Quartz Crystal Microbalance Frequency Response to Discrete Adsorbates in Liquids.

Quartz crystal microbalance with dissipation monitoring (QCM-D) has become a major tool enabling accurate investigation of the adsorption kinetics of nanometric objects such as DNA fragments, polypeptides, proteins, viruses, liposomes, polymer, and metal nanoparticles. However, in liquids, a quantitative analysis of the experimental results is often intricate because of the complex interplay of hydrodynamic and adhesion forces varying with the physicochemical properties of adsorbates and functionalized QCM-D sensors. In the present paper, we dissect the role of hydrodynamics for the analytically tractable case of stiff contact, whereas the adsorbed rigid particles oscillate with the resonator without rotation. Under the assumption of the low surface coverage, we theoretically study the excess shear force exerted on the resonator, which has two contributions: (i) the fluid-mediated force due to flow disturbance created by the particle and (ii) the force exerted on the particle by the fluid and transmitted to the sensor via contact. The theoretical analysis enables an accurate interpretation of the QCM-D impedance measurements. It is demonstrated inter alia that for particles of the size comparable with protein molecules, the hydrodynamic force dominates over the inertial force and that the apparent mass derived from QCM independently of the overtone is about 10 times the Sauerbrey (inertial) mass. The theoretical results show excellent agreement with the results of experiments and advanced numerical simulations for a wide range of particle sizes and oscillation frequencies.

Anisotropic Particle Deposition Kinetics from Quartz Crystal Microbalance Measurements: Beyond the Sphere Paradigm.

Deposition kinetics of polymer particles characterized by a prolate spheroid shape on gold sensors modified by the adsorption of poly(allylamine) was investigated using a quartz crystal microbalance and atomic force microscopy. Reference measurements were also performed for polymer particles of a spherical shape and the same diameter as the spheroid shorter axis. Primarily, the frequency and dissipation shifts for various overtones were measured as a function of time. These kinetic data were transformed into the dependence of the complex impedance, scaled up by the inertia impedance, upon the particle size to the hydrodynamic boundary layer ratio. The results obtained for low particle coverage were interpolated, which enabled the derivation of Sauerbrey-like equations, yielding the real particle coverage using the experimental frequency or dissipation (bandwidth) shifts. Experiments carried out for a long deposition time confirmed that, for spheroids, the imaginary and real impedance components were equal to each other for all overtones and for a large range of particle coverage. This result was explained in terms of a hydrodynamic, lubrication-like contact of particles with the sensor, enabling their sliding motion. In contrast, the experimental data obtained for spheres, where the impedance ratio was a complicated function of overtones and particle coverage, showed that the contact was rather stiff, preventing their motion over the sensor. It was concluded that results obtained in this work can be exploited as useful reference systems for a quantitative interpretation of bioparticle, especially bacteria, deposition kinetics on macroion-modified surfaces.

Deposition of Human-Serum-Albumin-Functionalized Spheroidal Particles on Abiotic Surfaces: Reference Kinetic Results for Bioparticles.

Human serum albumin (HSA) corona formation on polymer microparticles of a spheroidal shape was studied using dynamic light scattering and Laser Doppler Velocimetry (LDV). Physicochemical characteristics of the albumin comprising the zeta potential and the isoelectric point were determined as a function of pH for various ionic strengths. Analogous characteristics of the polymer particles were analyzed. The adsorption of albumin on the particles was in situ monitored by LDV. The stability of the HSA-functionalized particle suspensions under various pHs and their electrokinetic properties were also determined. The deposition kinetics of the particles on mica, silica and gold sensors were investigated by optical microscopy, AFM and quartz microbalance (QCM) under diffusion and flow conditions. The obtained results were interpreted in terms of the random sequential adsorption model that allowed to estimate the range of applicability of QCM for determining the deposition kinetics of viruses and bacteria at abiotic surfaces.

Quantifying Nanoparticle Layer Topography: Theoretical Modeling and Atomic Force Microscopy Investigations.

A comprehensive method consisting of theoretical modeling and experimental atomic force microscopy (AFM) measurements was developed for the quantitative analysis of nanoparticle layer topography. Analytical results were derived for particles of various shapes such as cylinders (rods), disks, ellipsoids, hemispheres (caps), etc. It was shown that for all particles, their root-mean-square (rms) parameter exhibited a maximum at the coverage about 0.5, whereas the skewness was a monotonically decreasing function of the coverage. This enabled a facile determination of the particle coverage in the layer, even if the shape and size were not known. The validity of the analytical results was confirmed by computer modeling and experimental data acquired by AFM measurements for polymer nanoparticle deposition on mica and silica. The topographical analysis developed in this work can be exploited for a quantitative characterization of self-assembled layers of nano- and bioparticles, e.g., carbon nanotubes, silica and noble metal particles, DNA fragments, proteins, vesicles, viruses, and bacteria at solid surfaces. The acquired results also enabled a proper calibration, in particular the determination of the measurement precision, of various electron and scanning probe microscopies, such as AFM.

QCM-D Investigations of Anisotropic Particle Deposition Kinetics: Evidences of the Hydrodynamic Slip Mechanisms.

Deposition kinetics of positively charged polymer microparticles, characterized by prolate spheroid shape, at silica and gold sensors was investigated using the quartz microbalance (QCM) technique. Reference measurements were also performed for positively charged polymer particles of spherical shape and the same mass as the spheroids. Primarily, the frequency and bandwidth shifts for various overtones were measured as a function of time. It is shown that the ratio of these signals is close to unity for all overtones. These results were converted to the dependence of the frequency shift on the particle coverage, directly determined by atomic force microscopy and theoretically interpreted in terms of the hydrodynamic model. A quantitative agreement with experiments was attained considering particle slip relative to the ambient oscillating flow. In contrast, the theoretical results pertinent to the rigid contact model proved inadequate. The particle deposition kinetics derived from the QCM method was compared with theoretical modeling performed according to the random sequential adsorption approach. This allowed to assess the feasibility of the QCM technique to furnish proper deposition kinetics for anisotropic particles. It is argued that the hydrodynamic slip effect should be considered in the interpretation of QCM kinetic results acquired for bioparticles, especially viruses.

Human Vimentin Layers on Solid Substrates: Adsorption Kinetics and Corona Formation Investigations.

Adsorption kinetics of human vimentin on negatively charged substrates (mica, silica, and polymer particles) was analyzed using atomic force microscopy (AFM), quartz microbalance (QCM), and the laser doppler velocimetry (LDV) method. AFM studies realized under diffusion conditions proved that the adsorbed protein layer mainly consisted of aggregates in the form of compact tetramers and hexamers of a size equal to 11-12 nm. These results were consistent with vimentin adsorption kinetics under flow conditions investigated by QCM. It was established that vimentin aggregates efficiently adsorbed on the negatively charged silica sensor at pH 3.5 and 7.4, forming compact layers with the coverage reaching 3.5 mg m-2. Additionally, the formation of the vimentin corona at polymer particles was examined using the LDV method and interpreted in terms of the electrokinetic model. This allowed us to determine the zeta potential of the corona as a function of pH and the electrokinetic charge of aggregates, which was equal to -0.7 e nm-2 at pH 7.4 in a 10 mM NaCl solution. The anomalous adsorption of aggregates exhibiting an average negative charge on the negatively charged substrates was interpreted as a result of a heterogeneous charge distribution. These investigations confirmed that it is feasible to deposit stable vimentin layers both at planar substrates and at carrier particles with well-controlled coverage and zeta potential. They can be used for investigations of vimentin interactions with various ligands including receptors of the innate immune system, immunoglobulins, bacterial virulence factors, and spike proteins of viruses.

Kinetics of Immunolatex Deposition at Abiotic Surfaces under Flow Conditions: Towards Quantitative Agglutination Assays.

Physicochemical properties of immunolatex, prepared by incubation of negatively charged polystyrene microparticles with polyclonal rabbit IgGs, were determined by a variety of experimental techniques. These comprised dynamic light scattering (DLS), laser Doppler velocimetry (LDV) and atomic force microscopy (AFM). The particle diffusion coefficient, the hydrodynamic diameter, the electrophoretic mobility, the zeta potential and the suspension stability were determined as a function of pH for different ionic strengths. The deposition of the immunolatex on bare and polyallylamine (PAH) functionalized mica was investigated using the microfluidic oblique impinging-jet cell, with an in situ, real-time image analysis module. The particle deposition kinetics was acquired by a direct particle enumeration procedure. The measurements enabled us to determine the range of pH where the specific deposition of the immunolatex on these substrates was absent. We argue that the obtained results have practical significance for conducting efficient flow immunoassays governed by specific antigen/antibody interactions.

SARS-CoV-2 Spike Protein (RBD) Subunit Adsorption at Abiotic Surfaces and Corona Formation at Polymer Particles.

The adsorption kinetics of the SARS-CoV-2 spike protein subunit with the receptor binding domain at abiotic surfaces was investigated. A combination of sensitive methods was used such as atomic force microscopy yielding a molecular resolution, a quartz microbalance, and optical waveguide lightmode spectroscopy. The two latter methods yielded in situ information about the protein adsorption kinetics under flow conditions. It was established that at pH 3.5-4 the protein adsorbed on mica and silica surfaces in the form of compact quasi-spherical aggregates with an average size of 14 nm. The maximum coverage of the layers was equal to 3 and 1 mg m-2 at pH 4 and 7.4, respectively. The experimental data were successfully interpreted in terms of theoretical results derived from modeling. The experiments performed for flat substrates were complemented by investigations of the protein corona formation at polymer particles carried out using in situ laser Doppler velocimetry technique. In this way, the zeta potential of the protein layers was acquired as a function of the coverage. Applying the electrokinetic model, these primary data were converted to the dependence of the subunit zeta potential on pH. It was shown that a complete acid-base characteristic of the layer can be acquired only using nanomolar quantities of the protein.

SARS-CoV-2 virion physicochemical characteristics pertinent to abiotic substrate attachment.

The structure, size, and main physicochemical characteristics of the SARS-CoV-2 virion with the spike transmembrane protein corona were discussed. Using these data, diffusion coefficients of the virion in aqueous media and in air were calculated. The structure and dimensions of the spike protein derived from molecular dynamic modeling and thorough cryo-electron microscopy measurements were also analyzed. The charge distribution over the molecule was calculated and shown to be largely heterogeneous. Although the stalk part is negatively charged, the top part of the spike molecule, especially the receptor binding domain, remains positively charged for a broad range of pH. It is underlined that such a charge distribution promotes the spike corona stability and enhances the virion attachment to receptors and surfaces, mostly negatively charged. The review is completed by the analysis of experimental data pertinent to the spike protein adsorption at abiotic surfaces comprising nanoparticle carrier particles. It is argued that these theoretical and experimental data can be used for developing quantitative models of virus attachment to surfaces, facilitating adequate analysis of future experimental results.

Deposition of Polymer Particles with Fibrinogen Corona at Abiotic Surfaces under Flow Conditions.

The deposition kinetics of polymer particles with fibrinogen molecule coronas at bare and poly-L-lysine (PLL) modified mica was studied using the microfluid impinging-jet cell. Basic physicochemical characteristics of fibrinogen and the particles were acquired using dynamic light scattering and the electrophoretic mobility methods, whereas the zeta potential of the substrates was determined using streaming potential measurements. Subsequently, an efficient method for the preparation of the particles with coronas, characterized by a controlled fibrinogen coverage, was developed. This enabled us to carry out measurements, which confirmed that the deposition kinetics of the particles at mica vanished at pH above 5. In contrast, the particle deposition of PLL modified mica was at maximum for pH above 5. It was shown that the deposition kinetics could be adequately analyzed in terms of the mean-field approach, analogously to the ordinary colloid particle behavior. This contrasts the fibrinogen molecule behavior, which efficiently adsorbs at negatively charged substrates for the entire range pHs up to 9.7. These results have practical significance for conducting label-free immunoassays governed by the specific antigen/antibody interactions.

Hydrodynamic Solvent Coupling Effects in Quartz Crystal Microbalance Measurements of Nanoparticle Deposition Kinetics.

Hydrodynamic coupling effects pertinent to quartz crystal microbalance (QCM) investigation of nanoparticle adsorption kinetics were evaluated using atomic force microscopy and the theoretical modeling. Monodisperse polymer particles of the size between 26 and 140 nm and the density of 1.05 g cm-3 were used. The ζ-potential of particles was opposite to the substrate ζ-potential that promoted their irreversible adsorption on the silica sensor. The experimental kinetic data were interpreted in terms of theoretical calculations derived from the hybrid random sequential adsorption model. This allowed us to determine the amount of hydrodynamically coupled solvent (electrolyte) for the absolute particle coverage range up to 0.5. The coupling function representing the ratio of the solvent to the particle volumes was also determined and used to explicitly calculate the solvent level in particle monolayers. It is shown that the solvent level abruptly increases with the particle coverage attaining values comparable with the particle size. One can expect that these results can serve as useful reference data for the interpretation of protein adsorption kinetics on rough surfaces where the presence of stagnant solvent is inevitable.

Applicability of QCM-D for Quantitative Measurements of Nano- and Microparticle Deposition Kinetics: Theoretical Modeling and Experiments.

A new theoretical model is formulated for the quantitative analysis of quartz crystal microbalance (QCM) response for heterogeneous loads consisting of nano- and microparticles. The influence of particle coverage and structure is described using a universal correction function in an ab initio manner. Explicit analytical expressions for the frequency and dissipation shifts are derived for the entire range of particle size under the rigid contact regime. The solvent coupling functions are also calculated to determine the dry coverage using the QCM measurements. These expressions furnish the upper limit of the QCM signal, which can be attained for a sensor providing perfect adhesion of particles. Correction functions accounting for the finite adhesion strength (soft contact regime) are also derived. The theoretical results are confronted with QCM and atomic force microscopy measurements of positively charged polymer particle deposition on silica sensors. The main features of the theoretical model are confirmed, especially the abrupt decrease in the QCM wet mass with the particle coverage and the overtone number. The latter effect is especially pronounced for microparticles under the soft contact regime, where the higher-number overtones produce a negligible QCM signal. These results represent a useful reference data for the interpretation of protein and bioparticles, for example, virus and bacteria attachment processes to various substrates.

Myoglobin molecule charging in electrolyte solutions.

All atom molecular dynamic modeling was applied in order to determine water molecule and electrolyte ion concentration profiles around and inside the myoglobin molecule at various pH values. Significant penetration of counter ions into the molecule was confirmed. The electric potential distribution within and outside the molecule was quantitatively described using the non-linear Poisson-Boltzmann (PB) approach. Using this model, calculations were performed, yielding the surface and zeta potential for various physicochemical parameters, comprising pH, the electric permittivity, the ion penetration depth and the protein volume fraction (crowding effect). The theoretical results were used for the interpretation of experimental data acquired under different ionic strengths and temperatures by electrophoretic mobility measurements. It is confirmed that the experimental data are adequately reflected for acidic pH values by the non-linear PB model where the nominal molecule charge was calculated from the H++ model. The deviations occurring for larger pH values were accounted for by considering additional non-electrostatic interactions stemming from the van der Waals and ion-induced dipole forces. In this way, it is both experimentally and theoretically confirmed that the effective charge of the myoglobin molecule in electrolyte solutions is considerably smaller than the nominal, structure-based, predicted charge. As a result, under physiological conditions prevailing, e.g. in skeletal muscles, the effective charge of the myoglobin molecule should practically vanish. One can expect that the approach developed in this work can be applied for predicting charging mechanisms of other protein molecules characterized by an analogous charge vs. pH characteristic, e.g., the SARS-CoV-2 virus spike proteins, and for soft particles with pH responsive characteristics.

Human Serum Albumin Adsorption Kinetics on Silica: Influence of Protein Solution Stability.

Adsorption kinetics of human serum albumin (HSA) on silica substrates was studied using optical waveguide lightmode spectroscopy (OWLS) and quartz microbalance (QCM) techniques. Measurements were performed at pH 3.5, 5.6, and 7.4 for various bulk suspension concentrations and ionic strengths. The diffusion coefficient measurements showed that for pH 3.5 the HSA molecules are stable for NaCl concentrations from 10-3 to 0.15 M. This allowed us to precisely determine the mass transfer rate coefficients for the OWLS and QCM cells. The experimental data were adequately interpreted in terms of a hybrid random sequential adsorption model. The OWLS maximum coverage of HSA at pH 3.5, which is equal to 1.3 mg m-2, agrees with the QCM result and with previous results derived from streaming potential measurements. Thus, the results obtained at pH 3.5 served as reference data for the analysis of adsorption kinetics at higher pHs. In this way, it was confirmed that the adsorption kinetics of HSA molecules at pH 5.6 and 7.4 was considerably slower than at pH 3.5. This effect was attributed to aggregation of HSA solutions and interpreted in terms of a theoretical model combining the Smoluchowski aggregation theory with the convective diffusion mass transfer theory. New analytical equations were derived that can be used for the interpretation of other protein adsorption from unstable solutions.

Mechanisms of Fibrinogen Adsorption on Silica Sensors at Various pHs: Experiments and Theoretical Modeling.

The adsorption kinetics of human serum fibrinogen at silica substrates was studied using optical waveguide lightmode spectroscopy (OWLS) and quartz crystal microbalance (QCM) techniques. Measurements were performed at pH 3.5, 4, and 7.4 for various ionic strengths. The experimental data were interpreted in terms of a hybrid random sequential adsorption model. This allowed the mass transfer rate coefficient for the OWLS cell and maximum coverages to be determined at various pHs. The appearance of different, pH-dependent mechanisms of fibrinogen adsorption on silica substrates was confirmed. At pH 3.5 the molecules mostly adsorb in the side-on orientation that produces a low maximum coverage of ca. 1 mg m-2. At this pH, the kinetics derived from the OWLS measurements agree with those theoretically predicted using the convective-diffusion theory. In consequence, a comparison of the OWLS and QCM results allows the water factor and the dynamic hydration of fibrinogen molecules to be determined. At pH 7.4, the OWLS method gives inaccurate kinetic data for the low coverage range. However, the maximum coverage that was equal to ca. 4 mg m-2 agrees with the QCM results and with previous literature results. It is postulated that the limited accuracy of the OWLS method for lower coverage stems from a heterogeneous structure of fibrinogen monolayers, which consist of side-on and end-on adsorbed molecules. One can expect that the results acquired in this work allow development of a robust procedure for preparing fibrinogen monolayers of well-controlled coverage and molecule orientation, which can be exploited for efficient immunosensing purposes.

Kinetics of Poly-l-lysine Adsorption on Mica and Stability of Formed Monolayers: Theoretical and Experimental Studies.

Various physicochemical parameters of poly-l-lysine (PLL) solutions comprising the diffusion coefficient, the electrophoretic mobility, the density, and the intrinsic viscosity were determined for the pH range 3.0-9.2. This allowed us to calculate derivative parameters characterizing the PLL molecule such as: zeta potential, the number of electrokinetic charges, ionization degree, contour length, and cross section area. These data were exploited in theoretical calculations of PLL adsorption kinetics on solid substrates under diffusion transport. A hybrid approach was used comprising a blocking function derived from the random sequential adsorption (RSA) model. In experiments, the PLL adsorption on mica was studied using the streaming potential measurements and interpreted in terms of a general electrokinetic model. This confirmed a side-on adsorption mechanism of the macroion molecules at the examined pH range. Additionally, using this method, the stability of PLL monolayers was determined performing in situ desorption kinetic experiments. In this way, the equilibrium adsorption constant and the energy minimum depth were determined. It was confirmed that the monolayer stability decreases with pH following the decrease in the number of electrokinetic charges per molecule. This confirmed the electrostatic interaction driven adsorption mechanism of PLL. It is also predicted that at pH 5.7-7.4 the monolayers were stable under diffusion-controlled desorption over the time exceeding 100 h. In addition to their significance for basic science, the results obtained in this work can be exploited for developing procedures for preparing stable PLL monolayers of well controlled coverage and electrokinetic properties.

Gold substrates of controlled roughness and electrokinetic properties formed by nanoparticle deposition.

The kinetics of positively charged gold nanoparticle self-assembly on oxidized silicon substrates (wafers) under diffusion-controlled transport was studied using scanning electron microscopy (SEM) and atomic force microscopy (AFM). The latter technique allowed the roughness parameters of the monolayer (root mean square) to be determined as a function of the particle coverage. These results were adequately interpreted in terms of a theoretical model developed for surfaces covered by features of spherical shape considering the tip convolution effect. The stability and the electrokinetic characteristics (zeta potential) of the monolayers were also acquired using streaming potential measurements. It was shown that the inversion of the negative zeta potential of the bare substrate (overcharging) occurs at the particle coverage equal to 0.15, and for larger coverages positive zeta potential values were asymptotically attained. Additionally, the desorption kinetics of the particles was investigated by the streaming potential method, which confirmed the stability of the monolayers for a broad range of pHs. It was argued that these results enable to develop an efficient method for the preparation of gold sensors exhibiting a well-controlled surface roughness and electrostatic charge comprising both negative and positive values.

Gold Nanoparticle Layers on Polystyrene Microspheres of Controlled Structure and Electrokinetic Properties.

Formation of positively charged gold nanoparticle layers on polystyrene microparticles (PSMs600) was studied using the electrokinetic and the concentration depletion methods based on atomic force microscopy (AFM) and scanning electron microscopy (SEM) imaging. Primarily, the dependence of electrophoretic mobility of microparticles on the gold nanoparticle concentration in the suspension was measured. These results were quantitatively interpreted in terms of the three-dimensional electrokinetic model. This allowed to derive a formula for calculating the coverage of nanoparticles under in situ conditions whose validity was confirmed by direct SEM imaging of deposited gold nanoparticles (AuNPs). Additionally, the maximum coverage of gold nanoparticles for various ionic strengths was determined using a concentration depletion method based on AFM imaging of residual particles deposited on the silica substrate. The maximum coverage increased with ionic strength attaining a value of 0.35 for the ionic strength of 3 × 10-3 M. This effect was attributed to the decreasing range of lateral electrostatic interactions among deposited particles. The electrokinetic properties of the gold nanoparticle layers were also evaluated in pH cycling experiments that confirmed their stability. Beyond significance to basic science, the new data acquired in this work confirm the feasibility of preparing gold nanoparticle layers on polymer microparticles characterized by a controlled structure, coverage, and electrokinetic properties.

Hematite/silica nanoparticle bilayers on mica: AFM and electrokinetic characterization.

Quantitative studies on self-assembled hematite/silica nanoparticle (NP) bilayers on mica were performed by applying scanning electron microscopy (SEM), atomic force microscopy (AFM), and streaming potential measurements. The coverage of the supporting hematite layers was adjusted by changing the bulk concentration of the suspension and the deposition time. The coverage was determined by direct enumeration of deposited particles from AFM images and SEM micrographs. Afterward, silica nanoparticle monolayers were assembled under diffusion-controlled transport. A unique functional relationship was derived connecting the silica coverage with the hematite precursor layer coverage. The formation of the hematite monolayer and the hematite/silica bilayer was also monitored in situ by streaming potential measurements. It was confirmed that the zeta potential of the bilayers was independent of the supporting layer coverage, exceeding 0.15. These measurements were theoretically interpreted in terms of the general electrokinetic model that allowed for deriving a formula for calculating nanoparticle coverage in the bilayers. Additionally, from desorption experiments, the interactions among hematite/silica particles in the bilayers were determined using DLVO theory. These results facilitate the development of a robust method of preparing nanoparticle bilayers with controlled properties, with potential applications in catalytic processes.

Spheroidal Microparticle Monolayers Characterized by Streaming Potential Measurements.

An efficient method was developed enabling the synthesis of spheroidal polymer microparticles. Thorough physicochemical characteristics of the particles were acquired comprising the size, shape, electrophoretic mobility, and the diffusion coefficient. The particles were monodisperse, and their shape was well-fitted by prolate spheroids having the axis ratio equal to 4.17. Knowing the diffusion coefficient, their hydrodynamic diameter of 449 nm was calculated, which matched the value derived from Brenner's analytical expression. Particle deposition kinetics on mica and silicon/silica substrates, modified by poly(allylamine hydrochloride) (PAH) adsorption, was studied by optical microscopy and AFM imaging. The validity of the random sequential adsorption model was confirmed. Additionally, monolayers of the particles on these substrates were thoroughly characterized in situ by the streaming potential measurements for different ionic strengths. These measurements confirmed that the ζ potential change with the spheroidal particle coverage is less abrupt than for spheres and agrees with theoretical predictions. Exploiting these results, a useful analytical expression was derived that allows one to calculate the spheroidal particle coverage in situ via the streaming potential measurements. This expression, especially accurate for low coverage range, can be used for a quantitative interpretation of adsorption and desorption kinetics of anisotropic macromolecules, e.g., proteins on solid substrates.