Low Angle Laser Light Scattering—Absolute Calibration

Wilbur Kaye; A. J. Havlik

doi:10.1364/AO.12.000541

Applied Optics
Vol. 12,
Issue 3,
pp. 541-550
(1973)
•https://doi.org/10.1364/AO.12.000541

Low Angle Laser Light Scattering—Absolute Calibration

Wilbur Kaye and A. J. Havlik

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Wilbur Kaye and A. J. Havlik, "Low Angle Laser Light Scattering—Absolute Calibration," Appl. Opt. 12, 541-550 (1973)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

A new method for the calculation of the Rayleigh factor from low angle light scattering measurements is developed. This method does not require a uniform intensity illuminating beam, hence efficiently utilizes all the beam from a focused laser source. Scattering volume is then very small, reducing sample volume and interference from contaminant particles. All the parameters necessary for the calculation of the Rayleigh factor (including the exact dependence on sample refractive index) are measurable, hence absolute calibration is possible. Over-all error is estimated to be less than 2.3% under specified conditions. Measurements are possible at scattering angles as small as 2° obviating the need for angular extrapolations in the determination of molecular weight of most dissolved samples. Rayleigh factors at 22°C, 633 nm, and a scattering angle of 4° for water, methanol, benzene, and toluene, were found to be, respectively, 0.907, 2.56, 12.15, and 13.45 × 10⁻⁶ cm⁻¹.

Full Article | PDF Article

More Like This

Low-Angle Laser Light Scattering—Rayleigh Factors and Depolarization Ratios

Wilbur Kaye and J. B. McDaniel
Appl. Opt. 13(8) 1934-1937 (1974)

Low Angle, Light Scattering Photometer Model LS-2

H. Utiyama and Y. Tsunashima
Appl. Opt. 9(6) 1330-1336 (1970)

Particle-Size Determination by Low-Angle Light Scattering: Effect of Refractive Index

E. J. Meehan and A. E. Gyberg
Appl. Opt. 12(3) 551-554 (1973)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (4)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (8)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (20)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Annulus No. 2
inner diameter 1.906 cm; outer diameter 2.232 cm.
n′	θ_i′	θ_ii′	σ′
1.00	101.02 mrad	118.15 mrad	11.405 msr
1.32	76.48	89.42	6.531
1.33	75.90	88.74	6.433
1.34	75.33	88.08	6.337
1.49	67.74	79.19	5.123
1.50	67.29	78.67	5.055

Annulus No. 2
k/n′_γ/H4	0.158	0.21	0.31	0.41	0.51
∞	0.1382	0.1882	0.2815	0.3695	0.4728
0.90	0.1382	0.1882	0.2814	0.3693	0.4720
0.80	0.1382	0.1882	0.2814	0.3692	0.4712
0.70	0.1381	0.1881	0.2813	0.3690	0.4703
0.65	0.1381	0.1881	0.2812	0.3688	0.4692
0.60	0.1381	0.1881	0.2811	0.3681	0.4679

H4	G_θD₀/G₀	B(SiO₂)	B(res)	σ′l′	R_θ′
	Annulus No. 1	θ′ = 3.4°	σ′ = 20.56 msr	γ = 1.0014
0.51	18.69 × 10⁻⁹	0.24 × 10⁻⁹	1.79 × 10⁻⁹	17.71 × 10⁻³	(0.940 × 10⁻⁶)
0.41	13.98	0.06	1.16	13.90	0.919
0.31	10.23	0.01	0.66	10.54	0.907
0.21	6.678	0	0.302	6.997	0.911
0.158	4.842	0	0.172	5.132	0.910
	Annulus No. 2	θ = 4.7°	σ′ = 6.409 msr	γ = 1.0026
0.51	3.957	0.003	0.281	4.048	0.907
0.41	3.062	0.001	0.182	3.164	0.910
0.31	2.294	0	0.104	2.411	0.908
0.21	1.500	0	0.047	1.612	0.901
0.158	1.101	0	0.027	1.184	0.907
	Annulus No. 3	θ′ = 3.2°	σ′ = 4.141 msr	γ = 1.0013
0.51	3.864	0.014	0.359	3.773	0.925
0.41	2.946	0.007	0.233	2.963	0.913
0.31	2.196	0.002	0.133	2.265	0.910
0.21	1.431	0.001	0.061	1.504	0.910
0.158	1.057	0	0.035	1.108	0.922
	Annulus No. 4	θ′ = 1.8°	σ′ = 2.42 msr	γ = 1.0004
0.51	6.801	0.888	2.230	3.197	(1.152)
0.41	4.641	0.212	1.440	2.777	(1.076)
0.31	3.008	0.053	0.824	2.167	(0.983)
0.21	1.697	0.017	0.377	1.446	0.901
0.158	1.193	0.007	0.214	1.068	0.910

Source	H₂O	C₆H₆	NBS706
D₀ bias	1.5%	1.3%	1.2%
D₀ random	0.8	0.7	0.6
σ′	0.7	0.7	0.7
l′	0.8	0.8	0.8
G_θ/G₀	0.7	0.3	0.6
Background	1.0	0.8	0.3
	—	—	—
Net	2.3	2.0	1.8

Annulus No. 2
n′ = 1.3274, T = 22°C, λ = 633 nm, θ′ = 4.7°, σ′ = 6.458 × 10⁻³, γ = 1.0030, k = 1.5 cm
H4	G_θD₀/G₀	B(SiO₂)	B(res)	σ′l′	R_θ
0.51	11.220 × 10⁻⁹	0.003 × 10⁻⁹	0.777 × 10⁻⁹	4.063 × 10⁻³	2.57 × 10⁻⁶
0.41	8.637	0.001	0.503	3.177	2.56
0.31	6.532	0	0.287	2.420	2.58
0.21	4.282	0	0.132	1.618	2.56
0.158	3.116	0	0.075	1.188	2.56

Annulus No. 2
n′ = 1.4971, T = 22°C, λ = 633 nm, θ′ = 4.2°, σ′ = 5.074 × 10⁻³, γ = 1.0033, k = 1.5 cm
H4	G_θD₀/G₀	B(res)	σ′l′	R_θ
0.51	45.68 × 10⁻⁹	1.70 × 10⁻⁹	3.604 × 10⁻³	12.20 × 10⁻⁶
0.41	35.84	1.10	2.817	12.33
0.31	26.86	0.63	2.146	12.22
0.21	17.70	0.29	1.435	12.13
0.158	12.93	0.16	1.054	12.12

K = 1.099 × 10⁻⁷, θ = 4.2°
c	${\bar{R}}_{θ}$	K_c/ ${\bar{R}}_{θ}$
NBS705
5.647 × 10⁻⁴ g/ml	10.04 × 10⁻⁶	61.81 × 10⁻⁷
11.294	18.26	67.97
14.118	22.18	69.95
18.824	27.80	74.42
NBS706
2.395	6.49	40.57
3.669	9.69	41.70
3.940	10.32	41.81
4.892	12.60	42.67
4.925	12.65	42.80
5.988	15.28	43.09
7.339	17.93	44.98
9.785	22.72	47.33
9.850	23.12	46.82
11.98	26.99	48.80
14.68	31.55	51.13
14.78	31.90	50.91
19.70	38.68	56.01
23.95	44.04	59.79

	Water	Methanol	Benzene	Toluene
R₄⁶³³(observed)	0.907 × 10⁻⁶	2.56 × 10⁻⁶	12.15 × 10⁻⁶	13.45 × 10⁻⁶
R₀⁶³³ (calc’d.)	0.910 × 10⁻⁶	2.57 × 10⁻⁶	12.19 × 10⁻⁶	13.49 × 10⁻⁶
ρ(633)	? (0.076)	0.050	0.438	0.528
R₉₀⁶³³	0.490 × 10⁻⁶	1.349 × 10⁻⁶	8.765 × 10⁻⁶	10.31 × 10⁻⁶
(n′₅₄₆/n′₆₃₃)²	1.0032	1.0042	1.0115	1.0111
(6328/5461)⁴	1.803	1.803	1.803	1.803
[dn′/dT(546)/dn′/dT(633)]²	? (1.0)	? (1.0)	1.03	1.06
ρ(546)	0.076	0.051	0.416	0.48
C(90,546)/C(90,633)	? (1.0)	1.002	0.936	0.845
R₉₀⁵⁴⁶ (extrap.)	0.886 × 10⁻⁶	2.45 × 10⁻⁶	15.41 × 10⁻⁶	16.83 × 10⁻⁶
R₉₀⁵⁴⁶ (pub. range)	0.865–1.25 × 10⁻⁶	2.42–2.93 × 10⁻⁶	15.4–17.2 × 10⁻⁶	17.2–21 × 10⁻⁶

Abstract

Cited By

Figures (4)

Tables (8)

Equations (20)

Applied Optics