Analysis of binary mixtures of spherical and cylindrical macromolecules from the measurement of n<sup>(2)</sup>(T)

J. C. Abad; M. A. Rebolledo

doi:10.1364/AO.21.002929

Applied Optics
Vol. 21,
Issue 16,
pp. 2929-2935
(1982)
•https://doi.org/10.1364/AO.21.002929

Analysis of binary mixtures of spherical and cylindrical macromolecules from the measurement of n⁽²⁾(T)

J. C. Abad and M. A. Rebolledo

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J. C. Abad and M. A. Rebolledo, "Analysis of binary mixtures of spherical and cylindrical macromolecules from the measurement of n⁽²⁾(T)," Appl. Opt. 21, 2929-2935 (1982)

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Abstract

In this paper we study the possibility of analyzing solutions of mixtures of spherical and cylindrical macromolecules, impinging on them with laser light and measuring the normalized second-order factorial moment, n⁽²⁾(T), of the scattered light. With this method we intend to determine the quotient of concentrations of the two solute fractions or the molecular weight of one of the components. The errors in these measurements are studied by means of a computer simulation method. The validity of the simulation method is experimentally proved with a mixture of two kinds of spherical particles of different size.

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	α From intensity measurements	α From n⁽²⁾ measurements	σ(α) (%) Experimental	σ(α) (%) From simulation
3972 and 1214 Å	0.101	0.131	53.3	52.8
	0.331	0.322	34.6	32.4
	1.021	1.059	19.1	19.4
θ = 90°	3.160	3.172	26.1	27.3
	9.876	11.700	92.2	102.9
3972 and 488 Å	0.101	0.108	59.2	52.8
	0.302	0.343	19.4	20.6
	0.988	1.116	10.0	10.8
θ = 90°	2.972	3.350	20.2	18.7
	9.614	11.744	90.2	86.9
3972 and 1214 Å	0.110	0.116	75.9	55.0
	0.318	0.346	31.9	30.1
	1.012	1.086	21.1	22.2
θ = 65°	3.118	3.400	32.5	31.6
	10.176	12.823	55.9	104.9

	Diameter D(Å) of the big sphere that is mixed with other smaller spheres with diameter Di
D/Di	300.0	375.0	468.75	585.94	732.42	915.53	1144.41	1430.51	1788.45	2235.17	2793.97
1.25	1.5492	1.5517	1.5503	1.5509	1.5519	1.5499	1.5528	1.5506	1.5489	1.5502	1.5482
1.25²	0.5200	0.5226	0.5226	0.5227	0.5204	0.5224	0.5222	0.5216	0.5219	0.5222	0.5220
1.25³	0.3831	0.3840	0.3831	0.3839	0.3834	0.3826	0.3839	0.3837	0.3840	0.3833	0.3840
1.25⁴	0.2810	0.2805	0.2819	0.2810	0.2821	0.2817	0.2808	0.2812	0.2809	0.2803	0.2806
1.25⁵	0.2110	0.2105	0.2109	0.2108	0.2109	0.2107	0.2113	0.2103	0.2103	0.2107	0.2104
1.25⁶	0.2334	0.2318	0.2315	0.2331	0.2330	0.2325	0.2327	0.2323	0.2326	0.2336	0.2333
1.25⁷	0.1600	0.1587	0.1591	0.1592	0.1593	0.1590	0.1592	0.1593	0.1592	0.1592	0.1589
1.25⁸	0.1394	0.1396	0.1395	0.1396	0.1395	0.1394	0.1394	0.1395	0.1390	0.1395	0.1393
1.25⁹	0.1354	0.1357	0.1354	0.1352	0.1355	0.1356	0.1354	0.1354	0.1355	0.1357	0.1356
1.25¹⁰	0.1282	0.1287	0.1286	0.1287	0.1283	0.1281	0.1281	0.1285	0.1285	0.1284	0.1284

		Scattering angle

Diam, Å		15°	45°	75°	105°	135°	165°
150	a	−0.37 10⁻³	−0.46 10⁻³	−0.69 10⁻⁴	0.27 10⁻⁴	−0.43 10⁻³	−0.14 10⁻³
	b	0.79	0.89	0.66	0.63	0.91	0.67
450	a	0.93 10⁻⁵	0.00	−0.35 10⁻³	0.15 10⁻³	0.15 10⁻³	−0.50 10⁻³
	b	0.92	1.00	1.33	1.18	1.06	1.67
750	a	−0.11 10⁻²	−0.94 10⁻³	−0.11 10⁻²	0.15 10⁻²	0.86 10⁻⁴	0.31 10⁻³
	b	2.55	2.51	2.84	3.92	4.50	4.15
1050	a	−0.11 10⁻²	−0.14 10⁻²	−0.27 10⁻²	0.39 10⁻²	−0.32 10⁻²	−0.23 10⁻²
	b	5.38	6.03	12.17	25.77	13.53	10.71
1350	a	−0.48 10⁻²	−0.43 10⁻²	−0.28 10⁻²	0.33 10⁻³	0.77 10⁻³	−0.42 10⁻³
	b	15.28	12.18	6.85	2.65	2.65	3.22
1650	a	−0.89 10⁻³	−0.88 10⁻³	−0.10 10⁻²	0.37 10⁻³	−0.63 10⁻³	−0.28 10⁻³
	b	4.09	3.58	3.28	1.72	2.08	1.80
1950	a	0.20 10⁻³	−0.64 10⁻³	0.16 10⁻³	−0.39 10⁻³	−0.35 10⁻⁴	−0.27 10⁻³
	b	2.26	2.59	1.75	1.91	1.44	1.60
2250	a	−0.61 10⁻³	−0.56 10⁻³	−0.14 10⁻³	−0.11 10⁻³	0.18 10⁻³	−0.24 10⁻³
	b	2.04	1.78	1.44	1.23	1.03	1.28

	α From intensity measurements	α From n⁽²⁾ measurements	σ(α) (%) Experimental	σ(α) (%) From simulation
3972 and 1214 Å	0.101	0.131	53.3	52.8
	0.331	0.322	34.6	32.4
	1.021	1.059	19.1	19.4
θ = 90°	3.160	3.172	26.1	27.3
	9.876	11.700	92.2	102.9
3972 and 488 Å	0.101	0.108	59.2	52.8
	0.302	0.343	19.4	20.6
	0.988	1.116	10.0	10.8
θ = 90°	2.972	3.350	20.2	18.7
	9.614	11.744	90.2	86.9
3972 and 1214 Å	0.110	0.116	75.9	55.0
	0.318	0.346	31.9	30.1
	1.012	1.086	21.1	22.2
θ = 65°	3.118	3.400	32.5	31.6
	10.176	12.823	55.9	104.9

	Diameter D(Å) of the big sphere that is mixed with other smaller spheres with diameter Di
D/Di	300.0	375.0	468.75	585.94	732.42	915.53	1144.41	1430.51	1788.45	2235.17	2793.97
1.25	1.5492	1.5517	1.5503	1.5509	1.5519	1.5499	1.5528	1.5506	1.5489	1.5502	1.5482
1.25²	0.5200	0.5226	0.5226	0.5227	0.5204	0.5224	0.5222	0.5216	0.5219	0.5222	0.5220
1.25³	0.3831	0.3840	0.3831	0.3839	0.3834	0.3826	0.3839	0.3837	0.3840	0.3833	0.3840
1.25⁴	0.2810	0.2805	0.2819	0.2810	0.2821	0.2817	0.2808	0.2812	0.2809	0.2803	0.2806
1.25⁵	0.2110	0.2105	0.2109	0.2108	0.2109	0.2107	0.2113	0.2103	0.2103	0.2107	0.2104
1.25⁶	0.2334	0.2318	0.2315	0.2331	0.2330	0.2325	0.2327	0.2323	0.2326	0.2336	0.2333
1.25⁷	0.1600	0.1587	0.1591	0.1592	0.1593	0.1590	0.1592	0.1593	0.1592	0.1592	0.1589
1.25⁸	0.1394	0.1396	0.1395	0.1396	0.1395	0.1394	0.1394	0.1395	0.1390	0.1395	0.1393
1.25⁹	0.1354	0.1357	0.1354	0.1352	0.1355	0.1356	0.1354	0.1354	0.1355	0.1357	0.1356
1.25¹⁰	0.1282	0.1287	0.1286	0.1287	0.1283	0.1281	0.1281	0.1285	0.1285	0.1284	0.1284

Abstract

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Applied Optics