Table 2. Summary of experimental and calculated data.

Weight fraction (w_Ligand), mole fraction (x_Ligand), helical pitch, p values, helical twisting power (β_w), molar helical twisting power (β_mol), average particle-particle distance (⟨D_P−P⟩), and number of nanoshapes per full helical pitch of the chiral cholesterol-thiol–capped nanoshape additives in 5CB based on a constant weight fraction of 0.5 wt %.

Nanoshape	wLigand × 10−3	xLigand × 10−4	p (μm)*		βw† (μm−1)	βmol†‡ (μm−1)	⟨DP−P⟩ (nm)	Nanoshapes per full pitch
			Free surface	Lens or wedge
GNP5 (48)	1.05	4.40	12.0	13.0	−76.0 ± 3.8	− 178 ± 9.0	24.0	52
GNP10 (48)	0.77	3.30	–§	–§	–||	–||	53.2	–||
LAR-GNR	1.10	4.68	50.0	–¶	−23.9 ± 1.2	−53.4 ± 2.7	42.8	1190
MAR-GNR (50)	2.00	8.50	1.3	1.1	−455 ± 23	−1064 ± 53	47.6	25
HAR-GNR	1.00	4.26	130.0	–¶	−7.70 ± 0.4	−18.1 ± 1.0	53.0	2452
LAR-GND	1.40	5.96	45.0	–¶	−15.6 ± 0.8	−37.3 ± 1.9	84.5	537
HAR-GND	1.35	5.75	40.0	–¶	−20.0 ± 1.0	−43.1 ± 2.2	59.4	666
GNS	1.50	6.38	15.0	14.8	−41.8 ± 2.1	−105.1 ± 5.3	106	141
GNPR	1.25	5.32	9.0	8.4	−94.6 ± 4.8	−216.0 ± 11	58.4	155
Ligand
Chol-thiol	5.0	21.2	58.0	58.0	−3.5 ± 0.2	−8.1 ± 0.4	14.6#	–

*The values of p obtained by the different measurement setups (Grandjean-Cano plano-convex lens, free surface, or homeotropic anchoring) are, as reported previously, in close agreement. Accuracy is ±0.3 μm.

†The negative sign indicates that the induced N*-LC phase is left handed as established by contact preparations with a known left-handed N*-LC material, cholesteryl oleyl carbonate (COC). Cooperativity among the nanoshapes leading to enhanced values for β_w and β_mol was again observed, supported by the anomalous trends in the plots of the inverse helical pitch (p⁻¹) versus the nanoshape concentration (fig. S12); the standard deviations partly accounted for this.

‡β_mol is the helical twisting power value when the dimensionless mole fraction (x_Additive) of the chiral additive is used. For the current dataset, x_Additive = x_Ligand because the nanoshapes are intrinsically achiral. To determine x_Ligand, the experimental TGA data (see table S7) were used.

§The helical pitch was too large to be measured and the sample appeared as an achiral N-LC phase in all experiments.

||Since p was too large to be measured, these values could not be calculated and would signify β_w and β_mol = 0 μm⁻¹.

¶The curvature of available plano-convex lenses did not allow for measurement of these larger p values; only values from free surface and preparation with homeotropic anchoring conditions were used.

#D_P–P here refers to the average distance between well-dispersed cholesterol disulfides used as chiral additive in 5CB.