Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions

Phase transitions in soft matter can change the scaffold structure, which has implications in the processing and final stability of the material^1,2,3. The characterization of soft materials during dynamic phase transitions provides essential information about the relationship between structural evolution and equilibrium structure and rheological properties. For example, many home care products require a phase change during consumer use. Also, during manufacturing, processing steps, including dilution and mixing, can impart shear affecting the rheological properties and final microstructure of the product. Understanding the rheological properties throughout a phase change ensures that the product performs as designed. Additionally, if forces alter the starting rheology of the material during manufacturing, phase transitions can yield unexpected and undesired results, changing the intended function and effectiveness.At the critical gelation point, defined as the point where the material transitions from a solution of associated colloids or polymers to a sample-spanning gel network, material properties change drastically with slight changes to association. Any modification to the structure at the critical gel point can impact the end product⁴. During these dynamic transitions, soft materials have weak mechanical properties and measurements that use classical experimental techniques can be within the measurement noise limit^5,6,7. To account for this, techniques such as microrheology, which is sensitive in the low moduli range (10^-3 – 4 Pa), are used to characterize the weak incipient gel during dynamic evolution. Some materials are susceptible to changes in microstructure due to external forces, which presents a challenge during characterization, as any transfer of material or fluid can affect the structure and, ultimately, the final material properties. To avoid altering the material microstructure, we have developed a microfluidic device that can exchange the environmental fluid around a sample while minimizing shear. By exchanging the fluid environment, changes in rheological properties and microstructure are measured during phase transitions with minimal contributions from shear. The device is combined with multiple particle tracking microrheology (MPT) in a technique called µ²rheology. This technique is used to quantify material properties during consecutive phase changes of a gel in response to an external driving force. The technique will be illustrated using a fibrous colloidal gel, hydrogenated castor oil (HCO)^9,10,11.

Gel scaffolds can undergo changes in association and dissociation due to their sample environment^12,13,14,15. The driving force for gelation and degradation are material specific and must be tailored for each material of interest. µ²rheology can be used to characterize gel systems that respond to external stimuli, including colloidal and polymeric networks. Altering pH, osmotic pressure or salt concentration are examples of driving forces that can induce changes in the material microstructure. For example, HCO undergoes controlled phase transitions by creating an osmotic pressure gradient. When a concentrated HCO gel sample (4 wt% HCO) is submerged in water, the attractive forces between colloidal particles weaken, causing degradation. Alternatively, when a dilute solution of HCO (0.125 wt% HCO) is contacted with a hydrophilic material (referred to as the gelling agent and composed of mostly glycerin and surfactant), the attractive forces return, causing gelation. This gel system will be used to show the operation of the device as a tool for measuring consecutive phase transitions on a single sample^9,10. To characterize these gel scaffolds during dynamic transitions and the delicate incipient gel structure at the critical phase transition, we use MPT to characterize these materials with high spatio-temporal resolution.

Microrheology is used to determine gel properties and structure, especially at the critical transition, of an array of soft materials, including colloidal and polymeric gels^5,6,9,16. MPT is a passive microrheological technique that uses video microscopy to record the Brownian motion of fluorescent probe particles embedded within a sample. The particle positions throughout the videos are precisely determined to within 1/10^th of a pixel using classical tracking algorithms^17,18. The ensemble averaged mean-squared displacement (MSD, (Δr²(t))) is calculated from these particle trajectories. The MSD is related to material properties, such as the creep compliance, using the Generalized Stokes-Einstein Relation^{17,19,20,21,22,23}. The state of the material is determined by calculating the logarithmic slope of the MSD curve as a function of lag time, α,

where t is the lag time, and comparing it to the critical relaxation exponent, n. n is determined using time-cure superposition, a well-documented technique that was modified to analyze MPT data by Larsen and Furst⁶. By comparison of n to α the state of the material is quantitatively determined. When α > n the material is a sol, and when α < n the material is a gel. Previous work has characterized the HCO system using microrheology to determine the critical relaxation exponent⁹. Using this information, we precisely determine when the material transitions from a gel to a sol during an experiment. Additionally, the non-Gaussian parameter, α_NG, can be calculated to determine the extent of structural heterogeneity of a system,

where Δx(t) is the one-dimensional particle movement in the x direction. Using MPT, we can characterize a single phase transition, but by characterizing materials with MPT in a microfluidic device, we are able to manipulate the surrounding fluid environment and collect data of several phase transitions on a single gel sample.

This microfluidic device is designed to investigate the critical transitions of a single gel sample that undergoes phase changes in response to changes in the surrounding fluid environment. The device exchanges fluid surrounding the sample when it is either in the gel or sol state by locking the sample in place to induce a phase transition while minimizing shear. A solvent basin is located directly above the sample chamber, which are connected by six symmetrically spaced inlet channels. This symmetry allows for the exchange of fluid from the solvent basin to the sample chamber while creating equal pressure around the sample, locking it in place. There have been several studies that use this technique for single particle and DNA trapping, but this work scales up the volume from single molecules to samples that are approximately 10 µL^24,25,26. This unique design also enables real-time microrheological characterization during phase transitions.

µ²rheology is a robust technique that is applicable to many soft matter systems. The technique described in this paper was designed for colloidal gels, but it can be easily adapted to other materials such as polymer or micellar solutions. With this technique, we determine not just how phase transitions affect the equilibrium material properties, but also how different processing steps can have lasting effects on the rheological evolution of the material and the final scaffold structure and properties.