# UserMichaelPetralia

I am working on soft mechanical systems at the Harvard Microrobotics Laboratory. My research focuses on creating changes in stiffness and damping properties, macroscopic motion, and force generation using 'soft' materials. The buzz word is artificial muscles, but the scope is much broader. I'm thinking about how we can create compliant devices that out perform the typical 'hard' systems engineers usually design.

## Fun facts on soft matter

Typically, we think of changing the degree/type of cross-linking in order to change the mechanical properties of a polymer. Lengthening of a polymer is accomplished by aligning the polymer chains. It seems that there are polymers where the monomer-monomer interactions are not covalently bonded and thus the lengths of the polymer chains themselves can change.

“. . . in other long-chain objects the subunits are joined not by covalent bonds, but by physical ones.
Examples of this are the giant worm-like micelles formed in some amphiphile solutions, and the long
chains of compact protein molecules which constitute, for example, actin ﬁlaments. Such objects are
sometimes called ‘living polymers’; their characteristic is that they can change their length in response
to changes in the environment. This contrasts with the more usual covalently linked polymers, in which
the length of the molecules, or the distribution of lengths, is ﬁxed during the polymerization process.”
page 73, Jones Soft Condensed Matter


Additionally, we do not need to be so rigid in our thoughts on cross-linking.

“Linear polymers may be connected by physical, rather than chemical, bonds, giving a thermoreversible
gel such as a gelatin. ”
page 95, Jones Soft Condensed Matter

"...the crosslinks need not be produced by chemical reaction.  Any physical process that favors
association between certain (but not all) points on different chains may also lead to gels."
page 133, de Gennes  Scaling Concepts in Polymer Physics


## Polymer Gels

### Introduction

One 'soft' actuation technology I'm looking into are polymer gels. Gels are materials that ﬁt somewhere between a solid and a liquid, consisting of a polymer network swollen with an interstitial ﬂuid. The properties of the gel are deﬁned by the polymer network, the interstitial ﬂuid, and the interaction between them.

Jones tells us

“A gel is a material composed of subunits that are able to bond with each other in such a way that one
obtains a network of macroscopic dimensions, in which all the subunits are connected by bonds. If one
starts out with isolated subunits and successively adds bonds, one goes from a liquid (a sol) to a material
with a non-zero shear modulus (a gel). A gel has the mechanical properties characteristic of a solid, even
though it is structurally disordered and indeed may contain a high volume fraction of liquid solvent.”
page 95,  Jones Soft Condensed Matter [3]


All gels process the unique ability to undergo abrupt changes in volume, often as a result of small changes in external conditions such as temperature, pH, electric ﬁelds, and solvent and ionic composition [1]. This phase change is a result of a shift in which forces dominate (entropic, attractive, repulsive).

There is some criticism in the soft robotics community about the usefulness of polymer gels for artificial muscle type technology. A recent review article by Madden intentionally omitted their consideration. [2] Madden claimed that the response time is typically slow (anywhere from seconds to minutes--I've seen it as short as fraction of a second and as long as weeks) and they are relatively weak (~100 kPa--I'm assuming he means this is the tensile stress). Despite these short comings, I believe they still have merit because of the breadth of stimuli that can be used to activate them (light, heat, pH, electric and magnetic fields, ionic strength) and the control we have over their swelling properties. What I lack is a good understanding of the physics and chemistry at work in polymer gels necessary to judge whether this technology is worth investigating.

So I picked up de Gennes classic Scaling Concepts in Polymer Physics to see if I could learn a few things.

### The polymer gel network

de Gennes has us think about the gel as a frozen system, very similar to glasses. In such a system we need two types of statistical information [4]:

• The situation at the moment of preparation (preparative ensemble)
• The situation at the moment of study (final ensemble)

The conditions under which a gel was formed will determine the microscopic structure of the gel. We should exploit this to great materials with the macroscopic properties we desire. As an example, segregation between polymer chains and a poor solvent will not happen quickly enough (because the polymer is already somewhat gelled) to be macroscopic. The phase separation manifests itself in separate microscopic pockets of solvent and polymers. [4] By controlling the solvent we use, it seems reasonable that we would have some control over the size and frequency of the pockets. Besides the mechanical response, this would help use control the swelling properties of the gel.

In gels which are chemically crosslinked, there is a threshold of the number of crosslinks, $p_c$, at which the polymer network is connected throughout the material. [4] We define $p$ as the fraction of reacted bonds and $\Delta p$ as some small fraction compared to $p_c$. Percolation theory will be used to understand the behavior of gels around the gelation threshold, $p_c$. Though the gel fraction ($S_\infty$, the fraction of monomers belonging to the infinite polymer network) increases rapidly with $\Delta p$, the elastic modulus of the gel ($E$) increases much more slowly.

$S_\infty \simeq \Delta p^\beta$ where $\beta = 0.39 \;$

$E \simeq \Delta p^t$ where $t \sim 1.7 \;\text{to}\; 1.9$ for three dimensions.

### Making interesting gel structures

The change in physical shape of polymer gels is dominated by diffusion, and over long time scales will be isotropic. In order to create useful motions, it is likely that the gels will be placed in systems which constrain part of their volume expansion, or geometries which will create anisotropic swelling over short time scales. Such macroscopic solutions will work, but efficiency or functionality will suffer. In systems where part of the volume expansion is constrained, the gel will have to exert energy to bend the substrate. In exploiting different diffusive time scales, we lose a level of control and we limit the length of time we can use the device.

Microscopic solutions may be more appropriate. By controlling the conformation of the polymer chains while they are cross-linking, we should be able to create gels with the mechanical properties we desire. de Gennes suggests that we incorporate polymer chains in various liquid crystalline systems, using them as a mold of sorts (e.g. incorporating hydrophillic polymers in the water layer of a lamellar phase of a lipid/water solution, cross-linking the chains, and washing out the lipid). [4]

de Gennes also mentions the hysteresis associated with the 'melting' and solidification of gelatin (1.5%)/water solutions [4]: At high temperatures the solution is a liquid (simple solution of chains, sol). Upon cooling, the solution gels. Raising the temperature again, the sol is recovered, but temperature at which this happens is higher than the temperature necessary for gelation. Hysteresis robs us of energy and thus decreases efficiency, but the ability to create a gel which is stable over a large temperature range and can reversibly transition between liquid and gel, has potential in soft robotic systems. This system is physically crosslinked, so we must be aware of the limitations. For gels formed with a physical process (i.e. weakly crosslinked), the crosslinks will eventually split under weak stress and the long-time behavior will always be liquid-like. [4]

It is possible to create block copolymers, let's say BAB, and place them in a solve good for A but not for B. Then the B portions will tend to coalesce, the nodules that form either being a solid state (liquid crystalline) or a fluid state (micelles) depending on the temperature. [4] Either way, by changing the solvent, or the temperature, we should be able to drastically affect the mechanical properties of the gel.

### Research questions

• We can control the pore size inside of gels, which allows us to decrease the swelling times dramatically, but it seems this would always be at the expense of mechanical strength. Can we decrease swelling time while maintaining mechanical integrity?

References: