of hydroxy-functionalized maleimide (N-2-hydroxyethylmaleimide: HEMI) and limonene resulted in another periodically functionalized copolymer possessing two hydroxyl groups for every three-monomer unit. These copolymerizations were fitted well by the penultimate model, where the hydroxyl functions did not have a significant effect on the selective propagation, as has been reported for a combination of nonfunctionalized limonene and CyMI. The periodic hydroxyl groups can be quantitatively converted into carbamate moieties by a polymer reaction with isocyanate to result in another series of 1:2 and 2:1 periodically functional...

Microstructure Analysis and Model Discrimination of Enzyme-Catalyzed Copolyesters.

The comonomer sequence distributions were analyzed for a series of poly(ε-caprolactone-co-δ-valerolactone) (PCV) copolymers using 13C nuclear magnetic resonance (NMR) spectroscopy. The four dyad sequences each showed well-resolved peaks in the NMR spectra that allowed easy quantification of the dyad and triad fractions. Although compositional analysis could not discriminate between terminal and penultimate model copolymerization kinetics, the monomer sequence distributions clearly indicated that the lipase-catalyzed copolymerization proceeds via terminal model kinetics. This NMR analytical tool enables rapid characterization of lipase-catalyzed copolymers.