Is optimization of the Rubber Formulation important for footwear?

Impact force remains the primary cause of foot injury and general discomfort with regard to footwear. The footwear industry traditionally relies on modified elastomers (including natural rubber) whose properties can be physically adjusted by varying the constituents in the rubber formulations. This work aims to investigate the effect of filler/plasticizer fractions on shock attenuation of natural rubber soles. The statistical response surface method (RSM) was used to optimize the loading of natural rubber, fillers (carbon black and china clay) and a plasticizer (paraffinic oil). A novel predictive equation addressing the effects of additives on the physical and mechanical properties of the shoe sole was successfully created using the RSM. 

Our results demonstrate how the concentrations of these components regulate final properties, such as impact force absorption and hardness, in the commercial manufacture of shoe soles. While a higher loading level of plasticizer promotes reductions in hardness and impact force, as well as energy dissipation, in these modified elastomers, these properties were improved by increasing the filler content.  Impact force constitutes the leading cause of foot injury, with pain and discomfort in both feet and legs resulting from long periods of walking or, even worse, running [1–4]. Previous studies have highlighted health problems, such as bone fractures, cartilage degeneration, and osteoarthritis, as well as chronic knee and back pain. During running in particular, the impact load is typically increased
to 1.5–5.0 × body weight [1–5]. The insertion of a cushion material in shoes can serve to protect the soft tissue on the human heel, along with the muscles in the legs and feet, and thus prevent improper body movement. 

Reducing the impact load can successfully prevent injury while increasing comfort when walking or running, thereby yielding a higher quality of life [2,4,6]. Presently, various foam materials derived from synthetic polymers, such as ethylene-vinyl acetate or polyurethane, are routinely employed in footwear products due to their well-known ability to absorb impact force. However, a nontrivial drawback of such foam materials is their relative lack of durability [2,7–11]. Therefore, to improve the durability of shoes and retain comfort, parts of many shoes are constructed from both natural rubber (NR) and synthetic materials. Previous studies of NR shoe soles in particular have focused on different elastomer considerations that are intended to reduce impact force. 

While products with a high NR content have been reported  to lower impact force, these studies have neglected , considering the accompanying role of different additives, including their loading levels, incorporated into NR. Due to its desirable combination of elasticity and durability, NR is also widely used in cushioning and shoe applications. A plethora of investigations has aimed at developing NR with designer properties, mostly in connection with the tire industry, by physically adjusting the content of fillers and oil. Increasing the content of carbon black (CB), for example, has been suggested as a means by which to improve the tensile properties, which are frequently related to hardness, of finished rubber, in contrast to increasing the content of a plasticizing oil [12–14]. 

Fillers and plasticizers have also been found to affect the internal energy loss, or equivalently the loss tangent, of elastomers due to internal friction (heat) generated by the material during compression [15–18]. The loss tangent correlates with the percentage resilience (PR) of an elastomer; that is, a higher loss tangent corresponds to a greater loss of energy and, in footwear, less force being transferred to the body [19]. A rebound pendulum can be used to measure PR, which is inversely proportional to the hysteresis loss or energy absorption. While such a device could be used to elucidate the systematic effect of varying the fraction of additives in NR products on relevant properties such as hardness, energy loss, and impact force, the necessary experimental matrix becomes unmanageably large. 

In this work, NR shoe soles containing different loading levels of two nanoscale fillers and one plasticizer are examined in a design of experiment (DoE) by using the RSM in conjunction with a quadratic regression model. The RSM examines the relationship between properties of interest and one or more response variables. Therefore, this work is novel in that it uses the RSM method to predict the effects of additives on physical and mechanical properties, focusing on

the cushioning attributes of rubber. Moreover, we conduct a series of hardness measurements under the presumption that rubber hardness relates directly to peak impact force instead of using a rebound pendulum. 

The RSM approach adopted in this study enables a fewer number of experiments while all important experimental factors remain considered. The objective here is to identify the optimal loading level of three commercial additives that are used together to generate a formulation exhibiting the greatest reduction in impact force. The DoE method employed in this work will be useful in future testing and design efforts, and our findings are anticipated to be of widespread interest to developers and manufacturers of footwear, especially with regard to shoes with soles that are produced from modified NR.