Relative Hardness of Fat Crystal Networks Using Force Displacement Curves

Figures & data

Table 1 Summary of testing parameters, geometries and analysis from the force-displacement curve literature

Material Tested	Speed(mm/s)	Depth (mm)	Geometry	Analysis Method
Stick margarine	0.167	15	Cone(30°)	Initial slopeMaximum force [10]
Alfalfa cubes	0.022	2.35 – 5.65	Sphere (d = 4.70, 7.75, 10.00, 11.30 mm)	Slope of linear portion of curveMeyer hardness [16]
Margarine Peanut butter Butter	0.4 – 1.2	5, 10, 15	Cone (20°, 40°, 60°)	Yield value [15]
Binary blends of vegetable oil fractions	0.5	5	Cone P/45C	Slope of linear portion of curve
				Maximum force
				Force at maximum displacement [17]
High and low erucic acid rapeseed oil blends	0.5	5	Cone P/45C	Max force
				Force at maximum displacement [13]
Blends of high and low melting TAGs and vegetable oil fractions	0.5	6	Cylindrical Probe (d = 3 mm)	Stress = Force/Area [12]
Refined, bleached, and deodorized palm oil	1	10	Cone (10°)	Force at maximum displacement [11]

Figure 1 Piling-up and sinking-in phenomena.

Figure 2 Typical force displacement curves for binary mixtures of the pure TAG LLS mixed with LSL (% w/w).

Figure 3 Typical force displacement curves for the 50% fully hydrogenated canola in canola oil sample penetrated to depths of 1.0, 2.0, 2.5, 3.0, 3.5, 4.0, and 5.0 mm.

Table 2 Relative hardness for each sample compared (a) within depths and (b) between depths

Sample (% w/w FHCO)	Relative Hardness - Comparing Within Depths
	1.0 mm	1.5 mm	2.0 mm	2.5 mm	3.0 mm	3.5 mm
50	1.0 ± 0.1^a	1.0 ± 0.2^a	1.0 ± 0.1	1.0 ± 0.1	1.0 ± 0.1^b	1.0 ± 0.2^b
75	5.4 ± 0.5	6.0 ± 0.8	6.8 ± 0.8	4.1 ± 0.5	4.8 ± 0.5	6.3 ± 0.8
100	28 ± 4	36 ± 5	38 ± 4	22 ± 2	21 ± 2	24 ± 3
Sample (% w/w FHCO)	Relative Hardness - Comparing Between Depths
	1.0 mm	1.5 mm	2.0 mm	2.5 mm	3.0 mm	3.5 mm
50	1.0 ± 0.1	1.3 ± 0.2	1.8 ± 0.2	4.3 ± 0.6	5.3 ± 0.7	5.4 ± 0.7
75	1.0 ± 0.1	1.4 ± 0.1	2.2 ± 0.2	3.3 ± 0.2	4.7 ± 0.3	6.2 ± 0.5
100	1.0 ± 0.1	1.7 ± 0.2	2.5 ± 0.3	3.4 ± 0.3	4.1 ± 0.4	4.7 ± 0.5
Average Increase	1.0 ± 0.0	1.5 ± 0.2	2.2 ± 0.3	3.6 ± 0.6	4.7 ± 0.6	5.4 ± 0.7
*Data entries with the same superscript are not significantly different from each other. All other entries are significantly different (P < 0.001).

Figure 4 Relative hardness within each sample (50, 75, and 100% fully hydrogenated canola in canola oil) at different penetration depths using the needle probe.

Figure 6 Force displacement curves for the 25 and 50% fully hydrogenated canola in canola oil and margarine samples using the ball probe with representative curves shown. a) 0.5 mm/s; and b) 1.5 mm/s.

Figure 5 Representative force-displacement curves using the needle probe recorded for the fully hydrogenated canola in canola oil samples. (a) 50%_FHCO at six different speeds of penetration; (b) 50, 75, and 100%_FHCO samples recorded with 0.5 mm/s; and (c) 50, 75, and 100%_FHCO samples recorded with 2.0 mm/s.

Table 3 Relative hardness for each sample compared (a) within speeds and (b) between speeds

Geometry	Sample (% w/w FHCO*)	Relative Hardness - Comparing Within Speeds
		0.5 mm/s	2.0 mm/s
ball	M	1.0 ± 0.1	1.0 ± 0.2
	25	3.3 ± 0.3	3.5 ± 0.6
	50	38 ± 5^a	35 ± 8^a
needle	50	1.0 ± 0.1	1.0 ± 0.1
	75	5.7 ± 0.9	4.9 ± 0.5
	100	13 ± 2	13 ± 2
*With the exception of the margarine sample, listed as “M”
Geometry	Sample (% w/w FHCO*)	Relative Hardness - Comparing Between Speeds
		0.5 mm/s	2.0 mm/s
ball	M	1.0 ± 0.1	1.0 ± 0.2
	25	1.0 ± 0.0	1.1 ± 0.1
	50	1.0 ± 0.1	1.0 ± 0.2
needle	50	1.0 ± 0.1	1.1 ± 0.1
	75	1.0 ± 0.2	1.0 ± 0.1
	100	1.0 ± 0.1	1.1 ± 0.2
*With the exception of the margarine sample, listed as “M”
*Data entries with the same superscript are not significantly different from each other. All other entires are significantly different (P < 0.1).

Figure 7 Typical force displacement curves obtained at 2 speeds with the measurement proceeding through air.

Figure 8 Using a penetration depth of 1.5 mm and speed of 0.5 mm/s, the effect of geometry type on the force displacement curve was elucidated using a margarine sample with representative curves shown.

Figure 9 Average relative hardness values as determined: a) by cone penetrometry using the Precision Penetrometer and the TA.XT+ Texture Analyzer; and b) by force displacement curves obtained with a depth of 1.5mm, speed of 0.5 mm/s and with each a ball and needle geometry.