Diffusion in “correlation length ≥ probe” regime

In the previous section, diffusion of GNRs was considered in solutions in which the size of the GNRs far exceeded the correlation length ξ of polymers (∼7-8 nm). In such situations, the underlying complex network of polymers can be considered a continuum at the length scale of the GNRs, which is a necessary condition for the application of the GSER formalism. However, at low concentrations such that the polymer correlation lengthξis comparable to or larger than the size of the probes, GSER is no longer a valid tool to analyze the viscoelasticity of the polymer solutions. In this section, we briefly discuss the diffusion of GNRs when the polymer correlation length ξ is comparable to or larger than the size of GNRs.

To consider the diffusion of GNRs in the “correlation length≥probe” regime, PEGy-

lated GNRs (size: 83± 7 nm by 22±3 nm) were diffused in aqueous PEO4M solutions

with polymer concentrations of 0.01% (ξ= 472 nm), 0.045% (ξ= 152 nm), and 0.1%

(ξ= 85 nm), and imaged in M-mode. To put the diffusion of GNRs in these PEO4M

solutions in perspective with that in the solvent (distilled water), M-mode images were acquired from the solvent with diffused GNRs as well. All M-mode images were acquired at a sampling rate of 25 kHz with in overall observation time of 480 ms.

Figure 5.16 shows well-resolved g(1)_ISO(τ) between the solvent and the PEO4M solu- tions, and table 5.6 lists the corresponding τ1/e of g

(1)

ISO(τ) along with the measured DT

in the solvent and the PEO4M solutions in the “correlation length ≥ probe” regime.

A small yet distinct increase in τ1/e of g (1)

ISO(τ) is observed with an increase in PEO4M

concentration. In all samples, theDRvalues of the GNRs were too fast to resolve accu-

rately at the sampling rate of 25 kHz. In the “correlation length ≥ probe” regime, the GNRs in the PEO4M solutions are diffusing primarily in the solvent with intermittent hinderance from the PEO4M polymers. With an increase in the polymer concentra- tion, the diffusion of GNRs in the solvent is obstructed by the polymers at a higher

Figure 5.16: g_ISO(1) (τ) in PEO4M in the “correlation length ≥ probe” regime. The decay times are observed to increase with a change in concentration of PEO4M in the solutions.

PEO4M ξ τ1/e, 1/e decay of DT η/ηsolvent= η/ηsolvent

samples (nm) g(1)_ISO(τ) (ms) (µm2/s) τ1/e/τ1/e,solvent in bulk

0.01% 472 0.29 ±0.01 7.9 ± 0.4 1.06 ± 0.05 1.12 ± 0.05 0.045% 152 0.33 ±0.01 6.8 ± 0.3 1.20 ± 0.05 1.56 ± 0.07 0.1% 85 0.47 ±0.09 5.0 ± 0.8 1.7 ± 0.3 2.6 ± 0.1 Solvent 0.274 ±0.007 8.2 ± 0.2 1.00 1.00 Table 5.6: Measured τ1/e of g (1)

ISO(τ), and the DT of PEGylated GNRs (size: 83 ±7 nm

by 22±3 nm) in the solvent (distilled water) and PEO4M solutions in the “correlation length≥probe” regime. g(1)_HV(τ) andg(1)_ISO(τ) were evaluated from M-mode data sampled at 25 kHz with an overall observation time of 480 ms. Rotational diffusion fromg(1)_HV(τ) was too fast to resolve in all samples (i.e., Nyquist criterion not satisfied). Relative viscosity η/ηsolvent in the vicinity of the GNRs are estimated from τ1/e/τ1/e,solvent, and

the bulk viscosities were measured using an Ubbelohde viscometer.

rate, which is reflected by a decrease in measured DT of GNRs. Table 5.6 also lists

the relative viscosity η/ηsolvent in the vicinity of the GNRs and the bulk viscosity of the

are observed to be slightly larger than the local relative viscosities encountered by the GNRs in the PEO4M solutions. This result highlights the mechanistic difference in measurements of bulk viscosity, which is due to the collective relaxation of polymers in the solution, and the nanoscale local viscosity encountered by the diffusing GNRs in the “correlation length ≥ probe” regime of polymer solutions.

The result of this section shows that the diffusion of GNRs is indicative of intermit- tent obstructions from the polymers in the solution even in the “correlation length ≥

probe” regime. Thus, understanding obstructed diffusion of GNRs can be a valuable tool in studying biological fluids at the nanoscale that have low concentrations of macro- molecules (such as saliva, low concentration mucus etc), which are not characterized by microrheological methods based on GSER, nor by bulk rheology. Particle-tracking techniques are also capable of measuring diffusion of probes in such biological fluids. However, conventional particle-tracking involves using micron- and sub-micron- sized beads which don’t portray the same obstructed diffusion encountered at the nanoscale. Thus, having a light scattering based tool using ensembles of nanoscale probes, as the one developed in this thesis, can aid as an important supplemental tool in rheological studies of various complex and biological fluids.

To summarize, in this chapter, we validated the Stokes-Einstein relation by mea-

suring DR of GNRs in Newtonian fluids. Secondly, validation of the Stokes-Einstein

relation was extended to the measured DT of GNRs in Newtonian fluids. In Newtonian

fluids, both DR and DT of GNRs were observed to scale inversely proportionally with

the viscosity of the sample. Next, the diffusion of GNRs in various PEO solutions which exhibit viscoleastic responses was discussed. In semi-dilute PEO solutions, the viscous and elastic moduli of the solutions were quantified using the GSER formalism based on

the MSDs of the GNRs. Polymer solutions in the “correlation length ≥ probe” regime

the diffusion of GNRs in the solvent with intermittent hinderance from the polymer

segments. Diffusion of GNRs in the “correlation length ≥ probe” regime discussed in

this section thus sets the stage for exploring the diffusion of GNRs in biological samples such as extracellular matrix andin vitro mucus, which are discussed in the next chapter.

Chapter 6

Biological studies

This chapter focuses on biological studies using GNRs as diffusion probes in 3D tissue

culture models and also in in vitro mucus. Using the custom-built PS-OCT system to

exploit the polarization sensitive scattering property of GNRs, the ability of GNRs to contrast various biological features of interest is demonstrated. Lastly, an imaging study of breast cancer 3D cultures using the OCT system is discussed in detail.