Analyte-receptor binding kinetics for biosensor applications

The diffusion-limited binding kinetics of antigen (analyte), in solution with antibody (receptor) immobilized on a biosensor surface, is analyzed within a fractal framework. Most of the data presented is adequately described by a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot. A single example of a dual-fractal analysis is also presented. It is of interest to note that the binding-rate coefficient (k) and the fractal dimension (D_f) both exhibit changes in the same and in the reverse direction for the antigen-antibody systems analyzed. Binding-rate coefficient expressions, as a function of the D_f developed for the antigen-antibody binding systems, indicate the high sensitivity of thek on the D_f when both a single- and a dual-fractal analysis are used. For example, for a single-fractal analysis, and for the binding of antibody Mab 0.5β in solution to gpl20 peptide immobilized on a BIAcore biosensor, the order of dependence on the D_f was 4.0926. For a dual-fractal analysis, and for the binding of 25-100 ng/mL TRITC-LPS (lipopolysaccharide) in solution with polymyxin B immobilized on a fiberoptic biosensor, the order of dependence of the binding-rate coefficients, k₁ and k₂ on the fractal dimensions, D_f1 and D_f2, were 7.6335 and-11.55, respectively. The fractional order of dependence of thek(s) on the D_f(s) further reinforces the fractal nature of the system. Thek(s) expressions developed as a function of the D_f(s) are of particular value, since they provide a means to better control biosensor performance, by linking it to the heterogeneity on the surface, and further emphasize, in a quantitative sense, the importance of the nature of the surface in biosensor performance.     

Surface Roughness Characterization of Poly(methylmethacrylate) Films with Immobilized Eu(III) β-Diketonates by Fractal Analysis

The structural complexity of the 3-D surface of poly(methylmethacrylate) films with immobilized europium β-diketonates was studied by atomic force microscopy and fractal analysis. Fractal analysis of surface roughness revealed that the 3-D surface has fractal geometry at the nanometer scale. Poly(methylmethacrylate) (PMMA) as immobilization matrix is dense and uniform, and a tendency for formation of chain structures was observed. Fractal analysis can quantify key elements of 3-D surface roughness such as the fractal dimensions D _f determined by the morphological envelopes method of the Eu(DBM)₃ and Eu(DBM)₃ · dpp nanostructures, which are not taken into account by traditional surface statistical parameters.     

Studies of physico-chemical properties and fractal dimensions of selected high-temperature superconductor surfaces

Properties relating to porosity of solids (fractal dimensions, surface roughness parameters) were evaluated from atomic force microscopy (AFM) and nitrogen adsorption-desorption isotherms measured at 77 K for selected high-temperature [(RE) Ba₂Cu₃O_7−x, RE=Y, Sm] superconductors. Adsorption capacity, specific surface area, fractal dimensions were determined from adsorption-desorption isotherms. The adsorption isotherms of all samples were S-shaped and belong to type II according to the IUPAC classification. A linear relationship was demonstrated between the fractal coefficients calculated by using the two methods and values of adsorption capacity of monolayer.     

Microporous SiO2 and SiO2/MOx (M=Ti,Zr, Al) for ceramic membrane applications: A microstructural study of the sol-stage and the consolidated state

Microporous SiO₂ and SiO₂/MO₂ (M=Ti, Zr, Al; 10 mol% MO_x) materials for gas separation membrane applications have been prepared from polymeric sols. Characterization of these sols with SAXS showed that the mean fractal dimension of the SiO₂ sols is 1.3–1.4 with a radius of gyration of approximately 2.5 nm. The dried and calcined films are microporous and the pore size distribution was bimodal with maxima at diameters of 0.5 nm and 0.75 nm. For the SiO₂/TiO₂, SiO₂/ZrO₂ and SiO₂/Al₂O₃ systems, much milder reaction conditions proved to be necessary to obtain sols with comparable fractal dimensions due to the high reactivity of the Ti/Zr/Al-alkoxides. Microporous supported membranes with molecular sieve-like gas transport properties can be prepared from a relatively wide range of sol structures: from polymers too small to characterize with SAXS to structures with fractal dimensions: 1<d _f<2.04.     

Analyte-receptor binding kinetics for different types of biosensors

A fractal analysis is presented for analyte-receptor binding kinetics for different types of biosensor applications. Data taken from the literature may be modeled using a single-fractal analysis, a single- and a dual-fractal analysis, or a dual-fractal analysis. The latter two methods represent a change in the binding mechanism as the reaction progresses on the surface. Predictive relationships developed for the binding rate coefficient as a function of the analyte concentration are of particular value since they provide a means by which the binding rate coefficients may be manipulated. Relationships are presented for the binding rate coefficients as a function of the fractal dimension D _f or the degree of heterogeneity that exists on the surface. When analyte-receptor binding is involved, an increase in the heterogeneity on the surface (increase in D _f ) leads to an increase in the binding rate coefficient. It is suggested that an increase in the degree of heterogeneity on the surface leads to an increase in the turbulence on the surface owing to the irregularities on the surface. This turbulence promotes mixing, minimizes diffusional limitations, and leads subsequently to an increase in the binding rate coefficient. The binding rate coefficient is rather sensitive to the degree of heterogeneity, D _f , that exists on the biosensor surface. For example, the order of dependence on D _f1 is 7.25 for the binding rate coefficient k ₁ for the binding of a Fab fragment of an antiparaquat monoclonal antibody in solution to an antigen in the form of a paraquat analog immobilized on a sensor surface. The predictive relationships presented for the binding rate coefficient and the fractal dimension as a function of the analyte concentration in solution provide further physical insights into the binding reactions on the surface, and should assist in enhancing biosensor performance. In general, the technique is applicable to other reactions occurring on different types of surfaces, such as cell-surface reactions.     

Fractal Dimensions of Coals and Cokes

Using adsorption data, we get formulas for the calculation of fractal dimensions: log[A_CO2(DP)/A_N2(BET)] = −5.3984(2 −D₁)/2 and log[A_CO2(BET)/A_N2(BET)] = −4.9569(2 −D₂)/2. The fractal dimensions (D) of 27 coals and 2 cokes have been obtained. TheDof coals decreased with the increase of f_aand reached a maximum at H/C equal to 0.66 (orC_dafabout 86%). The fractal dimension is relative to ash and volatiles of coal:D= 2.2237 + 0.6249V_daf+ 0.8863A_d. The relationship betweenDof coal coke and its conversions (X) obeys the following equation:D = aexp(−bX) +c.     

异相晶种诱导快速合成低硅菱沸石分子筛

在不含有机模板剂体系(OSDAs)中,利用异相晶种(T型分子筛)诱导快速合成出纯相的低硅菱沸石分子筛。采用XRD、SEM、TEM、27Al MAS NMR和紫外拉曼等手段表征分子筛的结构属性和形貌特点。详细研究了菱沸石分子筛的晶化过程以及晶种添加量、nAl2O3/nSi O2、nH2O/nSiO2和碱度对菱沸石分子筛晶化的影响,并探讨T型分子筛晶种诱导合成菱沸石分子筛的晶化机理。原位合成体系中仅形成L型分子筛晶相,而一定量T型分子筛异相晶种的加入诱导溶胶快速制备出纯相的菱沸石分子筛。T型分子筛晶体在一定的水热条件下不断溶解而释放的六元环(6R)和四元环(4R)迅速形成菱沸石分子筛特征笼(CHA笼),抑制了L型分子筛特征单元和特征笼(不含四元环的CAN笼)的形成。     

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.     

Gelation of tenuous titania gels in a reverse micellar medium

Tenuous gels of TiO₂ are synthesized from titanium isopropoxide in a reverse micellar medium. The volume fraction of TiO₂ in these gels is equal to 0.2%. The chemical and aggregative mechanisms are studied using ¹H NMR, small-angle X-ray scattering, dynamic and static light scattering. The alkoxide hydrolysis occurs at the first stage of the gelation. Small clusters (70–80 Å) are produced. The aggregation induces mass fractal structures with fractal dimensions depending on the solvent used in the synthesis: 1.4<D _f<1.9. The interpretation of these results is based on interactions between the growing inorganic chains and the surfactant molecules.     

Influence of N,O-carboxymethyl chitosan on the properties of octadecanoic acid/octadecylamine monolayers and the fractal structure of calcium carbonate

The properties of octadecanoic acid-otctadecylamine monolayers and growth of calcium carbonate (CaCO₃) induced by the monolayers on the surface of supersaturated CaCO₃ solution with N,O-carboxymethyl chitosan (CMC) are studied. The results suggest that CMC is either adsorbed on or inserted into the monolayers, as is confirmed by π-A, dπ/dA-A, and π-t isotherms. The adsorption of CMC changes the properties of the monolayers, a process that results in the transformation of the shape of CaCO₃ particles from crystal-like into the fractal pattern beneath the monolayers. Different fractal morphologies, such as butterfly and wicker branches consisting of hollow ellipsoidal, solid ellipsoidal, and spherical particles, correspondingly, are observed; these morphologies depend on the CMC concentration in the subphase. The dimensions of fractal patterns are determined. The mechanisms of the formation of CaCO₃ crystals and fractal structures are discussed. The text was submitted by the authors in English.     

Intracellular potassium under osmotic stress determines the dielectrophoresis cross‐over frequency of murine myeloma cells in the MHz range

Dielectrophoresis (DEP) has been widely studied for its potential as a biomarker‐free method of sorting and characterizing cells based upon their dielectric properties. Most studies have employed voltage signals from ∼1 kHz to no higher than ∼30 MHz. Within this range a transition from negative to positive DEP can be observed at the cross‐over frequency f_x01. The value of f_x01 is determined by the conductivity of the suspending medium, as well as the size and shape of the cell and the dielectric properties (capacitance, conductivity) of its plasma membrane. In this work DEP measurements were performed up to 400 MHz, where the transition from positive to negative DEP can be observed at a higher cross‐over frequency f_x02. SP2/O murine myeloma cells were suspended in buffer media of different osmolarities and measurements taken of cell volume, f_x01 and f_x02. Potassium‐binding benzofuran isophthalate (PBFI), a potassium‐sensitive fluorophore, and flow cytometry was employed to monitor relative changes in intracellular potassium concentration. In agreement with theory, it was found that f_x02 is independent of the cell parameters that control f_x01 and is predominantly determined by intracellular conductivity. In particular, the value of f_x02 is highly correlated to that of the intracellular potassium concentration.     

Studies of physico-chemical properties and fractal dimensions of MgB2 superconductor surface

The porous structure of MgB₂ has been investigated using atomic force microscopy (AFM) and sorption techniques. The fractal dimension and surface roughness parameters were evaluated from (AFM) and nitrogen adsorption?Cdesorption isotherms measured at ?196?°C for MgB₂ sample. Adsorption capacity, specific surface area, and fractal dimensions were determined from adsorption?Cdesorption isotherms. The sorption isotherms of MgB₂ samples were S-shaped and belong to type II according to the IUPAC classification. The results of fractal dimensions of MgB₂ surface determined on the basis sorptometry and AFM data are compared.     

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     

The effect of Fe-doping on superconductivity of YBa2Cu30 y

In the present paper, an approximate band-structure treatment based on the EHMO approach is suggested and used to calculate the electronic structures of the Fe-doped superconductors YBa₂Cu_3–x Fe _x O _y . The present treatment gives, indeed, average band structures and average densities of states as the doping fraction increases. From investigations of the influence of the Fe-doping at the Cu-site on their properties, it is shown that as the Fe-doping fractionx in YBa₂Cu_3–x Fe _x O _y is raised from 0.0 to 0.5, (i) the broad anisotropic bands arising from the 1D Cu-O chains and the 2D Cu-O planes are displaced and depart from the Fermi levelE _f toward the high-energy zone by degrees, while the total electronic densities of states nearE _f are drastically decreased; (ii) the band arising from the Cu-O chains doped by Fe is gradually separated from the broad anisotropic bands arising from the 2D Cu-O planes; (iii) at the doping fractionx = 0.5, the Fe-doping results in an energy gap (about 0.2 eV) near E_f; (iv) the oxygen content is not a predominant factor for the superconducting properties of the Fe-doped Y-Ba-Cu-O system; (v) the total densities of states atE _f,N(E _f), and their decrease caused by the Fe-doping arise mainly from the 2D Cu-O planes, which implies the important role of the 2D Cu-O planes in the Y-Ba-Cu-O superconducting system.     

Self‐Assembly Film of Zeolite Y Nanocrystals Loading Palladium on an Au Electrode for Electrochemical Applications

Nano‐scale zeolite Y crystals were synthesized, and palladium nanoparticles were prepared in the supercage of the zeolite by “ship‐in‐a‐bottle” approach. A novel method to fabricate zeolite‐modified electrode (ZME) loading Pd nanoparticles was developed, in which the zeolite Y loading Pd²⁺ ions was self‐assembled on (3‐mercaptopropyl) trimethoxysilane‐attached Au surface to form the stable and density packed multilayers (SAM‐ZME). The structures of zeolite Y and the SAM‐ZME were investigated by using TEM, XRD and SEM techniques. Pd²⁺ ions in the SAM‐ZME were converted into Pd nanoparticles (Pd_n⁰) by two steps consisting of the electrochemical reduction as well as the succeeding admission and release of CO. The redox couple [Fe(CN)₆]^3?/4? was used to probe the electron‐transfer barrier properties during self‐assembling process. Moreover, the special properties of the SAM‐ZME loading Pd_n⁰ were studied by using cyclic voltammetry and CO‐probe in situ FTIR spectroscopy. The results illustrated that Pd_n⁰ in the SAM‐ZME exhibits higher electrocatalytic activity for oxidation of adsorbed CO than that of ZME prepared in our previous study by zeolite coating method. The present study is of importance in design and preparation of SAM‐ZME, which poccesseses excellent properties for the immobilization of electrocatalysts or biomolecules.     

Formation and structure of pachyman aggregates in dimethyl sulfoxide containing water

The aggregation of pachyman, β-(1 → 3)-D -glucan (M_w = 1.68 × 10⁵) from the Poria cocos mycelia, was investigated using static and dynamic laser light scattering (LLS) in dimethyl sulfoxide (DMSO) containing about 15% water, which leads to large aggregates. Both the time dependence of hydrodynamic radius and the angle dependence of the scattering intensity were used to calculate the fractal dimension (d_f) of the aggregates. The aggregation rate and average size of aggregates increase dramatically with increasing the polymer concentration from 1.7 × 10⁻⁴ g/mL to 8.6 × 10⁻⁴ g/mL, and with the decrease of the solvent quality, that is, water content from 13 to 15%. In the cases, the fractal dimensions change from 1.94 to 2.43 and from 1.92 to 2.54, respectively, suggesting that transforms of aggregation processes: a slow process called reaction-limited cluster aggregation (RLCA) to a fast process called diffusion-limited cluster aggregation (DLCA) in different polymer concentrations and water content. The fractal dimensions above 2 of the fast aggregation is larger than the 1.75 predicted for the ideal DLCA model, suggesting that the aggregation involves a restructuring process through the interchain hydrogen bonding interaction. There are no aggregates of pachyman in DMSO without water, but aggregates formed in the DMSO containing 15% water at 25°C as a compact structure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3201–3207, 1999     

Isotope effect in gas transport. I. Measurement of the free volume element in four polymers above the glass transition temperature

The experimental observation of an isotope effect in diffusive gas transport across polymeric films is reported. The differences in energies of transport between hydrogen and deuterium are used to estimate the effective dimensions of characteristic minima or “wells” in the potential energy surface of rubbery polymers. The size of a well, determined by assuming it to be a cubical cavity, is interpreted as the effective free volume element v_f, as measured by the hydrogen molecule probe. Estimations are made of the entropy of activation and “jump distance” for the hydrogen diffusion process based on v_f values and experimentally determined pre-exponential factors.     

IDM‐1: A Zeolite with Intersecting Medium and Extra‐Large Pores Built as an Expansion of Zeolite MFI

IDM‐1 is a new silica zeolite with an ordered and well‐defined framework constructed by alternating pentasil layers and interrupted layers, giving rise to an intersecting system of straight medium pores and undulating extra‐large lobed pores. This unique structure was solved by rotation electron diffraction and refined against synchrotron powder X‐ray diffraction data. Despite the presence of both Si(OSi)₃(OH) and Si(OSi)₂(OH)₂ sites, this new zeolite presents high thermal stability, withstanding calcination even to 1000 °C. The location of defects at specific sites of the structure results in alternating hydrophobic SiO₂ and hydrophilic SiO_(2?x)(OH)_2x intracrystalline regions. This peculiar combination of intersecting medium and extra‐large pores and alternating regions of different chemical character may provide this zeolite with unique catalytic properties.     

Size exclusion chromatography on porous fractals

Summary Some porous packings used in chromatography have been claimed to be fractals with a scale of sizes a<l<L, where a is a molecular size and L is the size of the largest pores. For a fractal porous packing, the excluded volume for molecules in solution in the vicinity of the packing surface is directly related to D_f, the fractal dimension of the pore surface (2<D_f<3). Since retention in size exclusion chromatography is itself directly related to this excluded volume, the fractal nature of the packing provides a model of retention in this technique. According to this model there is a linear relationship between log R_s and log(1-K_d), where R_s is the hydrodynamic radius of the solute macromolecules and K_d the distribution coefficient. The fractal dimension is derived from the slope of this plot. Size exclusion chromatographic retention data have been analyzed according to the model. It is found that some HPLC packings are fractals with fractal dimensions ranging from about 2.15 to 2.6, depending on the material. Such a large range of D_f values indicates large variations in the selectivities and domains of applications of the different packings. For some classical gel filtration chromatographic gels, the fractal retention model does not seem to apply.Presented at the 17th International Symposium on Chromatography, September 25–30, 1988, Vienna, Austria.