Additional jamming transition in two-dimensional bidisperse granular packings

We present a jamming diagram for two-dimensional bidisperse granular systems, capturing two distinct jamming transitions. The first occurs as large particles form a jammed structure, while the second, emerging at a critical small-particle concentration, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msubsup><a:mi>X</a:mi><a:mrow><a:mi mathvariant="normal">S</a:mi></a:mrow><a:mo>*</a:mo></a:msubsup><a:mo>≈</a:mo><a:mn>0.21</a:mn></a:mrow></a:math>, and size ratio, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:msup><c:mi>δ</c:mi><c:mo>*</c:mo></c:msup><c:mo>≈</c:mo><c:mn>0.25</c:mn></c:mrow></c:math>, involves small particles jamming into the voids of the existing large-particle structure upon further compression. Below this threshold, small particles fill voids within the large-particle network, increasing packing density. Beyond this point, excess small particles disrupt efficient packing, resulting in looser structures. These results, consistent with previous three-dimensional studies, demonstrate that the second transition occurs at a well-defined point in the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mo>(</d:mo><d:msub><d:mi>X</d:mi><d:mi mathvariant="normal">S</d:mi></d:msub><d:mo>,</d:mo><d:mi>δ</d:mi><d:mo>)</d:mo></d:mrow></d:math> plane, independent of dimensionality, likely driven by the geometric saturation of available space around particles, void closure, and structural arrangement.