Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C. ch. 3.2, pp. 156-158

Section Gradient tube

F. M. Richardsa Gradient tube

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This technique is simple, versatile, and capable of the greatest sensitivity. It is the method of choice except in those cases where immersion liquids with an appropriate density and chemical inertness cannot be found.

Originally devised by Linderstrom-Lang (Linderstrom-Lang, 1937[link]; Linderstrom-Lang & Lanz, 1938[link]) for the determination of the density of aqueous solutions, the procedure has been adapted for the measurement of crystal densities by Low & Richards (1952a[link]). For the original solution measurements, a precision of 0.000001 g ml−1 was obtained, although no attempt has been made to attain that precision with solids. This technique was apparently developed and used quite independently in the sugar-cane industry [see, for example, Guo & White (1983[link]) and earlier references contained therein]. Technique

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When one liquid is layered over another of greater specific gravity, with which it is miscible, a linear gradient of density develops near the interface. Manipulation of a plunger-type stirrer in a vertical tube can extend the gradient over the greater part of the column. In the absence of convection, the process of diffusion in a column of this type is so slow that the gradient will be maintained virtually unchanged for many months.

A crystal introduced into the tube falls until it reaches a level corresponding to its own density, where it will remain stationary. The density gradient may be calibrated either by introducing immiscible liquid drops of known density, or by the use of a micro-Westphal balance designed for the purpose (Richards & Thompson, 1952[link]).

With an adequate thermostat, measurements may be made at any temperature between the freezing and boiling points of the mixtures involved.

Powders and crystals with cavities or inclusions may be ground to a slurry with the lighter column liquid, subjected to reduced pressure to remove trapped air bubbles, and then introduced into the gradient tube. With hygroscopic materials, these operations are carried out in a dry atmosphere. Finely divided material settles rapidly if the tube is centrifuged. Although centrifugation does not markedly affect the gradient, the column should be calibrated after this step.

If such samples are homogeneous, they will form a thin layer after centrifuging. If, on the other hand, some air bubbles or inclusions still remain, or if the sample is truly a mixture, a stable distribution of material will be observed. The density of the material of interest can then usually be obtained by measurement of the appropriate layer, generally the most dense, without further treatment of the sample. This is the only technique by which the homogeneity of the sample can be tested simply. All other methods provide an average density value. A satisfactory technique for removing crystalline powders from the gradient column has not been devised. If a precision of ±0.002 g ml−1 is adequate, it is simplest to prepare a new wide-range column for each determination in a 10 ml test tube.

Detailed specifications for the preparation of large density-gradient columns are contained in the records of the British Standards Institution (1964[link]). In the experience of the author, for ordinary laboratory use, the procedures described are unnecessarily complicated as is the large scale of the system. The large columns are not suitable for centrifuging and the settling times tend to be many hours. However, if extreme sensitivity (i.e. use of a shallow gradient) is required, the large column may be useful, as it was in the original studies of Linderstrom-Lang (Linderstrom-Lang, 1937[link]; Linderstrom-Lang & Lanz, 1938[link]).

In the specific application of this technique to protein crystals, where a gradient of organic liquids is used, it is necessary to have available crystals sufficiently large that they can individually be quickly wiped free of adhering mother liquor with dampened filter paper before insertion. The uncertainty of successful cleaning combined with rapid evaporation of liquid from the pores within the crystal always affect the estimated accuracy of the measurement. An important improvement in the technique has been made by Westbrook (1976[link], 1985[link]) through the use of concentrated aqueous solutions of the water-soluble polymer Ficoll. This very high molecular weight polysaccharide can be dissolved in water to concentrations of at least 60% by weight. The solutions are very viscous but do provide satisfactory water-based gradient columns. The polymer is both too large to enter the solvent-filled pores of the protein crystals and too high in molecular weight to develop a significant osmotic pressure. An aqueous suspension of crystals can be added directly to the column. This procedure has been adapted for measurements of protein-crystal density under hydrostatic pressures from 1 to 2000 atm (1 atm [\equiv] 101 325 Pa) (Kundrot & Richards, 1988[link]). The general principle of using high-polymer-based gradients can presumably be extended to other porous materials. Suitable substances for columns

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Some representative liquids are listed in Table[link]; all are readily available. For further information, see Meyrowitz, Cuttitta & Hickling (1959[link]), and for very heavy liquids Sullivan (1927[link]). Standardized solutions or mixtures from one list in Table[link] may be used as calibrating drops in gradients made from those of the other.

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Possible substances for use as gradient-column components

Hydrophobic componentsHydrophilic components
LiquidApproximate density at 298 K (g ml−1)αSoluteApproximate maximum density of concentrated aqueous solution at 298 K (g ml−1)
Isooctane (2-methylheptane) 0.69 −0.8 Sodium chloride 1.20
Kerosene 0.79 −0.5 −0.8 Potassium chloride 1.40
m-Xylene 0.86 −0.85 Potassium iodide 1.63
Chlorobenzene 1.10 −1.1 Iron(III) sulfate 1.80
Bromobenzene 1.49 −1.3 Zinc bromide 2.00
Carbon tetrachloride 1.60 −1.9 Zinc iodide 2.39
Methyl iodide 2.28 −2.7 Thallium(I) formate 3.5
Bromoform 2.89 −0.9 Thallium(I) formate–malonate 4.3
s-Tetrabromoethane 2.96 −2.2    
Methylene iodide 3.32 −2.6 Ficoll (60% w/w in water) 1.25

The density at temperature T K can be computed by substituting the values of the density at 298 K and α in the formula dT = d298 + 10−3α(T − 298).
Trade name for a synthetic high-molecular-weight polysaccharide derivative.

For rapid preparation of mixtures from stock solutions of the basic compounds, a nomogram is very useful, such as is given in Fig.[link] for the system bromobenzene–xylene at room temperature. In the construction of the nomogram, it has been assumed that the volumes of the liquids are additive. In general, this assumption is not valid, but it is a sufficiently good approximation for the purpose.


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Nomogram for the preparation of bromobenzene–xylene gradient column components at room temperature. From the desired component density and total volume, the required amount of bromobenzene is read from the chart, the volume difference being made up with xylene. To adapt this chart to any other pair of liquids, it is only necessary to change the component density scale. A uniform scale is drawn up such that the density of the heavy liquid lies at the point A while that of the light liquid is at B. The volume scales may be multiplied by any constant factor in order to change their range. Sensitivity

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The range of density covered by a column, and thus the accuracy of the determination, is controlled by the liquids or liquid mixtures chosen for the top and bottom components. A precision of about [\pm0.002] g ml−1 can easily be obtained without any special precautions. If narrow-range columns are carefully protected from temperature changes and vibration, the accuracy of the measurement may be increased 10- to 100-fold.


First citationBritish Standards Institution (1964). Concentration gradient density columns. British Standard 3715, pp. 1–17. British Standards Institution, London, England. Google Scholar
First citationGuo, S. Y. & White, E. T. (1983). Measurement on inclusions in sugar crystals using a density gradient column. Proc. Austr. Soc. Sugar Cane Technol. pp. 219–224.Google Scholar
First citationKundrot, C. E. & Richards, F. M. (1988). Effect of hydrostatic pressure on the solvent in crystals of hen egg-white lysozyme. J. Mol. Biol. 200, 401–410.Google Scholar
First citationLinderstrom-Lang, K. (1937). Dilatometric ultra-microestimation of peptidase activity. Nature (London), 139, 713–714. Google Scholar
First citationLinderstrom-Lang, K. & Lanz, H. Jr (1938). Studies on enzymatic histochemistry. XXIX. Dilatometric micro-estimation of peptidase activity. C. R. Trav. Lab. Carlsberg Ser. Chim. 21, 315–338. Google Scholar
First citationLow, B. W. & Richards, F. M. (1952a). The use of the gradient tube for the determination of crystal densities. J. Am. Chem. Soc. 74, 1660–1666.Google Scholar
First citationMeyrowitz, R., Cuttitta, F. & Hickling, N. (1959). A new diluent for bromoform in heavy liquid separation of minerals. Am. Mineral. 44, 884–885.Google Scholar
First citationRichards, F. M. & Thompson, T. E. (1952). Application of Mohr–Westphal balance to rapid calibration of wide range density-gradient columns. Anal. Chem. 24, 1052–1053. Google Scholar
First citationSullivan, J. D. (1927). Heavy liquids for mineralogical analyses. US Bur. Mines Tech. Pap. No. 381.Google Scholar
First citationWestbrook, E. M. (1976). J. Mol. Biol. 103, 659–664.Google Scholar
First citationWestbrook, E. M. (1985). Methods Enzymol. 114, 187–196.Google Scholar

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