Carbon nanomaterials offer formulators and designers of polymer composites additives that can boost mechanical strength. However, these improvements do not materialize as expected when such systems are made. This failure is understandable with a basic overview of what’s happening at the interface between the materials. This is extended to provide a rule-of-thumb guide to whether certain types of polymer composites will work and highlights what needs to happen before they will.
Carbon nanotubes (CNTs) are exactly that – carbon atoms arranged cylindrically and so closely together that their diameters are on the scale of several nanometers, or even smaller than that. However, their aspect ratio – the ratio of their length to that diameter – can range from a low end of 500 to several thousand, and tubes with ratios in excess of 100,000 are available. They typically come in two forms – those with just one wall (called a single walled nanotube or SWNT) and those with one tube stacked inside another concentrically (called a multiwalled nanotube or MWNT).
Following their discovery by Dr. Sumio Iijima almost 30 years ago, theoreticians predicted this unique atomic arrangement would give rise to structures with unique properties such as high mechanical strength. This has been demonstrated in the laboratory, with some tubes having tensile strengths and elastic moduli several times in excess of that of steel. This comes with a significant weight savings, as the true density of CNTs can be less than a quarter of that of steel.
Because of these unique properties, carbon nanotubes have been the subject of considerable research in manufacturing. The production processes for them have improved considerably both in cost and scale, with market prices dropping from a high of almost $500 per gram back in 2003 to $30 to $50 per kilo, which makes them comparable to those of other high-end chemical additives. A recent article in HS Today provided some real-world examples.
Therefore, with commercial pricing and availability of these materials, a natural development would be the creation of composite materials, especially those involving polymers. Over the last two decades there have been many attempts to formulate such composites with CNTs. These efforts have explored using both thermoset materials like epoxies and thermoplastic materials like ultra-high molecular weight polyethylene (UHMWPE), the latter being desirable for ballistic applications.
The end results are mixed. As examples, formulating nanotubes with epoxies for modest strength applications such as sporting goods showed that it was possible to introduce CNTs into the matrix at acceptable levels with conventional mixing technology. However, shear testing revealed at the site of fracture no CNTs would be found. They would simply fly out upon fracture as there was no adhesion between them and the matrix. The optimal level of mechanical strength promised by the Rule of Mixtures never materialized.
Understanding the Causes:
One way to understand the issue is view the nanotubes not as a new type of structure, but rather as polymers themselves. After all, nanotubes are long, narrow structures made of repeating units just like any other polymer. With this approximation, it is possible to use the tools developed for polymer miscibility to determine how strongly the nanotubes by themselves will interact with the matrix.
At the heart of all formulation science is the nature of the forces between two bodies. For a homogenous material the concept of cohesive energy in a liquid can be expressed according to the equation defined by Hildebrand in 1936:
Here is the molar enthalpy of vaporization, the energy required to transform a liquid into a gas. is the molar energy of the substance as an ideal gas, so the numerator is divided by the molar volume and the square root taken, one obtains a value of the attractive forces holding the molecules together, the cohesive energy density , typically called the Hildebrand parameter.
Hildebrand’s insight was to recognize the similarities between vaporization and solubility behavior. He saw that the same intermolecular attractive forces must be overcome when a liquid is vaporized as when it is mixed with another liquid. Miscibility of one liquid in another happens, therefore, when their attractive forces are equivalent, so the cohesive energy densities of two substances can predict whether they will be soluble with one another. The SI unit of measurement is (J/m3)1/2, or more conveniently Pa1/2. The magnitude of the effect is on the scale of millions of Pascals, so one sees the units expressed as MPa1/2.
This parameter has been used successfully for more than seven decades to design polymer blends. A further refinement came in 1967 when Charles Hansen realized that the overall attractive force between molecules could be semi-empirically assigned to a set of three different smaller forces that were based on where electrons were distributed in the molecules. While the exact nature of these forces is beyond the scope of this article (they are called the dispersive, hydrogen bonding, and polarizability forces), they are based on the chemical compositions and structure of the molecule. They are each represented by their own Hansen parameters analogous to the Hildebrand term. However, each of these the forces is unique to itself and does not interact with any other.
They have been used successfully with many polymer types, and like the Hildebrand parameters are expressed in units of MPa1/2. Table 1 shows the approximate values of both types of parameters associated with typical polymers:
Table 1 – Examples of Hildebrand parameters (d) and the Hansen parameters (dp, dd, dh) for common polymer systems. The closer the values are for two systems, the more likely they are to be compatible. This is a short list as the parameters for literally thousands of materials can be found in the literature.
Note that for poly(ethylene), a polymer system associated with ballistic applications, the attraction between molecules is almost entirely associated with the dispersive force. This is unlike carbon nanomaterials where typical values for the Hansen parameters are dd = 17.7 MPa1/2, dh = 7 MPa1/2, and dp = 7 MPa1/2. Therefore, it is understandable from this basic theory that the attractive forces between this polymer system and carbon nanotubes are far from optimized. It also provides a framework for understanding why nanotubes do not interact well with such polymer systems – poor adhesion due to each material experiencing attractive forces differently.
This is not to say that making a good composite is impossible. Some polymers such as PET are better suited than something like PE to mix with nanotubes due to the types of forces involved. And there are techniques for altering the interface between the polymer and the nanotube so that the parameters more closely match. However, alteration can require changes to the chemical structure of the nanotube, and in doing that one can reduce or even destroy the nanotube properties that one hopes to bring to the composite. In some cases, making a polymer blend can be helpful as the mixture will have parameters that are the sum of those materials used in the blend, weighted proportionally.
The successful formulation of carbon nanotube polymer composites requires more than simply combining the two. The nature and magnitude of attractive forces must be understood. By adapting the solubility parameter framework from polymer science to the nanotubes one can obtain a good, semi-quantitative measure of the types of forces involved and whether both materials will be compatible with each other. It also shows where changes need to be made in order to correct any incompatibilities. And this can be done by simply consulting a small set of known and well-documented parameters. This can serve as a reasonable rule-of-thumb to check a system before attempting to formulate it.
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