3.1. Key parameters in polyelectrolyte multilayer fabrication
As noted above, a process to produce a tightly packed PS microsphere coating on a glass substrate first involves the layer-by-layer deposition of electrostatic polyelectrolytes. A key parameter for polyelectrolyte suspensions involving dissociated electrolytes is the Debye or screening length scale beyond which the effect of the electrostatic charge no longer contributes to the surface attachment, as the counter-ions cluster near opposing charged surfaces to effectively screen the charge of a charged surface or polymer. This Debye length is given by
for polyelectrolyte solutions without any added salt.
is Avagadro’s number,
is the Bjerrum length,
is the polyelectrolyte concentration, and ξ
is the linear charge density of the polyelectrolyte. The Bjerrum length parameter describes the length scale at which the thermal energy equals the electrostatic potential energy between two elementary charges and is given by
where e is the elementary charge, ε is the dielectric constant of the medium, k is the Boltzmann constant, and T is the absolute temperature. Significant charge separation can only occur when the distance between two opposite charges is greater than these length scales such that both electrostatic screening and thermal energy inhibit charge recombination. In the presence of salt in the polyelectrolyte solution, since the Debye length varies as follows:
are the valency and concentration, respectively, of the salt counter-ions and c
is the polymer concentration where the addition of salt decreases the Debye length due to enhanced screening from the additional charges.
Polyelectrolytes are generally more rigid than uncharged polymers due to the fact that the entropic driving force toward coiling and random chain conformations is inhibited by the intramolecular electrostatic repulsion of the charges along the chain backbone resulting in more correlated packing of the intermolecular polymer backbone. A measure of this rigidity is the persistence length
, i.e. the length over which correlations in the direction of the backbone (at a given starting point) are lost or an essential measure of how long it takes for the chain to turn around. This length scale is given by the characteristic ratio,
, and the bond length, L
From this, we can infer that the polyelectrolyte chain conformation becomes more rod-like or stiffer with a concomitant increase in the charge density along the chain. When the concentration of counter-ion in a polyelectrolyte solution is increased, counter-ion condensation effectively reduces the charge density along the backbone, resulting in the increase of the mean spacing, b
, between charges on the chain, then so does the Debye length according to the following equation and Eq. (1)
Since the Debye length is linearly correlated with the persistence length,
, it increases as well and results in a stretched chain at higher charge densities. When ξ
is unity, the charge spacing equals the Bjerrum length and the entropic driving force towards coiling equals the electrostatic driving force toward chain stretching. When charge density increases further, polyelectrolyte chain stretching predominates over coiling which may result in an uniformly spaced charge distribution and lesser extent of interdigitation with an oppositely charged polyelectrolyte chain. For our polymer-microsphere system, the NaCl salt concentration was varied to identify the optimal regime for maximal particle-substrate binding yet mitigate the extent by which screening salt counter-ions interfere with the subsequent electrostatic adsorption of PS microspheres to the PEM and the charge-density dependent stretching of the polyelectrolyte chain conformation.
3.2. PS particle binding and recovery in delaminated polymer construct
Prior to particle transfer and inclusion into the host polymer, we modified the glass substrate with PEMs to confer charged attachment sites for PS microsphere immobilization. Compared to a sedimentation control group where microspheres were physiosorbed onto the unmodified glass substrate yielding predominately disorganized three-dimensional particle aggregates, microspheres adsorbed onto a PEM-modified glass substrate yielded qualitatively better surface attachment, more uniform spacing, and more coplanar two-dimensional array of microspheres. As previously stated, NaCl salt concentration in our PEM solutions were modulated to further augment the electrostatic adsorption of PS microspheres by the mechanism of polyelectrolyte chain stretching and mitigation of the screening counter-ions to expose higher charge densities for particle adsorption. For illustration, a comparison of the 5 μm PS microsphere binding for the two polyelectrolyte solution salt concentrations (2.0 mol/L NaCl versus 1.0 mol/L NaCl) is shown in
Fig. 4 Brightfield optical images of PS microspheres. (A) 2.0 mol/L NaCl polyelectrolyte salt concentration at room temperature showed nonplanar sporadic clustering typified by bright microspheres with dark halo formation positioned at variable focal distances. (more ...)
Compared to its higher salt concentration counterpart, the 1.0 mol/L NaCl polyelectrolyte salt concentration samples exhibited a larger number of substrate-bound PS microspheres with the shorter interparticle spacing. On the other hand, stacked or nonplanar clustering of microspheres was evident in the 2.0 mol/L NaCl polyelectrolyte salt concentration samples. In , non-uniform absorption and sporadic clustering (indicated by bright and black halos off the focal plane) of microspheres may have been attributed to the coiling of the PEM chains in the presence of high salt counter-ions, thereby exposing non-uniform and relatively low charge density regimes available for inter-particle electrostatic binding.
After the viscous PDMS liquid was cast on the PS microsphere anchored PEM glass substrate and allowed to cure into an elastic solid, the cured elastomeric layer was delaminated to transfer the microspheres onto its surface. The transfer efficiency of microspheres to the elastomer for the three experimental conditions was quantified from images of different regions (n = 5) for particle counts on the PS-bound glass substrate followed by the transferred particle counts in the elastomeric construct. Particle counts were done from these images displayed by the ImageJ software. The fractional recovery of particles in the PDMS elastomeric construct after polymer casting, curing, and delamination for the two molar salt concentrations in were 0.93 ± 0.08 and 0.74 ± 0.18, respectively. The particle transfer yield was higher for the high polyelectrolyte salt concentration due to a decrement in the initial bonding of the microspheres to the PEM-modified glass substrate, thereby facilitating ease of transfer to the elastomer. The particle transfer yield was lower for the low polyelectrolyte salt concentration case where higher charge density on the substrate enhanced microsphere-glass substrate bonding, requiring higher delaminating threshold forces to increase the particle transfer. For the fabrication of an ideal phantom, both the number density of microspheres and the transfer efficiency must be maximized. The increased density of microspheres would be achieved by using 1.0 mol/L NaCl solution as shown in . However, at this lower salt concentration, the transfer rate was lowest due to higher initial binding affinity of microspheres to the substrate. To mitigate the electrostatic interaction between spheres and a PEM-modified glass subsrate prepared at 1.0 mol/L NaCl solution, the substrate was preheated prior to binding of spheres. To further decrease the interparticle spacing and to increase the yield of bound microspheres as well, the PEM-modified glass substrates were pre-heated to initiate convective particle flux into a densely packed monolayer. There was concern that the heating would affect the thermal energy dependent Bjerrum length (Eq. (2)
), and thereby reduce the affinity of the PS microspheres to the PEM-modified glass substrate. However, this did not prevent the relative monodispersity of packed microspheres. On the other hand, the initial binding of PS spheres onto the substrate was further increased as shown in . Furthermore, the transfer rate was increased to 0.83 ± 0.11, compared with the case without pre-heating, indicating a higher transfer rate than both cases without pre-heating. This implies that the electrostatic bonds were relaxed with the introduction of thermal energy.
In order to confirm 1.0 mol/L NaCl solution as the optimal molar salt concentration for particle transfer yield in the polymer, a parametric study was carried out for the following salt concentrations: 0.5 mol/L, 1.0 mol/L, 1.5 mol/L, 2.0 mol/L, 2.5 mol/L, and 3.0 mol/L. In
, for 2 μm particle monolayers, XZ-scanned confocal reflectance images of subjacent PS microspheres demonstrated highest density particle packing subjacent to the elastomeric surface for the 1.0 mol/L NaCl solution. As the molar salt concentration increases periodically from 1.0 mol/L to 3.0 mol/L, a concomitant decrease in particles adsorb onto the glass substrate as non-uniform and relatively low charge density regimes predominate due to polyelectrolyte chain coiling. An interesting inflection point occurs between 1.0 mol/L and 0.5 mol/L as further decrease in the salt concentration leads to failure of the constitutent polyelectrolyte chains to interdigitate with the opposing charged chains. This results in discontinuities in the buildup of the multilayer polyelectrolytes at the 0.5 mol/L molar salt concentration and decrease in adsorption particles and subsequent transfer of particles into the polymer as shown in .
XZ-scanned confocal reflectance images of 2 μm PS microspheres. Comparison of molar salt concentrations of polyelectrolyte solution and effect on particle transfer yield in polymer.
In all cases, a predominance of coplanar subjacent microspheres was observed.
3.3. Surface profile of PS microspheres within monolayer
For the fabrication of the ideal axial resolution target with particle embedded polymer layers, it is important to control the axial position of the microspheres relative to the layer interfaces. Since axial resolution is critical to quantifying OCT resolution, the PS particle layer should have minimal deviation in the axial direction. This would allow for the stacked layers of particles and PDMS to have well-defined placement regardless of measurement location. Therefore, to determine axial locations the microspheres, the transfer pattern of the microspheres to the surface of delaminated elastomer was investigated with high resolution surface profilometry.
In the ideal case (Case I), the particle layer should be completely buried within the PDMS matrix, with the top of the particle contacting the exposed surface. When imaged by surface profilometry, this case should exhibit little to no surface roughness. However, due to problems in the multilayer assembly process, particles could have different position defects. High resolution surface profilometry allows for the identification of four different particle transfer patterns with regard to relative axial positions of particles as these unique patterns are illustrated in
: (1) particles completely submerged in the polymer and subjacent to surface; (2) particles protruding from the surface with polymer coverage of microsphere; (3) particles protruding from surface with no polymer coverage of microsphere; and (4) sunken particles submerged in the polymer and protruding from surface.
Variants of microsphere axial distributions within polymer
Firstly, for Case I, particles were completely submerged in the elastomer with an axial position directly subjacent to the polymer surface as a result of the delamination force required to detach the elastomer from glass being tantamount to that required to exfoliate the relatively weak elastrostatically stabilized particles from the PEM layer. Next, in Case II, the slight peaks above the polymer surface represented particles protruding from the surface capped with a slight amount of PDMS on top. This resulted when the polymer was cast over the PS-attached PEM glass substrate and the uncured PDMS intercalated between the particle and glass substrate. This intercalation of PDMS was attributed to the presence of negligible electrostatic interactions between particle and PEM where the microspheres were effectively physiosorbed onto the glass substrate. In Case III, particle protrusions above the polymer surface were observed due to the smaller delamination force required to detach the elastomer from the glass substrate compared to that required to mechanically exfoliate the strong electrostatically stabilized particles from the PEM layer. The resultant partially embedded microspheres assumed a higher axial position relative to the polymer surface after trailing behind the polymer during the delamination step. These particles were represented in primarily as red areas with ring-like bases corresponding to particles projecting through the surface and the ring representing a contact edge for the PDMS and particle. Finally, in Case IV, due to surface tension effects, some particles were not completely submerged in PDMS, and we observed divots typified by a depressed halo surrounding a black hole as shown in
. For SWLI profilometry, regions of high curvature cannot be measured, so null data points are positions unresolvable by the measurement technique. Since particles on a PEM substrate were unresolvable on using SWLI profilometry, these voids were indicative of exposed particles. This is corroborated by , where particle aggregates were randomly dispersed on the transfer substrate. For aggregates, intercalation of PDMS prior to curing would be difficult, leading to incomplete wetting and defects as described in Case IV.
Fig. 7 Surface profilometry of PS-embedded elastomer constructs. Five constructs were fabricated for each experimental group with surface profile sampling at four randomly selected regions. Contour plots shown were 1.50 mm x 1.10 mm in size. Traces for the height (more ...)
To mitigate these effects, a slight modification in the PEM method was implemented with a two-fold decrement in the PEM salt concentration to 1.0 mol/L NaCl to mitigate the polyelectrolyte chain charge screening effect of the counter-ions. PS particles under these modified conditions where the PEM charges were exposed resulted in a greater extent of electrostatic interaction. Under these modified conditions, the PEM were arranged in more linear chains containing higher charge density, resulting in greater number of particles in the same axial plane available (i.e. fewer stacked aggregates) for transfer into the polymer. A comparison of the different salt concentrations no divots in the polymer for the lower concentration 1.0 mol/L NaCl case in –. The particle packing density was increased by heating the PEM-modified glass substrate prior to coating with the PS microspheres. This induced convection particle flux maintained the relative coplanar arrangement of the PS microspheres on the PEM-modified glass substrate while reducing the interparticle spacing. However, this application of heat likely had the adverse effect of altering the polyelectrolyte chain conformation to a more coiled state and thereby blunting the electrostatic bond between the PS and PEM-modified glass substrate. The result was the re-emergence of particles resembling that in Case II with slightly surface exposed particles with polymer coverage in and . These samples contain both ideal properties for an optical phantom, with the highest packing density () and minimal axial drift (≈0.1 µm) in comparison to other processing conditions.
3.4. Phantom bulk layer thickness validation
The layered phantom fabrication method as described in yielded four types of sample specifications: 10 μm nominal thick PS monolayers separated by a 10 μm thickness PDMS film, and, similarly, 5 μm PS nominal thick monolayers separated by a 5 μm thickness PDMS film, 3 μm PS monolayers separated by a 3 μm nominal PDMS film, and, similarly, 2 μm PS monolayers separated by a 2 μm nominal PDMS film. The intervening dark layer in the phantoms was measured using surface profilometry and the PS monolayers thickness was calculated using the PS microsphere manufacturer’s diameter specifications provided in tandem with axial deviations from the polymer surface measured using confocal microscopy. The mean ± standard deviation of the bright and dark phantom layer thicknesses for the 10 μm, 5 μm, 3 μm, and 2 μm PS microsphere embedded constructs were 10.0 μm ± 0.4 μm and 11.3 μm ± 0.3 μm, 4.8 μm ± 0.4 μm and 4.9 μm ± 0.3 μm, 3.2 μm ± 0.3 μm and 4.2 μm ± 0.3 μm, and 2.1 μm ± 0.2 μm and 3.1 μm ± 0.2 μm, respectively.
3.5. OCT imaging
OCT images of the phantom samples as shown in
were acquired with the OCT system configuration operating in the spectral domain (FDOCT). The 3 um and 2 um embedded particle monolayer phantoms are shown since the theoretical axial resolution limit could be addressed at these phantom dimensions. In , the axial distance in microns was calibrated from the 3 μm particle monolayer sample by taking the peak-to-peak axial pixel separation. This separation is defined by the center-to-center separation of the bead monolayers. This is determined by summing the radii of the beads in the monolayers and the intervening particle spacing. The monolayer thickness was determined by confocal microscopy to be 3.2 μm ± 0.3 μm. The interparticle spacing was independently verified by surface profilometry to be 4.2 μm ± 0.3 μm. The peak-to-peak separation of 7.4 μm ± 0.6 μm led to a calibration of the OCT B-scan image with 2.0 pixels/μm in the axial dimension. This calibration scale was then used to measure the interparticle spacing shown in . The OCT measured axial distance of 3.3 μm between two scattering monolayers in was in statistical agreement with the result, 3.1 μm ± 0.2 μm, validated independently by surface profilometry. Furthermore, the 3D OCT reconstruction illustrates uniform coverage of the particle monolayer in the field of view.
Fig. 8 6 mm x 6 mm wide rectangular OCT scan of multilayered phantom constructs with 100 linear B-scans at 1000 A-scans per B-scan for 3 μm and 2 μm scattering PS particles. The scattering and intervening transparent layer thicknesses were validated (more ...)
The theoretical axial resolution ROCT for these OCT imaging systems is given by the following relation:
represents the coherence length,
is the source center wavelength and
is the source bandwidth. Therefore, the FDOCT system operated at a center wavelength of 840 nm with 93 nm FWHM spectral bandwidth has a theoretical axial resolution of ≈3 μm.
The layered phantoms did not demonstrate any surface specular reflections, because the layers of interest were buried ≈1 mm beneath the top PDMS layer. The bright and dark layers of both layered phantoms with embedded 4.2 μm and 3.1 μm particles were resolvable by SDOCT. However, the layers of the 3.1 μm spaced sample were less resolvable, where the intervening dark layer between the particle monolayers approached the resolution limit. For both specifications, both the primary and secondary peaks were observable, but the intensity trough between the peaks in the 3.1 μm case was shallower as the spacing between the bright particle monolayers approached the theoretical axial resolution for the optical imaging system. Furthermore, significant index mismatch between the PS and PDMS polymers may present a challenging imaging condition, particularly at larger spatial frequencies as the stronger reflections at the boundaries of the microspheres may obscure the intervening transparent layer.