Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures

Summary

Confocal microscopy is used to image quiescent and flowing colloid-polymer mixtures, which are studied as model systems for attractive suspensions. Image analysis algorithms are used to calculate structural and dynamic metrics for the colloidal particles that measure changes due to geometric confinement.

Abstract

The behavior of confined colloidal suspensions with attractive interparticle interactions is critical to the rational design of materials for directed assembly^1-3, drug delivery⁴, improved hydrocarbon recovery^5-7, and flowable electrodes for energy storage⁸. Suspensions containing fluorescent colloids and non-adsorbing polymers are appealing model systems, as the ratio of the polymer radius of gyration to the particle radius and concentration of polymer control the range and strength of the interparticle attraction, respectively. By tuning the polymer properties and the volume fraction of the colloids, colloid fluids, fluids of clusters, gels, crystals, and glasses can be obtained⁹. Confocal microscopy, a variant of fluorescence microscopy, allows an optically transparent and fluorescent sample to be imaged with high spatial and temporal resolution in three dimensions. In this technique, a small pinhole or slit blocks the emitted fluorescent light from regions of the sample that are outside the focal volume of the microscope optical system. As a result, only a thin section of the sample in the focal plane is imaged. This technique is particularly well suited to probe the structure and dynamics in dense colloidal suspensions at the single-particle scale: the particles are large enough to be resolved using visible light and diffuse slowly enough to be captured at typical scan speeds of commercial confocal systems¹⁰. Improvements in scan speeds and analysis algorithms have also enabled quantitative confocal imaging of flowing suspensions^11-16,37. In this paper, we demonstrate confocal microscopy experiments to probe the confined phase behavior and flow properties of colloid-polymer mixtures. We first prepare colloid-polymer mixtures that are density- and refractive-index matched. Next, we report a standard protocol for imaging quiescent dense colloid-polymer mixtures under varying confinement in thin wedge-shaped cells. Finally, we demonstrate a protocol for imaging colloid-polymer mixtures during microchannel flow.

Introduction

This paper demonstrates (a) confocal imaging of quiescent and flowing confined colloid-polymer mixtures in two and three dimensions and (b) particle-tracking and correlation analyses of the resultant images to obtain quantitative information on the phase behavior and flow properties.

Colloidal suspensions with attractive interparticle interactions appear ubiquitously in technological applications as materials for directed assembly^1-3, drug delivery⁴, improved hydrocarbon recovery^5-7, and energy storage⁸. A common feature of these applications is that the particles must be flowed through fine geometries, such as nozzles, print heads, microchannels, or porous media, and/or be shaped into thin films or rods. Techniques used to probe the structure of micron-sized colloids in confined geometries, including electron microscopy^17,18, x-ray microscopy¹⁹, and laser-diffraction microscopy²⁰, can be used to measure the structure and dynamics of particles on the microscale. These techniques, however, do not allow access to the trajectories of individual particles, from which structural and dynamic metrics can be computed for direct comparison to numerical simulations^21,22.

Confocal microscopy is a variant of fluorescence microscopy that enables imaging of thin sections of a fluorescent sample. For colloidal science¹⁰, this technique is particularly useful for imaging deep within dense suspensions or in three dimensions. Particle-tracking algorithms²³ applied to two- or three-dimensional time series of confocal micrographs yield the trajectories of all visible particles. As a result, the combination of confocal microscopy and particle-tracking has been applied to study the phase behavior, structure, and dynamics of colloidal suspensions, including ordered crystals^24-27 and disordered glasses^28-31 and gels^32-35.

Other image analysis algorithms can be applied to measure particle dynamics from time series of confocal micrographs. For example, diffusive particle dynamics can be studied by analyzing the fluctuations in intensity over time using confocal differential dynamic microscopy³⁶. When the particle displacements are larger than the interparticle spacing, image correlation³⁷ based on particle image velocimetry^38-40 can be applied to measure velocity profiles of the particles. The combination of tracking and correlation algorithms has allowed colloidal dynamics to be measured in systems undergoing slow and fast flow^11-16,41-45.

We use colloid-polymer mixtures as models for attractive colloidal suspensions⁹. In these mixtures, the range and strength of the attractive interparticle potential are controlled via the ratio of the polymer radius of gyration to the particle radius and the concentration of the polymer and the electrostatic repulsion is controlled via the addition of a monovalent organic salt⁴⁶. Because the interparticle interactions can be carefully tuned, the solidification of these mixtures has been extensively studied with confocal microscopy ^34,47-51.

Here we demonstrate confocal imaging and image analysis³⁷ of quiescent and flowing colloid-polymer mixtures, in which the colloid volume fraction is held fixed at Φ = 0.15, that probe the effect of confinement on the phase behavior and flow properties of these mixtures. These techniques are widely applicable to particulate systems that are refractive index-matched and in which the particles and/or solvent can be labeled with a fluorescent dye.

Protocol

1. Preparation of Colloid-polymer Mixtures

Note: This protocol uses poly(methyl methacrylate) (PMMA) particles, sterically stabilized using poly (12-hydroxystearic acid) and labeled with a fluorescent dye (such as Nile Red, rhodamine B, or fluorescein), that were synthesized following a standard recipe⁵².

1. Prepare a 3:1 w/w mixture of cyclohexyl bromide (CXB) and decahydronaphthalene (DHN) as a stock solvent. This mixture nearly matches the density and index of refraction of the particles. Add an organic salt, tetrabutylammonium chloride (TBAC)⁴⁶, to the solvent at a concentration of 1.5 mM to partially screen the charges on the particles.
2. To precisely determine the density of the particles, prepare a suspension at approximate particle volume fraction Φ = 0.10 in the CXB:DHN solvent. Centrifuge the suspension at 800 x g for 75 min and add CXB or DHN dropwise to improve the buoyancy matching. In these experiments, the density of the PMMA particles was measured to be ρ = 1.223 g/ml.
3. Prepare a concentrated stock suspension of PMMA particles (here, Φ = 0.40) in the CXB:DHN solvent mixture.
4. Prepare a concentrated solution of linear polystyrene (PS) in the CXB:DHN solvent mixture. Here, a solution of PS of molecular weight M_w ≈ 3,000,000 (radius of gyration r_g = 15 nm) is prepared at concentration c_p ≈ 50 mg/ml.
5. Mix appropriate weights of the particle, polymer, and solvent stock mixtures to formulate suspensions at the desired concentrations of particles and polymers.
   Note: Here, suspensions of monodispersed particles are prepared at constant colloid volume fraction Φ = 0.15 and variable polymer concentration in the free volume⁵³ c_p = 0–25 mg/ml, and bidispersed suspensions containing two sizes of colloidal particles, with each size bearing a distinct fluorescent label, are prepared at fixed total colloid volume fraction Φ = 0.15, volume fraction ratio of small particles r = 0.50, and polymer concentration in the free volume of 5 or 25 mg/ml.
6. After each suspension is prepared, add CXB or DHN dropwise and centrifuge the samples at 800 x g for at least 75 min to confirm that the particles and clusters within the suspension remain buoyancy matched.
7. Equilibrate all samples for at least 24 hr prior to imaging experiments.

2. Quiescent Sample Experiments: Phase Behavior

1. To determine the bulk phase behavior, fabricate rectangular chambers from glass coverslips (Figure 1a). For the colloid-polymer mixtures in this study, chambers of thickness h = 1 mm (set by the thickness of a microscope slide) give bulk behavior.
2. To access multiple confinements in a single microscopy experiment, fabricate thin wedge-shaped chambers, using a single coverslip as a spacer on one wedge (Figure 1b). The opening angle of the chamber is <0.5°, so that in a single field of view the walls are very nearly parallel. A representative chamber allows access to confinement thicknesses of h = 6 to >100 µm.
3. Build chambers on a coverslip base for imaging on an inverted microscope and seal with UV-curable epoxy, which does not dissolve in the CXB-DHN solvent mixture.
4. Image samples using a confocal microscope. This protocol demonstrates imaging with a line-scanning confocal attached to an inverted microscope equipped with a 100X oil immersion lens of numerical aperture NA = 1.40.
5. Excite the dyes using a laser source. Here wavelengths λ = 491 or 561 nm are used to excite the fluorescein and rhodamine/Nile Red dyes, respectively.
6. In the point-scanning system, generate an image by rapidly scanning the focal point across the sample (in the x-y plane) using the confocal software. A two-dimensional image of 512 pixels x 512 pixels, covering approximately 50 μm x 50 μm, can be acquired in 1/32 sec. Improve the image quality by averaging multiple images or increasing the acquisition time.
7. Locate the bottom of the chamber (z = 0), for example by focusing on particles adhered to its bottom. In this setup, the height (z) increases with increasing focus into the chamber.
8. As an example, characterize the effect of confinement on the dynamics of the particles by acquiring a 2-D time series of images (in the x-y plane) at the midplane of the chamber. In a typical experiment, 500 images of dimension 512 pixels x 512 pixels are acquired at a frame rate of 1 frame/sec (time spacing ∆t = 1 sec).
9. As a second example, characterize the 3-D structure of particles by acquiring a three-dimensional series of images (x,y,z). In a typical experiment, two-dimensional images (512 pixels x 512 pixels) are acquired at multiple z positions within the chamber, with a constant spacing of ∆z = 0.2 µm between consecutive images set by a piezo. A volume stack covering a thickness of h = 30 µm thus contains 151 images.
10. Locate and track particles over time in 2-D or 3-D using particle-tracking software written in IDL^23,54-56, MATLAB^57,58, LabView⁵⁹, or Python⁶⁰. These algorithms typically allow the centers of the particles to be resolved within 40–50 nm. Successful particle tracking requires that the particles move less than the interparticle spacing between consecutive frames.
11. From the particle positions, calculate structural and dynamic metrics. Three convenient metrics shown here are the 3-D pair correlation function g(r)⁶¹, the 2-D mean-squared displacement (MSD)^58,62, and the 2-D self part of the van Hove correlation function G_s(x,t)⁵⁸. The latter two metrics can be also calculated in 3-D.

3. Flowing Experiments: Flow Properties

1. Fabricate a simple flow cell using a glass microcapillary with square cross-section (100 μm x 100 μm) that is affixed to Teflon tubing. Use glass coverslips to support the capillary and provide mechanical rigidity, as shown in the schematic in Figure 7.
2. Load the colloid-polymer mixture into a glass syringe. Attach the syringe to a syringe pump or a pneumatic fluid dispensing system.
3. Mount the flow cell setup onto the inverted microscope. Keep the syringe, flow cell, and outlet at the same height to minimize the effect of gravity on the flow profile.
4. Control the flow rate of the suspension through the flow cell by the volumetric flow rate (for the syringe pump) or the applied pressure (for the pressure box). The average velocity of the suspension in the microchannel also depends upon the suspension formulation. Typical values of the maximum velocity in the square microchannel measured here are 200–2,000 μm/sec.
5. During flow, acquire a 2-D confocal time series at fast frame rates. Here, 500 images of dimension 512 pixels x 512 pixels are acquired at 32 frames/sec (time spacing Δt = 1/32 sec) at different heights above the bottom of the microchannel (z = 0 µm) ranging from z = 5–50 µm. Each image covers roughly half of the lateral dimension (y) of the microchannel, as shown in the inset to Figure 7. If the particles appear elliptical, increase the frame rate of acquisition.
6. As in quiescent experiments, locate the particles in 2-D using standard algorithms for locating and tracking particles in IDL or MATLAB. For slow flows, in which particles move less than the average interparticle distance between frames, use tracking algorithms to obtain the trajectories.
7. Use image correlation to calculate the velocity profiles for fast flows.
   1. Subdivide the image into horizontal images of constant height (y) along the direction of flow (x). For two sequential images I₁(x,y) and I₂(x,y) shift the latter image by a factor Δx and then calculate the cross-covariance between I₁(x,y) and I₂(x+Δx,y).
   2. Identify the peak position of the histogram of Δx values that maximize the cross-covariance between each pair of images to obtain the mean advection velocity at each lateral position y. If this distribution is not strongly peaked, acquire images at a faster frame rate.

Results

To demonstrate confocal imaging and particle-tracking, we investigated the effect of confinement on the phase behavior of colloid-polymer mixtures^63-65. For these experiments the colloid diameter was 2a = 0.865 μm. The colloid volume fraction was fixed at Φ = 0.15 and the concentration of polymer c_p was varied from 0 to 23.6 mg/ml. Representative confocal images are shown in Figure 2⁶³, left column. From the particle positions obtained using tr...

Discussion

Colloidal suspensions are widely studied as models for confined phase behavior, because micron-sized colloidal particles exhibit significantly slower dynamics than atoms and molecules and thus can be readily imaged and tracked over time¹⁰. For these fundamental studies, understanding the effect of interparticle attractions on confined phase behavior offers the opportunity to explore phenomena such as capillary condensation and evaporation^21,22,67. In addition, confined attractive suspensions appear ...

Materials

Name	Company	Catalog Number	Comments
Cyclohexyl bromide	Sigma Aldrich	135194	CAS Number  108-85-0, Molecular wt. = 163.06, Used in stock solvent
Decahydronapthalene	Sigma Aldrich	D251	CAS Number 91-17-8, Molecular wt. = 138.25, Used in stock solvent
Nile Red	Sigma Aldrich	72485	Fluorescent dye
Fluorescein 5(6)-isothiocyanate	Sigma Aldrich	F3651	Fluorescent dye
Rhodamine B	Sigma Aldrich	83689	Fluorescent dye
Dynamic Light Scattering	Brookhaven Instruments	BI-APD	DLS equipment used for particle size measurement
Polystyrene	Varian/Agilent	PL20138-23	Polystyrene (polymer) for inducing depletion attraction
Tetrabutyl(ammonium chloride) (TBAC)	Sigma Aldrich	86870	monovalent salt
UV Adhesive	Norland Adhesive	NOA 68T	Part Number 68T01 (UV cured adhesive)
VT Eye	Visitech	VT Eye	confocal scanner
VT Infinity	Visitech	VT Infinity	confocal scanner
Microscope	Leica	DMI3000B	Inverted Microscope
Centrifuge	Thermo Scientific	Sorvall ST 16	1-5,000 rpm
Teflon tubing	smallparts	SLTT 26-72	Zeus PTFE Sublite Wall Tubing 26 AWG 0.016" ID x 0.003" Wall
Epoxy	Devcon	DA051	5 min epoxy
Syringe	Micromate/Cadence	5004	glass syringe with metal luer lock tip
Syringe tips	Nordson	7018462	32 GA precision tips
Syringe pump	New Era Pump system Inc.	NE1002X	Programmable microfluidic pump (syringepump.com)
Weigh balance	Mettler Toledo	AB204-S	0.0001-220 g
PMMA particles	synthesized		poly(methylmethacrylate) colloidal particles