The effect of fractal dimension of porous catalysts on the activation energy of CO oxidation

An approach based on the interrelationship between the activation energy of the rate-limiting step of a heterogeneous catalytic reaction and the structure of the catalyst surface expressed in terms of fractal geometry is presented for the example of the oxidation of carbon monoxide. The activation energy of this reaction was shown to increase with increasing nonuniformity of the catalyst surface given by the fractal dimension D_F. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 1, pp. 43–46, January–February, 2007.     

Further Insights into the Porous Structure of TEOS Derived Silica Gels

The porous structure of TEOS derived silica gels was studied using nitrogen adsorption at 77 K. Silica gels were prepared using TEOS, H₂O and ethanol for different molar ratios. No catalyst was used in this study. Silica gels were also heat treated up to 1000°C. The nitrogen sorption isotherms were analyzed by two models: Fractal and Percolation Theories. Using the fractal analysis approach, the surface roughness of the porous structure of silica gels was determined. The surface fractal dimension depends on the hydrolysis conditions and heat treatment. The surface fractal dimension decreases with increasing H₂O/TEOS molar ratio or heating temperature. For the silica gels studied, the surface fractal dimension changed from 2.6 to 2.5 after heating the gels, and from 2.4 to 2.6 with decreasing H₂O/TEOS ratio.Using the Percolation theory, we have determined the connectivity of the porous structure of silica gels. The extent of sorption hysteresis of the nitrogen isotherms reflects the connectivity of the pore network. The mean coordination number (connectivity) Z, and the linear dimension of the network, L, have been calculated from the hysteresis of the isotherms. For the as-prepared silica gels, Z was about 8 and L close to 2. On heating the gels, Z decreases to 4 and L increases to 7, results which are in accordance with the collapse of the porous network.     

Determination of total heterogeneity and fractal dimensions of high-temperature superconductors

Using thermo-analytical and sorptometric methods physicochemical properties and especially surface heterogeneity of HgBa₂Ca₂Cu₃O₈₊, (Hg-1223) was investigated. The desorption energy distribution was derived from mass loss Q-TG and differential mass loss Q-DTG curves of thermodesorption in quasi-isothermal conditions of pre-adsorbed n-octane and water vapour. It is shown that the superconducting Hg-1223 phase is highly sensitive to water vapours. The mechanism of water adsorption depends largely on the activation time. By water vapour saturation in a period of 90 min, physisorption takes place. Prolonged periods result in a chemical decomposition. From nitrogen ad- and desorption isotherms the fractal dimension of superconductors were calculated. A new approach is proposed to calculate fractal dimension from Q-TG curves.This revised version was published online in November 2005 with corrections to the Cover Date.     

Correlation between the fractal dimension of fracture surfaces and fracture toughness for ductile polymer materials

A microcrack-shear band chain model for the fracture of ductile materials is proposed. The fractal dimension (D) of the fracture surfaces is derived and correlated with the fracture toughness (K_Ic) of ductile materials. The fractal dimension of the fracture surface is predicted to have an inverse trend with the fracture toughness. The theoretical results are consistent with the experimental results of some polymers and metals. © 1994 John Wiley & Sons, Inc.     

Fractality and activity of acid catalysts in the liquid-phase synthesis of ethyl <Emphasis Type="Italic">tert-</Emphasis>butyl ether

A study was carried out on the synthesis of ethyl tert-butyl ether from ethanol and 2-methylpropene on silica gel samples modified by the addition of ZrO₂ and Al₂O₃. A decrease in the turnover frequency (TOF) of the reaction is observed with increasing acidity of surface of the modified silica gels. A relationship was found between the TOF of the reaction and the fractal dimension of the catalyst. The TOF of the reaction decreases with increasing fractal dimension of the catalyst.     

Thiourea-Catalyzed C−F Bond Activation: Amination of Benzylic Fluorides

We describe the first thiourea-catalyzed C−F bond activation. The use of a thiourea catalyst and Ti(OiPr)₄ as a fluoride scavenger allows the amination of benzylic fluorides to proceed in moderate to excellent yields. Preliminary results with S- and O-based nucleophiles are also presented. DFT calculations reveal the importance of hydrogen bonds between the catalyst and the fluorine atom of the substrate to lower the activation energy during the transition state.     

Coupling Reactions of Alkynyl Indoles and CO2 by Bicyclic Guanidine: Origin of Catalytic Activity?

Density functional theory calculations were used to investigate the three possible modes of activation for the coupling of CO₂ with alkynyl indoles in the presence of a guanidine base. The first of these mechanisms, involving electrophilic activation, was originally proposed by Skrydstrup et al. (Angew. Chem. Int. Ed . 2015 , 54 , 6682). The second mechanism involves the nucleophilic activation of CO₂. Both of these electrophilic and nucleophilic activation processes involve the formation of a guanidine‐CO₂ zwitterion adduct. We have proposed a third mechanism involving the bifunctional activation of the bicyclic guanidine catalyst, allowing for the simultaneous activation of the indole and CO₂ by the catalyst. We demonstrated that a second molecule of catalyst is required to facilitate the final cyclization step. Based on the calculated turnover frequencies, our newly proposed bifunctional activation mechanism is the most plausible pathway for this reaction under these experimental conditions. Furthermore, we have shown that this bifunctional mode of activation is consistent with the experimental results. Thus, this guanidine‐catalyzed reaction favors a specific‐base catalyzed mechanism rather than the CO₂ activation mechanism. We therefore believe that this bifunctional mechanism for the activation of bicyclic guanidine is typical of most CO₂ coupling reactions.     

Characterising latex particles and fractal aggregates using image analysis

The fractal nature of latex particles and their aggregates was characterised by image analysis in terms of fractal dimensions. The one- and two-dimensional fractal dimensions, D ₁ and D ₂, were estimated for polystyrene latex aggregates formed by flocculation in citric acid/phosphate buffer solutions. The dimensional analysis method was used, which is based on power law correlations between aggregate perimeter, projected area and maximum length. These aggregate characteristics were measured by image analysis. A two-slopes method using cumulative size distributions of aggregate length and solid volume has been developed to determine the three-dimensional fractal dimension (D ₃) for the latex aggregates. The fractal dimensions D ₁, D ₂ and D ₃ measured for single latex particles in distilled water agreed well with D ₁ = 1, D ₂ = 2 and D ₃ = 3 expected for Euclidean spherical objects. For the aggregates, the fractal dimension D ₂ of about 1.67 ± 0.04 (±standard deviation) was comparable to the fractal dimension D ₃ of approximately 1.72 ± 0.13 (±standard deviation), taking the standard deviations into account. The measured three-dimensional fractal dimension for latex aggregates is within the fractal dimension range 1.6–2.2 expected for aggregates formed through a cluster-cluster mechanism, and is close to the D ₃ value of about 1.8 indicated for cluster formation via diffusion-limited colloidal aggregation. Received: 28 September 1998 Accepted: 29 October 1998     

Pitting Corrosion Mechanisms and Characteristics of Aluminum in Solar Heating Systems

The complex characteristics and mechanisms of aluminum pitting corrosion in a solar heating system were studied by the chemical immersion method and electrochemical techniques as well as fractal theory. The results showed that pitting corrosion of Al occurred in a tap water environment due to the local enrichment of Cl^? ions. The higher the Cl^? ions concentration, the more negative the critical pitting potential (E_b) of Al. A linear relationship between E_b and the logarithm of Cl^? ions concentration was observed. The pitting corrosion mechanism of Al in neutral water was explained in terms of complexation corrosion theory. The corrosion surface images of aluminum immersed in tap water were captured and analyzed by image processing technique and box‐dimension method. The fractal characteristics of pit distribution, described by fractal dimension, have been identified. The fractal dimension of the pit distribution increased with the increase of immersion time and had the same trend as that of the weight loss. Fractal dimension can, thus, be used as an important parameter for quantitative evaluation of pitting corrosion of aluminum.     

Microstructure Evolution of Nonhydrolytic Alumina Gels

Nonhydrolitic sol-gel processes of aluminum chloride and aluminum bromide with isopropyl ether and aluminum sec-butoxide were performed at various temperatures. Based on the Arrhenius type variation of the gelation time with temperature, activation energies for the gelation were found to be in the range 19–25 Kcal/mol range. The energies were found to be sensitive to the nature of the aluminum ligands and the chemical scheme. Due to the large activation energy, it is possible to stop the reaction at any time before gelation by cooling the sol to room temperature. Small angle X-ray scattering (SAXS) of sols from the AlClAlCl₃/Pr O system shows unique development of a fractal like structure with nanometer scale order, demonstrated by discrete peaks in the SAXS data. A fractal dimension D = 1.64 was found. An aggregation scheme is proposed to explain this phenomenon. A fractal dimension of 2.4 without small scale ordering found for xerogels prepared from the AlCl₃/ASB system reflects the effect of the different precursors on the microstructure of nonhydrolytic gels.     

污泥活性炭的结构特征及表面分形分析

以城市污水厂污泥为主要原料添加适量添加剂, 采用ZnCl₂化学活化法制备的污泥活性炭, 借助XRD, BET法, FT-IR, SEM等现代分析测试方法结合液相吸附法, 表征结构特征和分析表面分形维数. 结果表明: 在适宜的活化温度、活化时间、ZnCl₂浓度、原料粒度等工艺条件下, 加入少量添加剂制备的污泥活性炭, 最可几孔径分布在4.16 nm左右,平均孔容0.4484～0.5122 mL•g^－1, 比表面积为634.8～748 m²•g^－1, IR峰中出现C—OH, C—H, N＝O, C＝C功能组, 孔结构是具有平行壁的狭缝状介孔结构. 由液相吸附法得到的污泥活性炭分维近似为2, 属于低分维二维表面.     

Isomerization of Functionalized Olefins by Using the Dinuclear Catalyst [PdI(μ-Br)(PtBu3)]2: A Mechanistic Study

In a combined experimental and computational study, the isomerization activity of the dinuclear palladium(I) complex [Pd^I(μ-Br)(P^tBu₃)]₂ towards allyl arenes, esters, amides, ethers, and alcohols has been investigated. The calculated energy profiles for catalyst activation for two alternative dinuclear and mononuclear catalytic cycles, and for catalyst deactivation are in good agreement with the experimental results. Comparison of experimentally observed E/Z ratios at incomplete conversion with calculated kinetic selectivities revealed that a substantial amount of product must form via the dinuclear pathway, in which the isomerization is promoted cooperatively by two palladium centers. The dissociation barrier towards mononuclear Pd species is relatively high, and once the catalyst enters the energetically more favorable mononuclear pathway, only a low barrier has to be overcome towards irreversible deactivation.     

Viscoelastic scaling in polymer gels

New scaling laws for chain networks are derived to describe the fundamental relationships between the viscosity exponent (k), viscoelastic exponent (m), stretched exponent (β), spatial dimension (d). fractal dimension (d_f), and a universal constant (γ). The scaling of the total number of monomers and the radius of gyration is defined by d_f. We have discovered γ = m/β to be a universal constant which relates the shear modulus of a polymer gel melt to the shear modulus near the glass transition. Analyzing the size-dependent shear viscosity, we have determined γ = 3d_fcd/(7d−5d_fc) = 2.647 for d = 3 where d_fc is the fractal dimension of critical clusters at the gel point. By using γ, the present theory extends previous work pertaining to systems near the sol-gel transition, and shows how properties far from the critical point can be explained. The theoretical prediction is in good agreement with viscoelastic measurements.     

Quantitative Image Analysis of Fractal‐Like Thin Films of Organic Semiconductors

Morphology modulation offers significant control over organic electronic device performance. However, morphology quantification has been rarely carried out via image analysis. In this work, we designed a MATLAB program to evaluate two key parameters describing morphology of small molecule semiconductor thin films: fractal dimension and film coverage. We then use this program in a case study of meniscus‐guided coating of 2,7‐dioctyl[1]benzothieno[3,2‐b][1]benzothiophene (C₈‐BTBT) under various conditions to analyze a diverse and complex morphology set. The evolution of morphology in terms of fractal dimension and film coverage was studied as a function of coating speed. We discovered that combined fractal dimension and film coverage can quantitatively capture the key characteristics of C₈‐BTBT thin film morphology; change of these two parameters further inform morphology transition. Furthermore, fractal dimension could potentially shed light on thin film growth mechanisms. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1622–1634     

Sorption of strontium and fractal scaling of the heterogeneous media in a candidate VLLW disposal site

Because of the deposit and accumulation from the debris flow, the heterogeneous geological characteristics is obvious for a candidate very low level waste (VLLW) disposal site, with the grain size ranging from tens of microns to 75 cm. Therefore, it is challenging to directly measure the sorption capacity of the media and the distribution coefficient of some radionuclides, such as strontium. We have studies the correlation of the particle mass content with different grade size and the sorption capacity, which is important in the modeling of radionuclide migration in the heterogeneous disposal site. A total of three deep pits and five shallow trenches were excavated, and 21 solid samples were collected for laboratory experiments. The grade and percentage of the different-sized particles were obtained, and the fractal dimension (D) of the media was calculated from the results of sieved experiments. Steady state sorption time and sorption isotherm of strontium was determined in the heterogeneous media, and sorption and distribution of strontium in the heterogeneous media were evaluated by the relationship between the mass percentage and distribution coefficient (K _d) of the fine-particle media, which was comprised of selected particles with a diameter less than 1 mm, and the correlation on the K _d and D was regressed fit. The results indicated that fractal dimension bounded from 2.39 to 2.62 in the media, and K _d values of strontium ranged between 119 and 126 in the fine-particle media, and corresponding value was 11 and 43 in the original media. The correlation between K _d and D was approximately linear.     

Homogeneous and Heterogeneous Catalyzed Esterification of Acrylic Acid with Ethanol: Reaction Kinetics and Modeling

Kinetics of esterification of acrylic acid with ethanol in the presence of homogeneous (H₂SO₄, HCl, p‐TSA, HI) catalysts as well as heterogeneous catalysts (Dowex 50WX, Amberlyst 15) was studied. The effects and performance of these catalysts on the conversion of acrylic acid were evaluated. In the kinetics of homogeneous catalyzed reaction, both concentration and activity‐based model were employed. Activity coefficients were predicted by the Universal Functional group Contribution (UNIFAC) method to consider nonideal behavior of the liquid phase. The heterogeneous catalyzed reaction mechanisms were developed using Eley–Rideal theory. The model results were compared with the experimental results and were in good agreement. The temperature dependency of the constants, reaction enthalpy, and entropy, and activation energy were determined. The conversion of acrylic acid was obtained as 63.2%, 61.02%, 53.3%, 21.4%, 34.96%, and 14.84% for H₂SO₄, p‐TSA, HCl, HI, Dowex 50WX, and Amberlyst 15, respectively, under process temperature of 70°C, reactant molar ratio of 1:1, and catalyst concentration of 2% (v/v) for homogeneous and 2.17 g for heterogeneous catalyst. These outcomes provide an approach to understand the significant effect of each catalyst on the esterification kinetics of acrylic acid and ethanol.     

The homogeneous gas phase H2?D2 metathesis at room temperature: Reaction induced by specific vibrational excitation

We have demonstrated that reactions for which substantial activation energies are needed can be induced to occur at room temperature via specific vibrational excitation. Indeed, the indications are that the atom-switching reactions for which E_a > 25 kcal take place with high probability only when the activation energy is localized in the vibrational mode. In this preliminary report on the utilization of the stimulated Raman effect to generate substantial populations in the critical vibrational states required for the homogeneous atom exchange between H₂ and D₂, we first summarized the historical development of the concept. The experimental arrangement is then described and the analytical results tabulated; the observed dependence on relative concentrations is semiquantitatively rationalized on the basis of a model proposed in 1964. Independent shock tube and molecular beam investigations were similarly accounted for. Attention is called to the discrepancy between the generally concordant experimental results and the ab initio quantum mechanical calculations of the potential energy surface for 4H atoms.     

Kinetic study of ethylene polymerization with chromium oxide catalysts by a radiotracer technique

The quenching of polymerization with a chromium oxide catalyst by radioactive methanol ¹⁴CH₃OH enables one to determine the concentration of propagation centers and then to calculate the rate constant of the propagation. The dependence of the concentration of propagation centers and the polymerization rate on reaction time, ethylene concentration, and temperature was investigated. The change of the concentration of propagation centers with the duration of polymerization was found to be responsible for the time dependence of the overall polymerization rate. The propagation reaction is of first order on ethylene concentration in the pressure range 2–25 kg/cm². For catalysts of different composition, the temperature dependence of the overall polymerization rate and the propagation rate constant were determined, and the overall activation energy E_ov and activation energy of the propagation state E_p were calculated. The difference between E_ov and E_p is due to the change of the number of propagation centers with temperature. The variation of catalyst composition and preliminary reduction of the catalyst influence the shape of the temperature dependence of the propagation center concentration and change E_ov.     

Modification of Co/Al2O3 Fischer–Tropsch Nanocatalysts by Adding Ni: A Kinetic Approach

In this article, the effects of Ni (Co:Ni ratio = 4:1) on the performances and kinetic parameters of Co/Al₂O₃ nanocatalysts are explored in Fischer–Tropsch synthesis. As a result, the probability of chain growth increases and the deactivation rate decreases with addition of Ni. The properties of catalysts are characterized at different stages using Brunauer–Emmett–Teller analysis, Fourier transform infrared spectroscopy, scanning electron microscopy, and the vibrating sample magnetometer technique. The Co/Ni/Al₂O₃ catalyst with higher surface area and pore size exhibits higher activity and C₅₊ selectivity. The different results obtained for room‐temperature ferromagnetism have been attributed to the different metal oxides in the catalysts. The Fischer Tropsch kinetic study is done on the basis of the Langmuir–Hinshelwood–Hougen–Watson adsorption theory. Seven kinetic expressions based on the carbide and enolic mechanisms are selected. All experimental data are theoretically examined with these kinetic expressions to derive the best kinetic according to the linear and nonlinear approaches. The kinetic parameters of the fitted model, including the rate constant (k) and activation energy (E_a), are calculated with the Levenberg–Marquardt and genetic algorithm. The results show that by adding Ni the activation energy (E_a) decreases, the reaction rate (–R_CO) increases, and the CO adsorption on the Co/Ni/Al₂O₃ catalyst is faster as well.     

Antigen-antibody binding kinetics for biosensors

The diffusion-limited binding kinetics of antigen in solution to antibody immobilized on a biosensor surface is analyzed within a fractal framework. Changes in the fractal dimension, D_f observed are in the same and in the reverse directions as the forward binding rate coefficientk. For example, an increase in the concentration of the isoenzyme human creatine kinase isoenzyme MB form (CK-MB) (antigen) solution from 0.1 to 50 ng/mL and bound to anti-CK-MB antibody immobilized on fused silica fiber rods leads to increases in the fractal dimension D_f from 0.294 to 0.5080, and in the forward binding rate coefficientk from 0.1194 to 9.716, respectively. The error in the fractal dimension D_f decreases with an increase in the CK-MB isoenzyme concentration in solution. An increase in the concentration of human chorionic gonadotrophin (hCG) in solution from 4000 to 6000 mIU/mL hCG and bound to anti-hCG antibody immobilized on a fluorescence capillary fill device leads to a decrease in the fractal dimension D_f from 2.6806 to 2.6164, and to an increase in the forward binding rate coefficientk from 3.571 to 4.033, respectively. The different examples analyzed and presented together indicate one means by which the forward binding rate coefficientk may be controlled, that is by changing the fractal dimension or the ‘disorder’ on the surface. The analysis should assist in helping to improve the stability, the sensitivity, and the response time of biosensors.