Ohmic loss gradient multivariate analysis

The Ohmic loss gradient was analysed for co-varying factors in a backwards step, linear regression model. There was a slight ‘S’ curvature to the data, indicating a slightly flatter distribution: however, the Q-Q plot still passes the ‘pencil test’, as described in Chapter 3, where all data points can be covered a single ‘pencil’ width.

Figure 38: Q-Q plot Ohmic gradient (Ω.cm2)

4.5.4. Discussion of gO

The reduced order model for the Ohmic loss gradient was identified as the preferred output of the three gradient regions. The rank of significance for the key, lowest p-value, factors changed as the model order was reduced with backwards eliminaiton. A p-value >F probability of 0.00001 (see Table 21) for the PTFE content of the GDM was detected; and identified as the most significant factor in the gO model, which is in keeping with the existing literature as discussed previously (see Chapter 2 and section 4.5.2). The p-value>F probability relationship has been discussed in depth in

4-106 Chapter 3 (notably in sections 3.3, 3.6 and 3.6.1) and the value generated indicates it is highly unlikely that the null hypothesis (i.e. h0 = “PTFE connect is not significant”) is correct. For the first time significance in the structure (woven, paper or non-woven) in the gradient of the Ohmic loss region is registered. There were no multi-factor effects evidenced by the model, and the significance of test cell or test machine, is to be expected in a region dominated by contact losses and clamping pressures. These results somewhat contradict the previous inference that ambient temperature plays an interactive role on the clamping forces experienced by the system. However, it may be that the resistances across the various test cells (of the eight possible locations) overwhelm any such effect. The pore structure also factors into the Ohmic loss. At first consideration, this may be a little counter- intuitive. However, consider the porosity value (entered as a percentage presence of pores) as an estimate of the solidity, or density, of the system. With higher porosity increasing the gradient of the Ohmic loss region; as there is less material and therefore fewer conductive pathways. For non- wovens, there was a negative gradient modifier generated by the model, whereby the Ohmic loss gradients were further reduced to creat a single statisitcal modle that can include all three GDM types.

Table 14: Numeric designation of GDM structures

The requirement for separate numeric values to model the three types of GDM the first key instance in this thesis where it can be categorically stated that there is a quantifiable need for the ‘third category’ of ‘Non-Woven’ felt like materials. The evidence is certain (at the 5% level of significance) that the Ohmic losses were reduced for non-woven like material compared to any other carbon fibre based fabric system. Table 14 shows the numeric values assigned to the reduced complexity model developed (see section 4.8.2). Recall that in the automated software calculations, the actual numeric value attributed to the non-wovens (as a first entry data point) will be -1. So the actual impact on the gradient is 0.13: the Ohmic loss region will be less steep for non-woven materials (when taken in isolation from all other possible factors). The software, assigned the exact value required to reduce the sum of squares of the residuals between the actual data points and the predicted data points created by the model. Recall that many factors were included in the final model (see section 4.8.2), and an iterative adjustment of all factors in the model was undertaken by the software: The model value with the lowest error (the lowest sum of squares of the residuals) was presented as the final model. This process was originally introduced in Chapter 3 (most notably in section 3.2).

Factor Factor categorical numeric value

Factor modifier

Non-woven 1 -0.13

Paper 2 0.12

4-107 Interpretation of this was intuitively simple, the planar nature of paper means that through-thickness conductivity of the paper GDM is reduced. The three-dimensional nature of the woven structure facilitates the through-plane conductivity for the system, and the excellent performance of the non- woven (felt like) materials, was somewhat more surprising. A degree of improvement is perhaps expected, but the bettering the performance of the woven materials in this factor, was not.

Non-woven like materials have a number of fibres that penetrate the fabric in the z-direction (i.e. through the plane of the fabric). The exact number of these fibres is limited, and their primary purpose is to improve the structural integrity and stiffness of the non-woven like materials. In this case, it is suggested that the z-direction, though-thickness, fibres are acting as direct electrical conductors from side to side of the GDL; reducing the overall resistance of the MEA. There has been some work completed on a variety of gas diffusion media and assessment of their through plain conductivity [112] to support this suggestion. A systematic analysis of the different types of carbon fibre materials categorised as either paper, woven or non-woven (felt like) GDMs, has been missing from the literature until quite recently [16,24,55]. More information on this topic is coming to light as the modelling community develops more detailed modelling methods and validates them with high energy GDM characterisation techniques [101]. Interpretation of the initial linear regression model developed, is aided by plotting the results as a visual representation. This has been done for Ohmic gradient loss initial value models and is presented in Appendix 3. With more than three factors in the model it is not possible to visualise all vertices at once, but a Porosity, Mean temperature during polarising curve (T-bar), and gradient of the Ohmic loss region (gO) is useful. Analysis of these initial models indicates the lowest possible gradient in this case. This is the most desirable case as the Ohmic region is the area of preferred operation for the vast majority of fuel cell operations. Such Low gradients can be achieved by selecting a paper GDM with a lower porosity, with the non-woven (felt) geometry GDMs performing second best, closely followed by the woven materials.

There was a through-plane thickness and porosity interrelationship, which demonstrates a degree of more complex interaction, with the somewhat surprising finding that minimum porosity is preferable when coupled with very thin GDMs. It is possible that this is, in fact, a reflection on the gasket configuration of the test cell. A reduced complexity modelling step is required before firm conclusions can be drawn, however. While a variety of different thicknesses of GDM were tested, the gasket dimension remains unchanged, and so, for certain thicknesses of the GDM, the compression of the system may be sub-optimal. It is possible that this thickness factor could be removed by optimising the gasket geometry for each GDM. Lin et al. (2010) [58] make a point of limiting their paper selection to a single narrow size range to avoid any such effect. If this interpretation were correct, the optimum Ohmic gradient response would be expected to occur at a single thickness setting at all porosities. In this case, it was clear that the optimum performance at various porosities co-varies with thickness, reducing the likelihood that the lack of optimisation of the sealing gasket

4-108 height is the cause of this effect. A literature search on this topic revealed no pre-existing discussions of this effect, indeed the closest like to the topic that could be found [113] was focused on a novel geometry GDM that is not suited to this result. Millichap et al. (2015) [114] state that the primary impact of incorrect gasket geometries will be observed as accelerated degradation effects, and makes no mention of the thickness-porosity-performance relationship detected.

Based on the information available here, and assuming the gasket geometry was not a factor; the through-plane thickness and porosity interaction were present in all cases. Once again on this first iteration model, the paper structure provides the optimum Ohmic Loss region gradient (gO) and the non-woven (felt) structures slightly beating the performance of the woven materials. It is worth stressing once again that this three-factor interaction would be difficult, if not impossible, to detect in the traditional OFAT (one factor at a time) methods of data assessment.