# PH Sensitive Hydrogel Valves - Sydney Foster

CHEM-ENG 535: Microfluidics and Microscale Analysis in Materials and Biology

# pH Sensitive Hydrogel Valves

Mechanical and electrical valving techniques rely on large amounts of power, complex physical configurations, and control algorithms to control fluid flow within microfluidic systems. Some electrical actuators generate excess heat which can negatively impact sensitive organics flowing through the actuators. The need for autonomous flow control, cold valving and easy to manufacture valves can be addressed with pH sensitive hydrogel actuated valves. The valves can either be used to directly control the flow of liquids in response to changes in fluid pH or can be controlled by separate flows of buffers which have the advantage of requiring to additional pressure work.

For the purposes of this page, the valve types will be categorized as direct valving and indirect valving. Indirect valving relies on operator pH control to actuate either normally closed (NC) or normally open (NO) valves and direct valving involves the complete autonomous control of a fluid flow through the swelling of the hydrogel within the stream being controlled, an action depenedent on flow pH.[1]

## Hydrogels

Hydrogels are complex crosslinked polymer networks which are characterized by hydrophilic functional groups arranged along long chain polymer backbones. These loosely cross linked masses can come in a variety of meta-structures (sponge-like, fibrous, planar, monolithic) and the degree to which they swell can be controlled via pH, and temperature. Hydrogels can be used in all parts of a microfluidic device, depending on their formulation and toughness, and the ability of some hydrogels to change size, shape or rigidity due to stimulus makes them useful for flow control and manipulation. This ability to respond to stimulus is what makes them such useful and versatile tools for microfluidic design.In dry conditions, hydrogels have no water within the polymer framework, however the ability to modify the amount of water attracted to the hydrophilic functional groups is what makes hydrogels great for pH sensitive valving. In neutral conditions the gels are more stiff than ion shielded counterparts due to the swollen nature of the gel. It is this that allows for the control of flow in pH sensitive valves.[2]

### Ionic Division

Hydrogels, whether anionic or cationic (acidic or basic) will dissociate in water or other aqueous solvents. This dissociation action allows for the functional group moieties to interact with each other. This interaction is commonly ionic repulsion, the electrostatic repulsion of similarly charged polar groups with tent or balloon the structure. This expansion of the structure in aqueous solvent increases the osmotic pressure gradient and water is drawn into the structure. This sum of these actions is called swelling. For proper buffer solutions, high concentrations of counter ions induce ionic shielding and allow the hydrogel to settle into a more favorable compressed state. This action is dependent on the charge of the functional groups in the hydrogel. The amount of water is normally limited by the degree of cross linking and the structure of the hydrogel.[7][2] Hydrogels with low cross linking and high porosity can hold free water, while highly cross linked gels are limited by the hydrogen bonding capacity of the polymer chain.

Cationic hydrogels swell when introduced to acidic environments and are commonly based off of amine functionalized polymers.[3] The ammonia groups gain an additional proton in low pH, allowing the structure to draw in solvent as it is forced to expand from ionic repulsion.

Anionic hydrogels contain negatively charged ions when dissociated (like carboxylic acid).[4] The anionic moieties repel each other in acidic conditions and become shielding in high pH.

### Structural Variants

#### Super Porous

Super Porous Hydrogels (SPHs) are hydrogels with micro scale pore structures spread throughout the mass. These hydrogels react quickly (5-20 seconds) and are highly absorbent due to capillary effects and the amount of free water that can be held within the pores, however they are not durable and do not block fluid flow effectively. The unique characteristics are created during cross linking, where pH conditions can be utilized along with additives, to generate a fine froth which will impart the large void spaces that make up the pores of the hydrogel mass. Because these hydrogels are not durable and can be very easy to permanently deform under relatively low levels of stress, they are not frequently used in valving set ups.[5][6]

 Cryo SEM of poly(methacrylic acid-co-acrylamide) [6] Cryo SEM of poly(acrylamide-co-acrylic acid) while full swollen(scale 1.0 mm) [5]

#### Monolithic

These hydrogels are synthesized via standard sol-gel conditions, in solution, and can be poured or spin coated. Due to the lack of pores or distinguishable subdivisions, these hydrogel structures can be very slow to react to stimulus, as they rely on Fickian Diffusion.[4] Their physical durability is what makes these hydrogels useful, the tough and defined mass allows for high definition channels and repeated usability. The largest downside to their use is the very long time needed for complete diffusion, which makes them good for non microfluidic devices, like contact lenses.

#### Fibrous

A new form of hydrogel, these polymer structures are composed of micrometer scale fibers of hydrogel, which can be layered or made into entanglements. Commonly, planar expansion occurs rapidly (<5 seconds) while swelling throughout the mass acts more slowly (1-3 minutes).[4] Very little work has been done on using these hydrogels in valves, but their unique swelling character over short periods of time have potential.

SEM image of crosslinked PAA hydrogel fibers [4]

## Swelling

The mechanism for swelling has been extensively examined by material scientists and chemists alike, and the ratio of swell, from wet to dry is often used to characterize the degree to which a gel swells in a buffered solution. There is high variability in characterizing swelling but the ratio is usually respresentative of the ratio between swollen and dry states. Some more complex ratios take into account solvent-polymer interactions and densities. The consensus is that the ratio should be clearly defined whenever used and the right ratio should be derived to best suit the needs of comparison.

Swell ratios can be mass based:

$\displaystyle{ Q=\frac{w_s}{w_d} }$

• ws is the weight of the swollen gel
• wd is the weight of the dry gel

$\displaystyle{ Q=\frac{M_s-M_d}{M_d} }$ [6]

• Ms is the mass of the swollen gel
• Md is the mass of the dry gel

$\displaystyle{ Q=1+(\frac{w_s}{w_d}-1)\frac{\rho_p}{\rho_w} }$ [7]

• ρ is the density of the polymer or water, respectively

Or the ratio can be a relation of volumes:

$\displaystyle{ q=\frac{V_s}{V_d} }$[1]

• Vs is the volume of the swollen gel
• Vd is the volume of the dry gel

$\displaystyle{ q^{5/3} = \frac{(1/2-\chi)2M_c}{V_1\rho_0\nu^{2/3}(1-3M_c/M_n)} }$ [4]

• q is the volume swelling ratio
• χ is the interaction parameter between polymer and solvent
• V1 is the molar volume of the liquid
• ρ0 is the density of the dry polymer
• n is the volume fraction of the polymer after cross-linking
• Mc is the molecular weight of the segment between crosslinking junctions
• Mn is the molecular weight of polymer chain before cross-linking.

## Valve Types

### Direct Valving

Three hydrogel rings are placed upon pillars of PDMS inside the flow channel
Once pH has been suitably changed, the hydrogel swells, restricting the flow in the channel

Direct valving relies upon the responsive swelling of hydrogels placed in the desired stream to be controlled. These valves act as passive flow controllers, reacting to the changing pH in the subject stream and either swelling or shrinking. These types of valves commonly come as multiple pillars arranged in-line, perpendicular to the flow of the stream.[8] This valve set up is not commonly used because it relies on the speed at which the hydrogel responds to pH. This is usually on the order of hours to even days, depending on the thickness of the gel used. The largest benefit of this valve is the ability to have total autonomous and effortless control of fluid flow past the valve. The geometries of the hydrogel are highly customizable and optimization modeling has been thoroughly explored, allowing for effective bespoke valve design.[9][2]

### Indirect Valving

Indirect hydrogel valve: green fluid is used to control swell of hydrogel(pink) and blue fluid is the flow being controlled by the valve.Case A is the valve open, Case B is the valve closed.
Indirect valving is dependent on a controlled flow of specified pH.[10] Hydrogel pads are placed above points of restriction in a microfluidic device, entrapped, and their swelling action acts to push more durable and less permeable membranes to restrict flow across the valve.[1] The valves are almost always designed as NO type valves, unless the hydrogel is bonded to a NC valve while swollen.[3]

# References

1. Park, J.Y., et al. “A polymeric microfluidic valve employing a pH-responsive hydrogel microsphere as an actuating source”. J. Micromech. Microeng. 2006, 16. 656–663 [1]
2. Arbabi, N., et al. “Study on pH-sensitive hydrogel micro-valves: A fluid–structure interaction approach”. J. Int. Mater. Sys. Struct. 2016, 1-14 [2]
3. Mahdavinia, G.R. , et al. “Modified chitosan 4. Superabsorbent hydrogels from poly(acrylic acid-co-acrylamide) grafted chitosan with salt- and pH-responsiveness properties”. Eu. Poly. J. 2004, 40, 1399-1407 [3]
4. Jin, X., et al. “pH-responsive swelling behavior of poly(vinyl alcohol)/poly(acrylic acid) bi-component fibrous hydrogel membranes”. Poly. 2005, 46, 5149-5160 [4]
5. Gemeinhart, R., et al. “pH-sensitivity of fast responsive superporous hydrogels”. J. Biomater. Sci. Poly. 2000, 11, 1371-1380
6. Gupta, N.V., et al. “Investigation of Swelling Behavior and Mechanical Properties of a pH-Sensitive Superporous Hydrogel Composite”. Iranian Journal of Pharmaceutical Research (2012), 11, 481-493 [5]
7. Jeannine, E., et al. “Structure and swelling of poly(acrylic acid) hydrogels: effect of pH, ionic strength, and dilution on the crosslinked polymer structure”. Poly. 2004, 45, 1503-1510 [6]
8. He, T., et al. “Modeling deformation and contacts of pH sensitive hydrogels for microfluidic flow control”. Soft Matter, 2012, 8, 3083 [7]
9. Zhang, Y, et al. “pH-Sensitive Hydrogel for Micro-Fluidic Valve”. J. Funct. Biomater. 2012, 3, 464-479 [8]
10. Ayala, V.C., et al. “Design, Construction and Testing of a Monolithic pH Sensitive Hydrogel-Valve for Biochemical and Medical Application”. Journal of Physics: Conference Series 2007, 90 [9]