Optical control and characterisation of aerosol

Separation-dependent near-field effects in Mie scattering spectra of two optically trapped aerosol droplets

The backscattering of ultraviolet and visible light by a model organic (squalane) aerosol droplet (1.0 Collapse

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Raman spectroscopy for profiling physical and chemical properties of atmospheric aerosol particles: A review

Atmosphere aerosols have significant impact on human health and the environment. Aerosol particles have a number of characteristics that influence their health and environmental effects, including their size, shape, and chemical composition. A great deal of difficulty is associated with quantifying and identifying atmospheric aerosols because these parameters are highly variable on a spatial and temporal scale. An important component of understanding aerosol fate is Raman Spectroscopy (RS), which is capable of resolving chemical compositions of individual particles. This review presented strategic techniques, especially RS methods for characterizing atmospheric aerosols. The nature and properties of atmospheric aerosols and their influence on environment and human health were briefly described. Analytical methodologies that offer insight into the chemistry and multidimensional properties of aerosols were discussed. In addition, perspectives for practical applications of atmospheric aerosols using RS are featured.

Aerosol pH and Ion Activities of HSO4- and SO42- in Supersaturated Single Droplets

Accurate determination of acidity (pH) and ion activities in aqueous droplets is a major experimental and theoretical challenge for understanding and simulating atmospheric multiphase chemistry. Here, we develop a ratiometric Raman spectroscopy method to measure the equilibrium concentration of sulfate (SO₄^2-) and bisulfate (HSO₄^-) in single microdroplets levitated by aerosol optical tweezers. This approach enables determination of ion activities and pH in aqueous sodium bisulfate droplets under highly supersaturated conditions. The experimental results were compared against aerosol thermodynamic model calculations in terms of simulating aerosol ion concentrations, ion activity coefficients, and pH. We found that the Extended Aerosol Inorganics Model (E-AIM) can well reproduce the experimental results. The alternative model ISORROPIA, however, exhibits substantial deviations in SO₄^2- and HSO₄^- concentrations and up to a full unit of aerosol pH under acidic conditions, mainly due to discrepancies in simulating ion activity coefficients of SO₄^2--HSO₄^- equilibrium. Globally, this may cause an average deviation of ISORROPIA from E-AIM by 25 and 65% in predicting SO₄^2- and HSO₄^- concentrations, respectively. Our results show that it is important to determine aerosol pH and ion activities in the investigation of sulfate formation and related aqueous phase chemistry.

Water evaporation from solute-containing aerosol droplets: Effects of internal concentration and diffusivity profiles and onset of crust formation

The evaporation of droplets is an important process not only in industrial and scientific applications, but also in the airborne transmission of viruses and other infectious agents. We derive analytical and semi-analytical solutions of the coupled heat and mass diffusion equations within a spherical droplet and in the ambient vapor phase that describe the evaporation process of aqueous free droplets containing nonvolatile solutes. Our results demonstrate that the solute-induced water vapor-pressure reduction considerably slows down the evaporation process and dominates the solute-concentration dependence of the droplet evaporation time. The evaporation-induced enhanced solute concentration near the droplet surface, which is accounted for using a two-stage evaporation description, is found to further slow-down the drying process. On the other hand, the presence of solutes is found to produce a lower limit for the droplet size that can be reached by evaporation and, also, to reduce evaporation cooling of the droplet, which tend to decrease the evaporation time. Overall, the first two effects are dominant, meaning that the droplet evaporation time increases in the presence of solutes. Local variation of the water diffusivity inside the droplet near its surface, which is a consequence of the solute-concentration dependence of the diffusion coefficient, does not significantly change the evaporation time. Crust formation on the droplet surface increases the final equilibrium size of the droplet by producing a hollow spherical particle, the outer radius of which is determined as well.

Micro-droplet Trapping and Manipulation: Understanding Aerosol Better for a Healthier Environment

Understanding the physicochemical properties and heterogeneous processes of aerosols is key not only to elucidate the impacts of aerosols on the atmosphere and humans but also to exploit their further applications, especially for a healthier environment. Experiments that allow for spatially control of single aerosol particles and investigations on the fundamental properties and heterogeneous chemistry at the single-particle level have flourished during the last few decades, and significant breakthroughs in recent years promise better control and novel applications aimed at resolving key issues in aerosol science. Here we propose graphene oxide (GO) aerosols as prototype aerosols containing polycyclic aromatic hydrocarbons, and GO can behave as two-dimensional surfactants which could modify the interfacial properties of aerosols. We describe the techniques of trapping single particles and furthermore the current status of the optical spectroscopy and chemistry of GO. The current applications of these single-particle trapping techniques are summarized and interesting future applications of GO aerosols are discussed.

Using Mie Scattering to Determine the Wavelength-Dependent Refractive Index of Polystyrene Beads with Changing Temperature

Polystyrene beads are often used as test particles in aerosol science. Here, a contact-less technique is reported for determining the refractive index of a solid aerosol particle as a function of wavelength and temperature (20-234 °C) simultaneously. Polystyrene beads with a diameter of 2 μm were optically trapped in air in the central orifice of a ceramic heating element, and Mie spectroscopy was used to determine the radius and refractive index (to precisions of 0.8 nm and 0.0014) of eight beads as a function of heating and cooling. Refractive index, n, as a function of wavelength, λ (0.480-0.650 μm), and temperature, T, in centigrade, was found to be n = 1.5753 - (1.7336 × 10^-4)T + (9.733 × 10^-3)λ^-2 in the temperature range 20 < T < 100 °C and n = 1.5877 - (2.9739 × 10^-4)T + (9.733 × 10^-3)λ^-2 in the temperature range 100 < T < 234 °C. The technique represents a step change in measuring the refractive index of materials across an extended range of temperature and wavelength in an absolute manner and with high precision.

Bessel Beam: Significance and Applications-A Progressive Review

Diffraction is a phenomenon related to the wave nature of light and arises when a propagating wave comes across an obstacle. Consequently, the wave can be transformed in amplitude or phase and diffraction occurs. Those parts of the wavefront avoiding an obstacle form a diffraction pattern after interfering with each other. In this review paper, we have discussed the topic of non-diffractive beams, explicitly Bessel beams. Such beams provide some resistance to diffraction and hence are hypothetically a phenomenal alternate to Gaussian beams in several circumstances. Several outstanding applications are coined to Bessel beams and have been employed in commercial applications. We have discussed several hot applications based on these magnificent beams such as optical trapping, material processing, free-space long-distance self-healing beams, optical coherence tomography, superresolution, sharp focusing, polarization transformation, increased depth of focus, birefringence detection based on astigmatic transformed BB and encryption in optical communication. According to our knowledge, each topic presented in this review is justifiably explained.

In Situ pH Measurements of Individual Levitated Microdroplets Using Aerosol Optical Tweezers

The pH of microscale reaction environments controls numerous physicochemical processes, requiring a real-time pH microprobe. We present highly accurate real-time pH measurements of microdroplets using aerosol optical tweezers (AOT) and analysis of the whispering gallery modes (WGMs) contained in the cavity-enhanced Raman spectra. Uncertainties ranging from ±0.03 to 0.06 in pH for picoliter droplets are obtained through averaging Raman frames acquired at 0.5 Hz over 3.3 min. The high accuracy in pH determination is achieved by combining two independent measurements uniquely provided by the AOT approach: the anion concentration ratio from the spontaneous Raman spectra, and the total solute concentration from the refractive index retrieved from WGM analysis of the stimulated cavity-enhanced Raman spectra. pH can be determined over a range of -0.36 to 0.76 using the aqueous sodium bisulfate system. This technique enables direct measurements of pH-dependent chemical and physical changes experienced by individual microparticles and exploration of the role of pH in the chemical behavior of confined microenvironments.

Investigation of gel formation and volatilization of acetate acid in magnesium acetate droplets by the optical tweezers

Hygroscopicity and volatility of single magnesium acetate (MgAc₂) aerosol particles at various relative humidities (RHs) are studied by a single-beam optical tweezers, and refractive indices (RIs) and morphology are characterized by cavity enhanced Raman spectroscopy. Gel formation and volatilization of acetate acid (HAc) in MgAc₂ droplets are observed. Due to the formation of amorphous gel structure, water transposition in droplets at RH < 50% is significantly impeded on a time scale of 140,000 s. Different phase transition at RH < 10% is proposed to explain the distinct water loss after the gel formation. To compare volatilization of HAc in different systems, MgAc₂ and sodium acetate (NaAc) droplets are maintained at several different stable RHs during up to 86,000 s. At RH ≈ 74%, magnesium hydroxide (Mg(OH)₂) inclusions are formed in MgAc₂ droplets due to the volatilization of HAc, and whispering gallery modes (WGMs) of MgAc₂ droplets in the Raman spectrum quench after 50,000 s. In sharp contrast, after 86,000 s at RH ≈ 70%, NaAc droplets are in well-mixed liquid states, containing soluble sodium hydroxide (NaOH). At this state, the RI of NaAc droplet is increased, and the quenching of WGMs is not observable.

Repartitioning of glycerol between levitated and surrounding deposited glycerol/NaNO3/H2O droplets

Repartitioning of semi-volatile organic compounds (SVOCs) between particles is an important process to understand the particle growth and shrinkage in the atmosphere environment. Here, by using optical tweezers coupled with cavity-enhanced Raman spectroscopy, we report the repartitioning of glycerol between a levitated glycerol/NaNO₃/H₂O droplet and surrounding glycerol/NaNO₃/H₂O droplets deposited on the inner wall of a chamber with different organic to inorganic molar ratios (OIRs). For the high OIR with 3 : 1, no NaNO₃ crystallization occurs both for levitated and deposited droplets in the whole relative humidity (RH) range, the radius of the levitated droplet decreases slowly due to the evaporation of glycerol from the levitated droplet at constant RHs. The levitated droplets radii with OIR of 1 : 1 and 1 : 3 increase with constant RHs that are lower than 45.3% and 55.7%, respectively, indicating that the repartitioning of glycerol occurs. The reason is that NaNO₃ in the deposited droplets is crystallized when RH is lower than 45.3% for 1 : 1 or 55.7% for 1 : 3. So the vapour pressure of glycerol at the surface of deposited droplets is higher than that of the levitated droplet which always remains as liquid droplet without NaNO₃ crystallization, resulting in the transfer of glycerol from the deposited ones to the levitated one. The process of the glycerol repartitioning we discussed herein is a useful model to interpret the repartitioning of SVOCs between the externally mixed particles with different phase states.

Emulsified and Liquid-Liquid Phase-Separated States of α-Pinene Secondary Organic Aerosol Determined Using Aerosol Optical Tweezers

We demonstrate the first capture and analysis of secondary organic aerosol (SOA) on a droplet suspended in an aerosol optical tweezers (AOT). We examine three initial chemical systems of aqueous NaCl, aqueous glycerol, and squalane at ∼75% relative humidity. For each system we added α-pinene SOA-generated directly in the AOT chamber-to the trapped droplet. The resulting morphology was always observed to be a core of the original droplet phase surrounded by a shell of the added SOA. We also observed a stable emulsion of SOA particles when added to an aqueous NaCl core phase, in addition to the shell of SOA. The persistence of the emulsified SOA particles suspended in the aqueous core suggests that this metastable state may persist for a significant fraction of the aerosol lifecycle for mixed SOA/aqueous particle systems. We conclude that the α-pinene SOA shell creates no major diffusion limitations for water, glycerol, and squalane core phases under humid conditions. These experimental results support the current prompt-partitioning framework used to describe organic aerosol in most atmospheric chemical transport models and highlight the prominence of core-shell morphologies for SOA on a range of core chemical phases.

Dynamic measurements and simulations of airborne picolitre-droplet coalescence in holographic optical tweezers

We report studies of the coalescence of pairs of picolitre aerosol droplets manipulated with holographic optical tweezers, probing the shape relaxation dynamics following coalescence by simultaneously monitoring the intensity of elastic backscattered light (EBL) from the trapping laser beam (time resolution on the order of 100 ns) while recording high frame rate camera images (time resolution <10 μs). The goals of this work are to: resolve the dynamics of droplet coalescence in holographic optical traps; assign the origin of key features in the time-dependent EBL intensity; and validate the use of the EBL alone to precisely determine droplet surface tension and viscosity. For low viscosity droplets, two sequential processes are evident: binary coalescence first results from the overlap of the optical traps on the time scale of microseconds followed by the recapture of the composite droplet in an optical trap on the time scale of milliseconds. As droplet viscosity increases, the relaxation in droplet shape eventually occurs on the same time scale as recapture, resulting in a convoluted evolution of the EBL intensity that inhibits quantitative determination of the relaxation time scale. Droplet coalescence was simulated using a computational framework to validate both experimental approaches. The results indicate that time-dependent monitoring of droplet shape from the EBL intensity allows for robust determination of properties such as surface tension and viscosity. Finally, the potential of high frame rate imaging to examine the coalescence of dissimilar viscosity droplets is discussed.

Characterising the evaporation kinetics of water and semi-volatile organic compounds from viscous multicomponent organic aerosol particles

Here we present methods to simultaneously investigate diffusivities and volatilities in studies of evolving single aerosol particle size and composition.

Development of a Tandem Electrodynamic Trap Apparatus for Merging Charged Droplets and Spectroscopic Characterization of Resultant Dried Particles

Materials work in multicomponent forms. A wide range of compositions must be tested to obtain the optimum composition for a specific application. We propose optimization using a series of small levitated single particles. We describe a tandem-trap apparatus for merging liquid droplets and analyzing the merged droplets and/or dried particles that are produced from the merged droplets under levitation conditions. Droplet merging was confirmed by Raman spectroscopic studies of the levitated particles. The tandem-trap apparatus enables the synthesis of a particle and spectroscopic investigation of its properties. This provides a basis for future investigation of the properties of levitated single particles.

Raman Spectroscopy of Optically Trapped Single Biological Micro-Particles

The combination of optical trapping with Raman spectroscopy provides a powerful method for the study, characterization, and identification of biological micro-particles. In essence, optical trapping helps to overcome the limitation imposed by the relative inefficiency of the Raman scattering process. This allows Raman spectroscopy to be applied to individual biological particles in air and in liquid, providing the potential for particle identification with high specificity, longitudinal studies of changes in particle composition, and characterization of the heterogeneity of individual particles in a population. In this review, we introduce the techniques used to integrate Raman spectroscopy with optical trapping in order to study individual biological particles in liquid and air. We then provide an overview of some of the most promising applications of this technique, highlighting the unique types of measurements enabled by the combination of Raman spectroscopy with optical trapping. Finally, we present a brief discussion of future research directions in the field.

Optical trap for both transparent and absorbing particles in air using a single shaped laser beam

Optical trapping of airborne particles is emerging as an essential tool in applications ranging from online characterization of living cells and aerosols to particle transport and delivery. However, existing optical trapping techniques using a single laser beam can trap only transparent particles (via the radiative pressure force) or absorbing particles (via the photophoretic force), but not particles of either type-limiting the utility of trapping-enabled aerosol characterization techniques. Here, we present the first optical trapping technique capable of trapping both transparent and absorbing particles with arbitrary morphology using a single shaped laser beam. Such a general-purpose optical trapping mechanism could enable new applications such as trapping-enabled aerosol characterization with high specificity.

Slow water transport in MgSO4 aerosol droplets at gel-forming relative humidities

The effect of gel formation on water transport in MgSO₄ aerosol droplets is investigated by deriving apparent diffusion coefficients of water.

Photophoretic trapping of multiple particles in tapered-ring optical field

We demonstrate the photophoretic trapping of more than several hundreds of absorbing particles by tapered-ring optical traps diffracted from a circular aperture. The experiments with different laser powers show the influence of air flow acting on particles. Three kinds of particles with different densities (about 1~7 g/cm(3)) and different shapes (spherical, non-spherical) can be trapped. The non-spherical particles (toner particles) disperse in optical field, while the spherical particles (ink droplets and iron particles) arrange as a straight line. More importantly, in the experiments of two counter-propagating tapered-ring beams, the agglomeration of particles is achieved and can help research the dynamics of aerosols.

Probing the micro-rheological properties of aerosol particles using optical tweezers

The use of optical trapping techniques to manipulate probe particles for performing micro-rheological measurements on a surrounding fluid is well-established. Here, we review recent advances made in the use of optical trapping to probe the rheological properties of trapped particles themselves. In particular, we review observations of the continuous transition from liquid to solid-like viscosity of sub-picolitre supersaturated solution aerosol droplets using optical trapping techniques. Direct measurements of the viscosity of the particle bulk are derived from the damped oscillations in shape following coalescence of two particles, a consequence of the interplay between viscous and surface forces and the capillary driven relaxation of the approximately spheroidal composite particle. Holographic optical tweezers provide a facile method for the manipulation of arrays of particles allowing coalescence to be controllably induced between two micron-sized aerosol particles. The optical forces, while sufficiently strong to confine the composite particle, are several orders of magnitude weaker than the capillary forces driving relaxation. Light, elastically back-scattered by the particle, is recorded with sub-100 ns resolution allowing measurements of fast relaxation (low viscosity) dynamics, while the brightfield image can be used to monitor the shape relaxation extending to times in excess of 1000 s. For the slowest relaxation dynamics studied (particles with the highest viscosity) the presence and line shape of whispering gallery modes in the cavity enhanced Raman spectrum can be used to infer the relaxation time while serving the dual purpose of allowing the droplet size and refractive index to be measured with accuracies of ±0.025% and ±0.1%, respectively. The time constant for the damped relaxation can be used to infer the bulk viscosity, spanning from the dilute solution limit to a value approaching that of a glass, typically considered to be >10(12) Pa s, whilst the frequencies of the normal modes of the oscillations of the particle can be used to infer surface properties. We will review the use of optical tweezers for studying the viscosity of aerosol particles and discuss the potential use of this micro-rheological tool for probing the fundamental concepts of phase, thermodynamic equilibrium and metastability.

Manipulation of aerosols revolving in taper-ring optical traps

We designed taper-ring optical traps by a weakly focused laser beam through a circular aperture. By railing-like potential barriers, these optical traps are partitioned into enclosed rings, in which irregular light-absorbing microparticles can be driven by photophoretic force to revolve around optical axis in air. The diameter of revolution can reach about 700 μm, which is much larger than that in traditional optical traps based on radiation pressure and gradient force. More importantly, multiple particles were driven to revolve simultaneously in different planes in air for the first reported time to the best of our knowledge.

Measurement of Raman spectra of single airborne absorbing particles trapped by a single laser beam

We demonstrate a method for optical trapping and Raman spectroscopy of micron-sized, airborne absorbing particles using a single focused laser beam. A single Gaussian beam at 532 nm is used to trap and precisely manipulate absorbing airborne particles. The fluctuation of the position of the trapped particles is substantially reduced by controlling the power of the laser beam with a position-sensitive detector and a locking circuit. Raman spectra of the position-stabilized particles or clusters are then measured with an objective and CCD spectrograph.

Comparing the mechanism of water condensation and evaporation in glassy aerosol

Atmospheric models generally assume that aerosol particles are in equilibrium with the surrounding gas phase. However, recent observations that secondary organic aerosols can exist in a glassy state have highlighted the need to more fully understand the kinetic limitations that may control water partitioning in ambient particles. Here, we explore the influence of slow water diffusion in the condensed aerosol phase on the rates of both condensation and evaporation, demonstrating that significant inhibition in mass transfer occurs for ultraviscous aerosol, not just for glassy aerosol. Using coarse mode (3-4 um radius) ternary sucrose/sodium chloride/aqueous droplets as a proxy for multicomponent ambient aerosol, we demonstrate that the timescale for particle equilibration correlates with bulk viscosity and can be ≫10(3) s. Extrapolation of these timescales to particle sizes in the accumulation mode (e.g., approximately 100 nm) by applying the Stokes-Einstein equation suggests that the kinetic limitations imposed on mass transfer of water by slow bulk phase diffusion must be more fully investigated for atmospheric aerosol. Measurements have been made on particles covering a range in dynamic viscosity from < 0.1 to > 10(13) Pa s. We also retrieve the radial inhomogeneities apparent in particle composition during condensation and evaporation and contrast the dynamics of slow dissolution of a viscous core into a labile shell during condensation with the slow percolation of water during evaporation through a more homogeneous viscous particle bulk.

Photophoretic trapping of absorbing particles in air and measurement of their single-particle Raman spectra

A new method is demonstrated for optically trapping micron-sized absorbing particles in air and obtaining their single-particle Raman spectra. A 488-nm Gaussian beam from an Argon ion laser is transformed by conical lenses (axicons) and other optics into two counter-propagating hollow beams, which are then focused tightly to form hollow conical beams near the trapping region. The combination of the two coaxial conical beams, with focal points shifted relative to each other along the axis of the beams, generates a low-light-intensity biconical region totally enclosed by the high-intensity light at the surface of the bicone, which is a type of bottle beam. Particles within this region are trapped by the photophoretic forces that push particles toward the low-intensity center of this region. Raman spectra from individual trapped particles made from carbon nanotubes are measured. This trapping technique could lead to the development of an on-line real-time single-particle Raman spectrometer for characterization of absorbing aerosol particles.

Towards an integrated optical single aerosol particle lab

We present a manipulation and characterization system for single airborne particles which is integrated onto a microscope slide. Trapped particles are manipulated by means of radiation pressure and characterized by cavity enhanced Raman spectroscopy. Optical fibers are used to deliver the trapping laser light as well as to collect the Raman scattered light, allowing for a flexible usage of the device. The system features a sample chamber which is separated from an aerosol-flooded injection chamber by means of a light guiding glass-capillary. The coupling of this device with an aerosol optical tweezers setup to selectively load its trapping sites is demonstrated. Finally, a route towards chip-integrated handling and processing of multiple particles is shown and the first results are presented.

Spectroscopic characterization of aqueous microdroplets containing inorganic salts

We have developed and studied methods to characterize the time-varying composition of liquid microdroplets, under controlled changes to environmental conditions, using Raman tweezers. This work has focussed on measurements of inorganic salts, such as nitrate and sulfate anions, which comprise a major fraction of the dissolved solutes in atmospheric aerosols. The experimental Raman intensities for the anions of inorganic salts in optically tweezed droplets were found to be in good agreement with theoretical estimates of photon scattering. The detection limit for sodium nitrate salt in a single particle was found to be ~4 pg. The mass of an inorganic salt in the droplet can be estimated from the Raman intensity of the anion bands using a calibration curve which is independent of droplet volume. The volume of the droplet, and concentration of solute, can be found directly from the spacing of morphology dependent resonances in the Raman band of water, or indirectly from the integrated-intensity of the Raman band for the solvent. The later strategy eliminates the uncertainty in the collection efficiency of Raman-scattered light related to varying particle sizes.

On-the-fly cross flow laser guided separation of aerosol particles based on size, refractive index and density-theoretical analysis

Laser separation of particles is achieved using forces resulting from the momentum exchange between particles and photons constituting the laser radiation. Particles can experience different optical forces depending on their size and/or optical properties, such as refractive index. Thus, particles can move at different speeds in the presence of an optical force, leading to spatial separations. In this paper, we present a theoretical analysis on laser separation of non-absorbing aerosol particles moving at speeds (1-10 cm/sec) which are several orders of magnitude greater than typical particle speeds used in previous studies in liquid medium. The calculations are presented for particle deflection by a loosely focused Gaussian 1064 nm laser, which simultaneously holds and deflects particles entrained in flow perpendicular to their direction of travel. The gradient force holds the particles against the viscous drag for a short period of time. The scattering force simultaneously pushes the particles, perpendicular to the flow, during this period. Our calculations show particle deflections of over 2500 µm for 15 µm aerosol particles, and a separation of over 1500 µm between 5 µm and 10 µm particles when the laser is operated at 10 W. We show that a separation of about 421 µm can be achieved between two particles of the same size (10 µm) but having a refractive index difference of 0.1. Density based separations are also possible. Two 10 µm particles with a density difference of 600 kg/m3 can be separated by 193 µm. Examples are shown for separation distances between polystyrene, poly(methylmethacrylate), silica and water particles. These large laser guided deflections represent a novel achievement for optical separation in the gas phase.

Giant optical manipulation

We demonstrate a new principle of optical trapping and manipulation increasing more than 1000 times the manipulation distance by harnessing strong thermal forces while suppressing their stochastic nature with optical vortex beams. Our approach expands optical manipulation of particles into a gas media and provides a full control over trapped particles, including the optical transport and pinpoint positioning of ∼100  μm objects over a meter-scale distance with ±10  μm accuracy.

Selective trapping of multiple particles by volume speckle field

We suggest a new approach for selective trapping of light absorbing particles in gases by multiple optical bottle-beam-like traps created by volume speckle field. We demonstrate stable simultaneous confinement of a few thousand micro-particles in air with a single lowpower laser beam. The size distribution of trapped particles exhibits a narrow peak near the average size of an optical speckle. Thus, the speckleformed traps act as a sieve with the holes selecting particles of a similar size.