# Compute composite k

Prediction of effective thermal conductivity of functionalized aligned polymer-graphene nanocomposites using effective medium theory

#### To predict the thermal conductivity of aligned polymer-graphene nanocomposites (both with and without functionalization), we use effective medium theory, specifically, the model developed by Nan et al. [C. Nan, R. Birringer, D. R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance”, Journal of Applied Physics 81, 10, 1997]. The model provides the advantage of using the exact orientation of nanoplatelets in aligned polymers and also taking into account the interfacial thermal resistance between polymer and graphene. By varying the interfacial thermal resistance, effect of functionalization can be incorporated in to the prediction. For unfunctionalized composites a nominal interfacial thermal resistance of ~5e-8 m^{2}K/W can be used. Functionalization decreases interface thermal resistance by promoting stronger force interactions leading to significantly lower interface thermal resistance values of ~5e-9 m^{2}K/W.

#### Predicted effective thermal conductivity of aligned polymer-graphene nanocomposite (with functionalization) for the following set of involved parameters,

*k*-graphene, in -plane (*kin*): 1000.0 W/mK

*k*-graphene, in -plane (

*kin*): 1000.0 W/mK

*k*-graphene, out-of-plane (*kout*): 10.0 W/mK

*k*-graphene, out-of-plane (

*kout*): 10.0 W/mK

*k of *base polymer matrix (*km*): 3.3 W/mK

*k of*base polymer matrix (

*km*): 3.3 W/mK

**Volume fraction of graphene (***f*): 15%

*f*): 15%

**Lateral dimension of graphene (***L*): 5 µm

*L*): 5 µm

**Thickness of nanoplatelets (***t*): 60 nm

*t*): 60 nm

**Interface thermal resistance (***R*): 5e-09 (m^{2}K/W)

*R*): 5e-09 (m

^{2}K/W)

**Orientation of graphene nanoplatelets (cos**^{2}Φ): 0.63

^{2}Φ): 0.63

#### is achieved to be **32.3 W/mK**, more than **two orders of magnitude** higher compared to thermal conductivity values of typical pristine polymers (*k*~0.2 W/mK) and *~60-fold higher* compared to *k* of pristine unoriented polyethylene (*k*~ 0.5 W/mK). It should be noted that this high predicted *k* of polymer-graphene composite is in part due to the **high ***k* of the base aligned polymer itself (measured to be 3.3 W/mK in our recent work at a draw ratio of 5.0). These results highlight the **large potential of alignment and functionalization effects** in enhancing thermal conductivity of polymer composites.

**two orders of magnitude**

*~60-fold higher*

*k*of the base aligned polymer

### Prediction of composite *k* for **other** set of parameters can be achieved by filling out the values in the following form. Role of the k of the base polymer matrix and functionalization effect can be studied by varying the relevant paramaters.

**other**