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<TITLE>Re: [RASMB] 3mm centerpieces - the SVENSSON EQUATION</TITLE>
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<BLOCKQUOTE><FONT COLOR="#800000">Greetings everyone -<BR>
<BR>
I come into this discussion a little late - having been away for a week. But reading through some very informative contributions, it does appear that one significant point has been missed, when we are talking about the effect on focussing of the optics in the context of 3 mm path length c'pieces.<BR>
<BR>
The need to focus on the 2/3rds plane to avoid ('Wiener') skewing of the fringe pattern is obvious when you look at the Svensson (1954) equation, which gives the optical difference delta-S (between solution and solvent sectors) as<BR>
<BR>
delta-S = a*dn + a^2(beta*dn/dr)(1-2*r)/2*n0 + a^3((dn/dr)^2*(2-3r))/6n0<BR>
<BR>
where a is the optical path length, beta is the angular aperture, n0 is the refractive index of the solvent and 0<r<1 is measured from the front face of the cell window. dn/dr is the refractive index gradient.<BR>
<BR>
The second term - which to eliminate one would have to focus on the <U>mid</U>-point of the cell - contributes a degree of 'blurring' to the fringe pattern when it is non-zero, but this one can live with. The 3rd term is the killer one. Obviously it becomes zero when the optics are focussed <U>exactly</U> on the 2/3rds position (r = 0.666667). This may not be easy to achieve with 12 mm p'length cells, and - one might suppose - becomes 4x harder if 3 mm p'length cells are used.<BR>
<BR>
However - let us look at that equation a bit more closely. The 3rd term involves the 3rd power (cube) of the optical p'length (= a<I>). </I>So - if we decrease 'a' 4-fold, then the 3rd term becomes 4^3 = 64 times smaller! OK - it is not actually as good as that, since it is the <I>ratio</I> of the 3rd to the 1st term which matters, so in those terms the skewing arising from the 3rd term becomes 4^2 =16 times less important. In other words, a given amount of error in focussing (epsilon-r) will produce <B><U>16 times less problem</U></B> if you are using 3 mm p'length c'pieces as compared to 12 mm ones.<BR>
<BR>
But how big are these effects in real life? Tom correctly recalls that the bigger the gradient of refraction, the worse the effect (note: the 3rd term has the <U>square</U> of the gradient in it): and gives a figure of around 50 fringes/mm for what one can tolerate. Let us have a look at some figures to see what the actual size of the effect can be under plausible conditions.<BR>
<BR>
Peter Lloyd long ago computed that in a 10 mm optical path length cell, optics focussed on the <U>mid</U>-point position (i.e.error of 0.166667 in r), one had to keep the gradient down to <76 fringes/mm** in order to avoid errors in fringe shift of greater than 0.02 fringes. In modern practice the latter level of error is quite unacceptable. In SV work it would result in TD (time-dependent) noise, whilst in SE work one would be for ever identifying small amounts of ill-defined - and in fact non-existent - 'oligomers' as being present.<BR>
<BR>
As a ball-park, to avoid systematic problems arising from this effect, one might go for limiting the problem to stay within the gradient levels which one can actually measure by keeping the error in r to within around ± 0.01, for 12 mm cells: thus confining fringe errors to 0.002 fringes. This means focussing to ± 0.12 mm in real space. Or ± 0.48 mm for 3 mm cells (4x not 16x, because r is scaled relative to a).<BR>
<BR>
The question is: are we happy that these levels of precision are attainable/attained in the XL-I?<BR>
<BR>
Arthur<BR>
<BR>
**Peter's book has a typo in it - the limit of 76 fringes/<U>cm</U> is given. I long ago re-computed this, and checked that the actual figure is 76 fringes/<U>mm</U> for the conditions quoted.<BR>
<BR>
Peter H Lloyd (1974) "Optical Methods in Ultracentrifugation Electrophoresis and Diffusion" Clarendon Press, Oxford, pp. 87=88.<BR>
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</BLOCKQUOTE>-- <BR>
*************************<BR>
Arthur Rowe<BR>
Lab at Sutton Bonington<BR>
tel: +44 115 951 6156<BR>
fax: +44 115 951 6157<BR>
*************************<BR>
<BR>
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<BR>
<BR>
<BR>
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<BLOCKQUOTE><TT>Kristian,<BR>
we've actually made these spacers and systematically compared data quality <BR>
and boundary shapes observed with the 3 mm centerpieces in different <BR>
positions. In our hands, our conclusion was that for most cases there was <BR>
no difference in data quality or information. We will make this data <BR>
available soon.<BR>
Peter<BR>
<BR>
<BR>
<BR>
At 09:34 AM 9/18/2006, you wrote:<BR>
>Hi-<BR>
>Yes you can calculate (or measure) the correct 2/3rds position for the <BR>
>centerpiece, make unequal spacers and drill the cell housing holes at that <BR>
>level. Be aware that the 2/3 position is not the mechanical location, but <BR>
>the optical. These positions differ by a mm or more, and are different for <BR>
>sapphire and quartz window. Those cells would be useful for the <BR>
>interference optics, so it would be best to determine the 2/3 position for <BR>
>sapphire windows. The absorbance optics are focused at the midpoint, so <BR>
>the new housings would not be helpful for them.<BR>
>Best wishes,<BR>
>Tom<BR>
><BR>
>Kristian Schilling wrote:<BR>
>>Tom and Borries,<BR>
>><BR>
>>I am wondering whether we might modify cell housings to overcome that <BR>
>>problem. There is no other need for equal spacers but to align the <BR>
>>centerpiece with the filling holes, so we might just drill the filling <BR>
>>holes at a modified position. Of course that would mean that these <BR>
>>housings can be used only with 3-mm-cps, but the first question is: can <BR>
>>we match the ideal position for the centerpiece and enhance data quality?<BR>
>><BR>
>>Kristian<BR>
>><BR>
>>At 01:07 15.09.2006 -0400, you wrote:<BR>
>>>Hi-<BR>
>>>The spacers for the 3 mm centerpieces place the centerpiece at the <BR>
>>>mid-point of the cell, which is out of focus for the interference <BR>
>>>system, which is focused at the 2/3 plane of a 12-mm centerpiece, with <BR>
>>>sapphire windows and a solvent refractive index of water. Mis-focusing <BR>
>>>will lead to mis-registration of the true radial position with the <BR>
>>>apparent radial position in regions of the image with steep gradients in <BR>
>>>the concentration (1). For the 3 mm centerpieces, the focal plane is <BR>
>>>below the sample 2/3 plane, causing steeper fringes than might be <BR>
>>>expected... i.e. analysis will reveal what appears to be a weak <BR>
>>>association or a heterogeneous system. This problem would also affect <BR>
>>>the absorbance system, but the absorbance optics cannot trace a steep <BR>
>>>enough gradient.<BR>
>>>So long as you keep gradients low enough (as I recall, about 50 fringes <BR>
>>>displacement per mm), your data will be OK.<BR>
>>>Best wishes,<BR>
>>>Tom<BR>
>>><BR>
>>>(1) D. A. Yphantis. Equilibrium Ultracentrifugation of Dilute <BR>
>>>Solutions. Biochemistry 3:297-317, 1964.<BR>
>>><BR>
>>>Borries Demeler wrote:<BR>
>>>>Question about 3 mm centerpieces - the spacers that come with them seem<BR>
>>>>to take it out of the focal plane for the interference system, at least<BR>
>>>>we cannot get 3 mm CPs to work in interference mode. Are there spacers<BR>
>>>>that will correct this issue, or is there something else we should try?<BR>
>>>><BR>
>>>>thanks, -Borries<BR>
>>>>_______________________________________________<BR>
>>>>RASMB mailing list<BR>
>>>>RASMB@rasmb.bbri.org<BR>
>>>>http://rasmb.bbri.org/mailman/listinfo/rasmb<BR>
>>>><BR>
>>><BR>
>>>--<BR>
>>>Department of Biochemistry and Molecular Biology<BR>
>>>University of New Hampshire<BR>
>>>Rudman Hall 379<BR>
>>>46 College Road<BR>
>>>Durham, NH 03824-3544<BR>
>>>Phone: 603-862-2459<BR>
>>>FAX: 603-862-0031<BR>
>>>www.camis.unh.edu<BR>
>>>www.bitc.unh.edu<BR>
>>><BR>
>>><BR>
>>>_______________________________________________<BR>
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>><BR>
>><BR>
>><BR>
>>=================================<BR>
>>Nanolytics<BR>
>>Gesellschaft fuer Kolloidanalytik mbH<BR>
>>Dr. Kristian Schilling<BR>
>><BR>
>>Hauptstr. 20<BR>
>>D-14624 Dallgow<BR>
>><BR>
>>Tel.: +49 3322 24200-5<BR>
>>Fax: +49 3322 24200-6<BR>
>>e-mail: schilling@nanolytics.de<BR>
>>Internet: www.nanolytics.de<BR>
>><BR>
>><BR>
>>_______________________________________________<BR>
>>RASMB mailing list<BR>
>>RASMB@rasmb.bbri.org<BR>
>>http://rasmb.bbri.org/mailman/listinfo/rasmb<BR>
><BR>
>--<BR>
>Department of Biochemistry and Molecular Biology<BR>
>University of New Hampshire<BR>
>Durham, NH 03824-3544<BR>
>Phone: 603-862-2459<BR>
>FAX: 603-862-0031<BR>
>E-mail: Tom.Laue@unh.edu<BR>
>www.bitc.unh.edu<BR>
>www.camis.unh.edu<BR>
><BR>
>_______________________________________________<BR>
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