From: Tom Laue <Tom.Laue@unh.edu>
  To  : rasmb@bbri.harvard.edu
  Date: Wed, 30 Jul 1997 11:05:40 -0400

dn/dc at 670 nm

Dear RASMBers,
I received several useful responses about calibrating a differential
refractometer to measure dn/dc at 670 nm. The responses are excerpted
below. Thanks to David Yphantis, Todd Schuster, Walter Machtle, Alfred
Esser and M.D. Lechner.

Here is a presentation of a general method for visible wavelenths, using a
calculation for 785 nm as an example. This is from David Yphantis.
 
Derivation of estimates for the number of fringes per unit concentration at
785nm

Basis:
	Cauchy equation as used by Perlmann and Longsworth, JACS 70:2719(1948)

	(dn/dc)     = (dn/dc)   * [0.94 + 2E4/lamda**2]
             lamda          578

Data:   (Perlmann & Longsworth)
		BSA @ 435.8nm 			 0.195					$

	(Herskovits,T.T., L.J.Erhunmwunsee, R.C.SanGeorge &A.Herp
	Biochim.Biophys.Acta 667:44-58(1981)
		Callinectes Sapidus HCY @436nm   	0.191+/-0.005 pH7.8  		$
					 		0.196   	pH10.5 		$

	(T.T.Herskovits,R.C.SanGeorge & L.J..Erhunmwunsee
	Biochemistry 20:2580-2587(1981)	)
        	Homarus Americanus HCY @630	 	0.180+/-0.003 @pH7.8 & pH9.5
		see also values with 1M ++ salts, Urea....      			$

	(Ingrid, ChenHo and Casassa)
		Hb @632.8nm 				0.196+/-0.001 in H2O
		    					0.192+/-0.001 in PO4 buffer

	[Stevens + Lauffer (1965)]		
		TMVP @546nm  				0.1856/0.1859           		$

	[Longsworth in chapter on electrophoresis]
		BSA 	@578nm				0.1901	*
		HSA 	@578nm				0.1887	*
	ovalbumin 	@578nm        		0.1876	*
beta-lactoglobulin 	@578 				0.1865	*
gamma-globulin 	@578nm				0.1875	*
human-a1-lipoprotein					0.181
human-b1-lipoprotein					0.174

Data marked by $ was adjusted to the value expected at 578 nm. 
Calculated values of (dn/dc)   from data above marked by  $
                            578
		BSA					0.1866	*
		Calinectes Sapidus HCY  pH7.8	0.1827	*
		Homarus Americanus HCY  pH7.8	0.1817	*
		TMVP                            	0.1844	*

	Average of Starred values:	0.1862 +/-0.0028 cc/g

	From this we estimate that (dn/dc)  = 0.1810+/-0.0028 cc/g
                                         785

	So # fringes at 785 for 1 mg/mL = C[in mg/mL]*0.001* (dn/dc)*1.2
/ 7.85E-5
			       	     = 0.001 * 0.1810 *1.2 / 7.85E-5
			       	     = 2.767+/-0.043 fringes in 12mm
	So 1 fringe @785nm = 0.3614+/-0.0055 g/L

At 670 nm (dn/dc)=0.1833 +/-0.0028
	So # fringes at 670 for 1 mg/mL = 3.283 +/-0.05 fringes

The laser used will produce light at slightly different lines depending on
the drive current and lasing mode (670 - 675). If 675 nm is used instead of
670, dn/dc is 0.1832 and the number of fringes for a 1 mg/ml solution is
3.257+/-0.05. This means that the laser must be driven the same on each
pulse, or there will be a 1% variation in the fringe displacement. 

According to the Wyatt Optilab manual the values for sodium chloride
solutions are:
0.172 mL/g at 690 nm
0.174 ml/g at 633 nm
0.181 ml/g at 488 nm
These values can be used for determining the needed calibration constant at
670 nm.

Other suggested references:

Kruis A. (1936) Zeit Physik. Cem, B34, 13.  

W. Machtle and H. Fischer, Angew. Makromol. Chem. 7 [1969] 147

M.B. Huglin, Specific Refractive Index Increments ......, in J. Brandrup,
E.H. Immergut (Ed.), Polymer Handbook, Wiley, New York 1989

Landolt-Börnstein, New Series, Group III, Volume 38, Optical Constants,
Springer Berlin 1996

A.V. Wolf, G.M. Brown, P.G. Prentiss, Concentrative Properties of Aqueous
Solutions: Conversion Tables, in CRC Handbook of Chemistry and Physics, CRC
Press, Boca Raton, Florida, 1996


Best wishes to all,
Tom Laue