Chain Propagation Research Articles

Effects of carbonization on the combustion of rice husks briquettes in a fixed bed

Carbonization of raw materials for making briquettes has been identified as a possible way of improving calorific values and fixed carbon contents of briquettes. In spite of these benefits, the main challenges of carbonization are increased percentage of ash content and energy required to process the fuel. In this study, fuels with mixtures of carbonized and raw rice husks were combusted in a fixed bed to examine the effect of carbonization on their combustion properties with an aim of establishing an optimum ratio. Bed temperature distribution, ignition, flame propagation speed, combustion rates and reaction zone thickness were investigated. All experiments were performed in a fixed bed operated in a reverse counter-current flame propagation mode. Four mixtures consisting of different ratios of carbonized rice husks were used to process briquettes; namely, 25 wt%, 50 wt%, 75 wt% and 100 wt% biochar. Air-mass flux for combustion of each mixture was varied between 0.02 and 0.6 kg/m2s. It was established that carbonization increases ignition time and peak bed temperature but lowers flame propagation speed, reaction zone thickness, and combustion rates. Briquettes with lower percentage of biochar had higher volatiles and higher devolatilization rate that shortened combustion period. Briquettes with carbonized rice husk of between 50 wt% and 75 wt% were found to have optimum combustion properties. Processing of briquettes should be done within these carbonization ratios in order to achieve desirable combustion properties.

Insights into the mechanism of cumene catalytic oxidation using ionic liquid [Bmim]OH

Experiment indicates that [Bmim]OH can effectively accelerate the oxidation reaction rate of cumene and improve the conversion of cumene. To investigate the catalytic effect of [Bmim]OH, the mechanism of molecular oxygen-activated [Bmim]OH-catalyzed oxidation reaction of cumene was proposed using the dispersion-corrected DFT-D3 calculation method. The nature of the catalytic effect of [Bmim]OH ionic liquid and the catalytic active site were investigated. The [Bmim]OH carbine-water structure plays an obvious catalytic role in the oxidation of cumene, which can induce the OO homolytic cleavage in cumyl hydroperoxide (CHP), leading to the formation of cumylhydroxy radicals (RO•) and carbene-OH radical-like intermediates, both of which are beneficial to the reactant with H of benzylic CH bond to accelerate the formation of cumyl radicals, involving in the propagation reaction that resulting in the formation of hydroperoxide and increasing the conversion of cumene. The overall reaction rate control step is the OO activation of CHP by [Bmim]OH carbine-water structure, which needs to overcome the energy barrier of 20.2 kcal/mol, lower than the auto-decomposition reaction energy barrier of CHP. The present results provide some new insights and understanding for the mechanism of the cumene oxidation catalyzed by ionic liquids.

Thermal decomposition, flame propagation, and combustion reactions behaviours of stearic acid by experiments and molecular dynamic simulation

To better look into the thermal decomposition and combustion progress of stearic acid (C18H36O2), the experimental tests and Reaction Force Field (ReaxFF) molecular dynamics simulation were conducted. Also, an investigation into the flame propagation characteristics and the reaction mechanisms of stearic acid was explored under different conditions. The thermal decomposition activation energy of stearic acid obtained by the TG tests was 105.01 kJ/mol. This is consistent with the initial decomposition stage reaction activation energy calculated to be 94.273 kJ/mol in the simulation. The flame propagation process of stearic acid combustion was explored and involved three stages: the flame growth stage, the stable flame stage, and the flame decay stage. The flame growth stage was subdivided into the flame growth inside the tube, upper the tube, and mushroom-shaped cloud. Besides, the flame growth stage could correspond to three flame propagation velocity peaks. Furthermore, the simplified reaction mechanism scheme for stearic acid radicals could explain the macro flame propagation behaviours. The main reaction pathway through which the C18H36O2 molecules were decomposed into C2H4 and C2H3, C2H5, and other free radicals was found to correspond to the initial flame growth stage, and the flame decay stage was dominated by the generation of final reaction products (H2O, CO2, and CO2, etc.). Concerning the overall reaction mechanism, the unburned stearic acid was continuously ignited, and the combustion products were continuously generated at the same time, thereby corresponding to the stable flame propagation stage. According to the flame propagation process and the simulation results, combustion reaction mechanisms of stearic acid were constructed.

Detailed Understanding of Solvent Effects for the Cationic Ring-Opening Polymerization of 2-Ethyl-2-oxazoline

Polymerization of 2-ethyl-2-oxazoline (EtOx) has often been in the spotlight for fundamental studies of poly(2-alkyl/aryl-2-oxazoline)s (PAOx) polymerization, especially initiator screening, solvent screening, and copolymerization trends. In this work, we build on previous observations of solvent effects on the cationic ring-opening polymerization (CROP) of EtOx, with additional experimental observations of previously unreported solvents to expand the explored parameter space. Our objective is to find solvents with the lowest activation energy (Ea) and higher Arrhenius preexponential factor (A), which will allow us to produce narrow molar mass distributions at higher molecular weights, in the least time. To achieve this, we examined the various single factors like Dimroth ET(30) values, the Kamlet–Abraham–Taft (KAT) linear free-energy relationship (LFER) equation(s), and the Catalan LFER equations. Only one of Catalan’s equations sufficiently disentangled dipolarity and polarizability to give a good fit due to contradictory effects. It was found that solvent nucleophilicity, electrophilicity, and polarizability affected the Ea, but not dipolarity. All four factors affected the A. This indicates that the Ea is minimized in solvents that do not solvate ions well (i.e. force ion-pairing), and A was minimized in more dipolar solvents that solvate the polymer chains well. A strongly negative activation entropy (ΔS‡) shows that the propagation reaction is associative. The Catalan LFER allows for the prediction of Ea, A, ΔH‡, and ΔS‡, and the derived kp, across a broad range of solvents.

Chemical mechanism of ammonia-methanol combustion and chemical reaction kinetics analysis for different methanol blends

As a carbon-free fuel, ammonia is considered as an attractive alternative fuel for internal combustion engines. However, ammonia has the problems of high ignition temperature and NOx emissions while using in engines. Methanol as liquid fuel is easy to store and transport. Ammonia-methanol blended fuel is probably-one of the most appropriate methods to solve the problem. However, there are few studies of chemical mechanism for the combustion of ammonia/methanol dual fuel. Moreover, it is important to study ammonia-methanol combustion by chemical reaction path analysis. In this paper, a chemical reaction mechanism of ammonia-methanol blends with 60 species and 399 reactions was developed. This mechanism can accurately predict the laminar burning velocity (LBV) and ignition delay time (IDT) in a wide range of equivalent ratios (Φ) and methanol blends. By using this chemical reaction mechanism, the effects of methanol addition on ammonia combustion and emissions at different equivalent ratios were numerically studied. Results showed that the addition of methanol significantly improves the chemical reactivity of ammonia, and blending a small amount of methanol can greatly reduce the IDT. However, the accumulation of radical HO2 caused by ammonia production enhances the fuel NOx path of NH2 → H2NO, which, together with high temperature and oxygen enrichment, leads to a NOx peak of 12500 ppm at equivalent ratio of 0.8. However, with the increase of equivalent ratio, NOx emission will decrease, which is only 2500 ppm at equivalent ratio of 1.4. Due to the existence of cross reaction of NH2 + CH3OH = NH3 + CH2OH and NH2 + CH3OH = NH3 + CH3O between ammonia and methanol, NH2 is difficult to participate in the thermal DeNOx process in the premixed combustion process, resulting in high NOx emissions. In addition, it is also found that after equivalent ratio of 1.1, H will replace OH as the most important chain propagation carrier.

Semiclassical bounds on the dynamics of two-dimensional interacting disordered fermions

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous $1/f$-noise at strong disorder.

The Effect of Ca, Sr, and Ba Chloride Complexes with Dibenzo-18-Crown-6 Ether as Catalysts on the Process Criteria for the Efficiency of Cumene Oxidation (the First Stage in the Chain of Polymer Composite Production)

A study was made on the effect of Ca, Sr, and Ba chloride complexes with dibenzo-18-crown-6 ether as catalysts on the process criteria of the efficiency of industrial cumene oxidation using kinetic modeling. It is the first stage in the process chain of polymer composite production. The kinetic scheme of the process is made of classical reactions of the radical chain mechanism (reactions of initiation, chain propagation, and chain termination), molecular reactions, reactions of formation of intermediate adducts “component of the reaction mixture—catalyst” and their decomposition, as well as reactions that take into account the specifics of the catalyst used: (1) formation of planar catalyst complexes with various substances; (2) formation of acetophenone along the catalytic path; (3) hydration of the intermediate adduct “α-methylstyrene—catalyst” to the required alcohol. It is shown that the kinetic model fully reproduces the experimental time dependencies of the cumene hydroperoxide concentration in the cumene oxidation and cumene hydroperoxide decomposition. Using the kinetic model, computational experiments were carried out, as a result of which the following conclusions were made: (1) among the considered catalysts, the complex of Sr chloride with dibenzo-18-crown-6 ether should be recognized as the best, provided that it is used at temperatures of 393–413 K and an initial concentration < 2 mmol/L; (2) to ensure selectivity comparable to the selectivity of a non-catalytic process, it is necessary to conduct the catalytic process at a lowest possible initial concentration of any of the considered catalysts.

Super-Grignard reagents (R2Mg·LiCl) mediated covalent-anionic-radical polymerization capable of low Đ and reactive hydrogen compatibility

The precise synthesis of polymer with narrow molecular weight distribution (Đ) and well-defined architectures is very essential to exploring the functions and properties of polymer materials. Here, a universal polymerization method capable of low Đ and reactive hydrogen compatibility is reported by introducing super-Grignard reagents (R2Mg·LiCl) into polymer chemistry. Under mild conditions, various monomers, including nonpolar polystyrene and 4-methoxystyrene that cannot be initiated by Grignard reagents, and polar methacrylate, are successfully polymerized with full monomer conversion and low Đ. This approach is amenable to wide varieties of initiators, polymerization temperature, and feed ratio, which makes it attractive for applications in polymer synthesis. By adding methanol and water during the polymerization process, the reactive hydrogen compatibility of this method is confirmed, which makes this method avoid the rigorous restriction on polymerization conditions of anionic polymerization. Moreover, chain extension polymerization and block copolymerization are achieved and demonstrate the livingness of chain propagation, enabling the facile synthesis of well-defined macromolecular architectures. This work therefore expands the methodology libraries of living polymerization, which may cause inspirations to polymer science.

Anti-Markovnikov hydrochlorination and hydronitrooxylation of α-olefins via visible-light photocatalysis

Conventional hydrofunctionalization of α-olefins with mineral acids proceeds with Markovnikov selectivity to afford branched isomers. The direct formation of linear constitutional isomers is challenging, yet anti-Markovnikov addition would be valuable for the synthesis of commodity chemicals, such as primary alcohols, which are currently only accessible via stoichiometric redox reactions, with a full equivalent of waste of both oxidant and reductant. Strategies that utilize radical intermediates have been demonstrated, but only for activated alkenes, and the direct use of aqueous mineral acids remains elusive. Here we present anti-Markovnikov addition reactions of aqueous hydrochloric and nitric acid to unactivated alkenes. The transformation is enabled by the in situ generation of photoredox-active ion pairs, derived from acridine and the mineral acid, as a combined charge- and phase-transfer catalyst. The introduction of a hydrogen atom transfer catalyst enabled us to bypass the challenging chain propagation by hydrochloric and nitric acids that originates from the high bond dissociation energy.

Overevaluation of Electro-oxidation for Chemical Oxygen Demand Removal Using a Boron-Doped Diamond Anode: The Roles of Various Electrogenerated Oxychlorides and Countermeasure

Electrochemical oxidation using a boron-doped diamond (BDD) anode has been extensively investigated in various wastewater treatments, where the electrogenerated oxychlorides (ClOx–, x = 1 to 4) from Cl– oxidation have been well illustrated. However, the false chemical oxygen demand (COD) reduction induced by ClOx– adulteration has been almost completely overlooked when evaluating the electrochemical wastewater treatment performance. In this study, it was revealed that all the ClOx– species except ClO4– served as strong oxidants in lieu of dichromate to degrade organic matter under digestion conditions during the COD test procedure. To eliminate the interference of ClOx– mixtures on the assessment of electrochemical COD removal performance, the modified sulfite-based reduction method was developed for the electrochemical case to remove ClOx– mixtures from the BDD-treated water samples before the COD test. It was demonstrated that the unadulterated COD removal performance of the BDD-based electrochemical system used for both synthetic and real wastewater treatments could be obtained after sulfite-based reduction of the electrogenerated ClOx– mixtures within 30 min in a sealed reaction chamber with the molar [sulfite]ini/[ClOx–]ini ratio of 1–3, where the reactants were isochronously depleted without producing oxidative radicals (SO4•– and •OH). Due to extreme lack of oxygen in the sealed ClOx–-sulfite system, radical propagation reactions were terminated and ClOx– constituents (ClO3–, ClO2–, and ClO–) were reduced by sulfite stoichiometrically via the oxygen transfer process with Cl– and SO42– as the final products. This new sulfite-based protocol could be regarded as a robust and adulteration-proof countermeasure for evaluating the real COD removal performance of an electrochemical system.

Nonthermal plasma for capturing CO2 as a path to ecologically clean energy

One of the serious environmental problems of our time is the impact on global climate change of the atmospheric pollution processes with greenhouse gases. Carbon dioxide is the most significant component of the anthropogenic impact on the heat balance of the earth. Therefore, reducing the concentration of greenhouse gases in the atmosphere is becoming increasingly important. Non-thermal plasma technology is considered as an attractive alternative for converting greenhouse gases into syngas and other valuable chemicals at lower temperatures. Highly active species generated in such a plasma are favourable for both initiation and propagation of chemical reactions. The combined effect of plasma and heterogeneous catalysis for fuel production from CH4 reforming has attracted increasing attention. The coupling between plasma and catalyst become complex when the catalyst is placed directly in the plasma. Both chemical and physical properties of the plasma and catalyst can be changed by the presence of each other. In this paper we studied resent progress in non-thermal plasma-catalysis research for CO2 capturing application.

High-yield production of liquid fuels in CO2 hydrogenation on a zeolite-free Fe-based catalyst.

Catalytic conversion of CO2 to long-chain hydrocarbons with high activity and selectivity is appealing but hugely challenging. For conventional bifunctional catalysts with zeolite, poor coordination among catalytic activity, CO selectivity and target product selectivity often limit the long-chain hydrocarbon yield. Herein, we constructed a singly cobalt-modified iron-based catalyst achieving 57.8% C5+ selectivity at a CO2 conversion of 50.2%. The C5+ yield reaches 26.7%, which is a record-breaking value. Co promotes the reduction and strengthens the interaction between raw CO2 molecules and iron species. In addition to the carbide mechanism path, the existence of Co3Fe7 sites can also provide sufficient O-containing intermediate species (CO*, HCOO*, CO3 2*, and ) for subsequent chain propagation reaction via the oxygenate mechanism path. Reinforced cascade reactions between the reverse water gas shift (RWGS) reaction and chain propagation are achieved. The improved catalytic performance indicates that the KZFe-5.0Co catalyst could be an ideal candidate for industrial CO2 hydrogenation catalysts in the future.

Organocatalyzed ring-opening reactions of γ-carbonyl-substituted ε-caprolactones.

Side-chain-functionalized aliphatic polyesters are promising as functional biodegradable polymers. We have investigated ring-opening reactions of γ-carbonyl-substituted ε-caprolactones (gCCLs) to obtain poly(ε-caprolactone) (PCL) analogues. Organic catalysts and Sn(Oct)2 often used for the ring-opening polymerization (ROP) of ε-caprolactone (CL) have been explored to find the conditions for the formation of polymeric products of gCCLs. We confirmed the consumption of gCCLs in all catalyzed reactions. However, chain propagation hardly occurs, as the propagating species are preferentially transformed to α-substituted five-membered lactones when the substituents are linked by ester or not sterically hindered. Intramolecular cyclization to form thermodynamically stable five-membered lactones releases alcohols and amines, serving as nucleophiles for the subsequent ring opening of other gCCLs. Thus, apparent chain reactions are realized for continuous consumption of gCCLs. The reaction preference remains unchanged independent of the catalysts, although the reactions of the amide-linked gCCLs by acidic catalysts are slightly mitigated. Finally, copolymerization of CL and a gCCL catalyzed by diphenyl phosphate has been investigated, which enables the chain propagation reaction to yield the linear oligomers of PCL analogues containing up to 16 mol% of gCCL units. This study contributes to understanding the chemistry of ring-opening reactions of substituted lactones for designing functional degradable polymers.

The Coupled Thermo-Chemo-Mechanical Peridynamics for ZrB2 Ceramics Ablation Behavior

The ablation of ultra-high-temperature ceramics (UTHCs) is a complex physicochemical process including mechanical behavior, temperature effect, and chemical reactions. In order to realize the structural optimization and functional design of ultra-high temperature ceramics, a coupled thermo-chemo-mechanical bond-based peridynamics (PD) model is proposed based on the ZrB2 ceramics oxidation kinetics model and coupled thermo-mechanical bond-based peridynamics. Compared with the traditional coupled thermo-mechanical model, the proposed model considers the influence of chemical reaction process on the ablation resistance of ceramic materials. In order to verify the reliability of the proposed model, the thermo-mechanical coupling model, damage model and oxidation kinetic model are established respectively to investigate the applicability of the proposed model proposed in dealing with thermo-mechanical coupling, crack propagation, and chemical reaction, and the results show that the model is reliable. Finally, the coupled thermo-mechanical model and coupled thermo-chemo-mechanical model are used to simulate the crack propagation process of the plate under the thermal shock load, and the results show that the oxide layer plays a good role in preventing heat transfer and protecting the internal materials. Based on the PD fully coupled thermo-mechanical model, this paper innovatively introduces the oxidation kinetic model to analyze the influence of parameter changes caused by oxide layer growth and chemical growth strain on the thermal protection ability of ceramics. The proposed model provides an effective simulation technology for the structural design of UTHCs.

Synthesis of lightly branched ultrahigh-molecular-weight polyethylene using cationic benzocyclohexyl nickel catalysts

The ultra-fast chain propagation rate in this contribution can simultaneously promote an increase in molecular weight and a decrease in branching density to achieve lightly branched UHMWPEs (Mn up to 1846 kg mol−1).

Direct conversion of amino acids to oxetanol bioisosteres via photoredox catalysis.

Carboxylic acids are an important structural feature in many drugs, but are associated with a number of unfavorable pharmacological properties. To address this problem, carboxylic acids can be replaced with bioisosteric mimics that interact similarly with biological targets but avoid these liabilities. Recently, 3-oxetanols have been identified as useful carboxylic acid bioisosteres that maintain similar hydrogen-bonding capacity while decreasing acidity and increasing lipophilicity. However, the installation of 3-oxetanols generally requires multistep de novo synthesis, presenting an obstacle to investigation of these promising bioisosteres. Herein, we report a new synthetic approach involving direct conversion of carboxylic acids to 3-oxetanols using a photoredox-catalyzed decarboxylative addition to 3-oxetanone. Two versions of the transformation have been developed, in the presence or absence of CrCl3 and TMSCl cocatalysts. The reactions are effective for a variety of N-aryl α-amino acids and have excellent functional group tolerance. The Cr-free conditions generally provide higher yields and avoid the use of chromium reagents. Further, the Cr-free conditions were extended to a series of N,N-dialkyl α-amino acid substrates. Mechanistic studies suggest that the Cr-mediated reaction proceeds predominantly via in situ formation of an alkyl-Cr intermediate while the Cr-free reaction proceeds largely via radical addition to a Brønsted acid-activated ketone. Chain propagation processes provide quantum yields of 5 and 10, respectively.

Formation pathways of aldehydes from heated cooking oils.

Cooking emissions account for a major fraction of urban volatile organic compounds and organic aerosol. Aldehyde species, in particular, are important exposure hazards in indoor residential and occupational environments, and precursors to particulate matter and ozone formation in outdoor air. Formation pathways of aldehydes from oils that lead to their emissions are not well understood. In this work, we investigate the underlying mechanisms involved in the formation of aldehydes from heated cooking oil emissions, through studying how antioxidants and oil composition modulate oxidation chemistry. Our results demonstrate that gaseous emissions are driven by radical-mediated autoxidation reactions in cooking oil, and the composition of cooking oils strongly influences the reaction mechanisms. Antioxidants have a dual effect on aldehyde emissions depending on the rates of radical propagation reactions. We propose a mechanistic framework that can be used to understand and predict cooking emissions under different cooking conditions. Our results highlight the need to understand the rates and mechanisms of autoxidation and other reactions in cooking oils in order to accurately predict the gas- and particle-phase emissions from food cooking in urban atmospheres.

A General Reconstruction Framework for Deflectometric Measurement Based on Nonuniform B-Splines

Phase measuring deflectometry (PMD) is a powerful tool well suited for precision measurement of optical surfaces. However, accurate and efficient surface reconstruction from gradients is challenging for the PMD. Because most reconstruction algorithms are not well adapted to complex surface forms with local undulations, and a large number of tedious operations are demanded for calculating the ray intersections. Besides, the format of the reconstructed data is usually not compatible to the machine tools and additional format conversion is required, which increases the computational effort and lengthens the error propagation chain. Therefore, a general reconstruction framework is proposed for the deflectometric measurement based on the non-uniform B-spline (NUBS), which embeds the NUBS into the PMD framework to enhance the local representativity. The correspondences between the points on the screen, camera and workpiece can be established by the parameter mapping instead of by the ray intersections. Simulations and experiments prove the effectiveness of the proposed method, and the measurement accuracy can achieve a level of one hundred nanometers in practice.

Combustion characteristics of three linear monohydric alcohols CH3(CH2)n-1OH (n = 16, 18, 22): Combined ignition experiments and molecular dynamics simulations

Higher fatty alcohols play a vital position in modern industry, while the dust explosion hazard cannot be ignored. Three kinds of linear monohydric alcohols CH3(CH2)n-1OH (n = 16, 18, 22) were selected to explore the combustion characteristics through ignition tests and molecular dynamics simulations. The experiment consequences indicated that the flame propagation height of alcohols dust gradually aggrandized as the enlargement of dust concentration of 30–750 g/m3 and the flame propagation velocity presented two peaks. CH3(CH2)15OH had the highest flame propagation height and velocity, followed by CH3(CH2)17OH and CH3(CH2)21OH. The first flame propagation velocities of CH3(CH2)15OH, CH3(CH2)17OH, and CH3(CH2)21OH reached the maximum value at 500 g/m3, which were 16.47, 13.25, and 12.53 m/s, respectively. The second peak reached the maximum value at 750 g/m3, which were 20.07, 19.05, and 18.23 m/s, respectively. The combustion reactions of alcohols revealed that the decomposition of molecules was first due to the breakage of the CC bond, and the main products were mainly C2H4, H2O, CH2O, CO, and CO2. The production and consumption reaction processes of C2H4, CH2O, and other combustible gas products reasonably explained the flame continuous process and the variation of flame propagation. The TG test results indicated that the volatility and thermal conductivity of CH3(CH2)15OH, CH3(CH2)17OH, and CH3(CH2)21OH decreased sequentially, which confirmed the flame propagation and molecular dynamics combustion reactions of the three alcohols. The volatility of alcohols was the key factor determining the difference in the flame propagation behavior of alcohols dust.

Entanglement measures for two-particle quantum histories

Quantum entanglement is a key resource, which grants quantum systems the ability to accomplish tasks that are classically impossible. Here, we apply Feynman's sum-over-histories formalism to interacting bipartite quantum systems and introduce entanglement measures for bipartite quantum histories. Based on the Schmidt decomposition of the matrix comprised of the Feynman propagator complex coefficients, we prove that bipartite quantum histories are entangled if and only if the Schmidt rank of this matrix is larger than 1. The proposed approach highlights the utility of using a separable basis for constructing the bipartite quantum histories and allows for quantification of their entanglement from the complete set of experimentally measured sequential weak values. We then illustrate the nonclassical nature of entangled histories with the use of Hardy's overlapping interferometers and explain why local hidden variable theories are unable to correctly reproduce all observable quantum outcomes. Our theoretical results elucidate how the composite tensor product structure of multipartite quantum systems is naturally extended across time and clarify the difference between quantum histories viewed as projection operators in the history Hilbert space and those viewed as chain operators and propagators in the standard Hilbert space.