We present new [ C i ] ( 1–0 ) and ^ { 12 } CO ( 4–3 ) Plateau de Bure Interferometer ( PdBI ) observations of five Sub-Millimeter Galaxies ( SMGs ) and combine these with all available [ C i ] ( 1–0 ) literature detections in SMGs to probe the gas distribution within a sample of 14 systems . We explore the [ C i ] ( 1–0 ) properties of the SMG population , particularly investigating the ratio of the [ C i ] ( 1–0 ) luminosity to various ^ { 12 } CO transition and far-infrared luminosities . We find that the SMGs with new observations extend the spread of L _ { [ CI ] ( 1 - 0 ) } / L _ { FIR } to much higher values than found before , with our complete sample providing a good representation of the diverse z > 2 SMG population . We compare the line ratios to the outputs of photodissociation region ( PDR ) models to constrain the physical conditions in the interstellar medium ( ISM ) of the SMGs , finding an average density of \langle \log ( n / cm ^ { -3 } ) \rangle = 4.3 \pm 0.2 and an average radiation field ( in terms of the local field value , G _ { 0 } ) of \langle \log ( G _ { 0 } ) \rangle = 3.9 \pm 0.4 . Overall , we find the SMGs are most comparable to local ULIRGs in G _ { 0 } and n , however a significant tail of 5 of the 14 SMGs are likely best compared to less compact , local starburst galaxies , providing new evidence that many SMGs have extended star formation distributions and are therefore not simply scaled up versions of local ULIRGs . We derive the ISM properties of a sample of quasars also finding that they have higher densities and radiation fields on average than the SMGs , consistent with the more extreme local ULIRGs , and reinforcing their interpretation as transition objects . We explore the limitations of using simple PDR models to understand [ C i ] , which may be concomitant with the bulk H _ { 2 } mass rather than PDR-distributed . We therefore also assess [ C i ] as a tracer of H _ { 2 } , finding that for our sample SMGs , the H _ { 2 } masses derived from [ C i ] are often consistent with those determined from low excitation ^ { 12 } CO. We conclude that [ C i ] observations provide a useful tool to probe the bulk gas and gas processes occurring within merging SMGs , however more detailed , resolved observations are required to fully exploit [ C i ] as a diagnostic .