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Towards an understanding of refractometers in wort and beer.

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Lyrebird_Cycles

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As has been well documented, refractometers and densitometers give different results in wort and beer, reflected in multiple sources giving calculations for correction factors for refractometers. This first post will delve into the background of why the discrepancies exist. A follow up will give some data on a better approach to correction factors than the ones commonly used, but still imperfect. This is a work in progress, more data is needed before we can get to a definitive approach.


The density of a solution is determined by the way the molecules pack together which depends on the partial molar volumes of the solutes and solvent and the electrostatic interactions between them. In the case of sugar solutions in water there is very little difference between the ratios of partial molar volume to molecular weight for different sugars so their density / concentration functions are also very similar. For more than you could ever want to know on this see: http://www.ub.uib.no/elpub/2001/h/415001/Hovedoppgave.pdf



A consequence of this is that wt% solutions of glucose, sucrose and maltose as functions of density are almost identical in the ranges in which we are interested.

Refractive index, however, does change between different sugars.

Why?

Refractive index is the ratio of the speed of light in a vacuum to the speed of light in a material. The explanation of why the speed of light changes in different materials involves some fundamental physics: the speed of light in a material is dependent on the square root of the dielectric constant of the material, which in turn is the product of the electric permittivity and the magnetic permeability. Fortunately for us the magnetic permeability of most materials at light wavelengths equals 1 (ferromagnetic materials being the obvious exception). This means we only have to worry about the electric permittivity, which depends on polarisable dipoles: any pair of charged particles separated in space are a dipole, so all materials have plenty of them. These dipoles are excited by the incoming electric field and respond by vibrating at the same frequency but 90 degrees out of phase, with the response wave behind the excitation wave. This causes a net slowing in the speed of light in the material (phase delay).

This means that the number and polarizability of the dipoles determines the net speed of light (Lorentz- Lorenz relation). The number of dipoles per unit volume increases with density, so for a given material the speed of light is inversely proportional to square root of density and refractive index follows this same relationship. Different materials have different dipole arrangements, this changes the mean polarizability which in turn changes the relationship between refractive index and density.

This applies to sugars: different sugars, even when they are isomers of one another, have different dipole arrangements so the relationship between refractive index and density will also change.

Another factor that affects the relationship between refractive index and density is the degree of polymerisation* of the sugar: as the degree of polymerisation increases, the ratio of refractive index to density decreases. The reason for this goes back to the Lorentz Lorenz relation, which depends on the number of molecules per unit volume. This logically decreases with increasing polymerisation (assuming constant density).

Practical refractometers work by using total internal reflection to determine the ratio between the refractive index of the sample and the refractive index of a transparent solid, usually quartz in cheap models and aluminium oxide (sapphire) in better ones.

Assuming you are still following this, we now have the theoretical basis on which we can construct a rational interpretation of the available empirical data.

That will be tomorrow.

* Degree of polymerisation (DP) is a shorthand for the number of hexose moieties per molecule eg glucose DP = 1, sucrose and maltose DP =2, maltotriose DP = 3, maltotetrose DP = 4. For dextrins, another method of expressing this is the dextrose equivalence (DE), the two are related:
DP x DE = 120. The degree of polymerisation of malt derived dextrins varies with the mash profile, a mean degree of polymerisation of 6-8 appears to be typical of the maltodextrin fraction in ordinary worts.
 

GibboQLD

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Reckon you might be one of my favourite posters on AHB Lyrebird, and now you've got me hanging out for the next part...
 

Killer Brew

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Thanks for this LC. If I'm honest a lot of it is beyond my comprehension but I will follow as I'm sure there will be elements I can take away to improve my refractometer usage.
 

MHB

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According to both Kunze and the Handbook of brewing oP is a comparison to a w/w Sucrose solution - really an improved Brix scale.
The current definition most people are using is the one published by the ASBC it takes a whole swath of factors into account, including bouncy in air...

When I'm being really picky (i.e. for research/testing) I fill a 1L Class A Vol flask and weigh it to 0.1g, apply temperature corrections as needed. which give me an error 0.5/1000 (0.05%) close enough and way better than you can measure with anything other than an extremely narrow range hydrometer or a couple of thousand dollar bench top refractometer.

Interesting enough subject, the but being, when the error is smaller than the resolution of the instruments doing the measuring, it all becomes just that interesting, but not very useful in practical home brewing.
Mark
 

Lyrebird_Cycles

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MHB said:
According to both Kunze and the Handbook of brewing oP is a comparison to a w/w Sucrose solution - really an improved Brix scale.
Thanks for that, if I could edit the OP I would.

The last sentence is also wrong: it should read "an average DP of 6 to 8 appears to eb typical".
 

manticle

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Lyrebird_Cycles said:
Thanks for that, if I could edit the OP I would.

The last sentence is also wrong: it should read "an average DP of 6 to 8 appears to eb typical".
You can request a mod to edit for you, especially if information is incorrect or contains typos. If it's merely someone being a dick, we'll usually let that remain as proof (unless it breaches guidelines and we hide it)

So - which sentences would you like changed or replaced? Let me know verbatim here or by PM and I'll change it.
 

Lyrebird_Cycles

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manticle said:
You can request a mod to edit for you, especially if information is incorrect or contains typos. If it's merely someone being a dick, we'll usually let that remain as proof (unless it breaches guidelines and we hide it)

So - which sentences would you like changed or replaced? Let me know verbatim here or by PM and I'll change it.
Lyrebird_Cycles said:
A consequence of this is that Brix (wt% sucrose), Balling (wt% glucose) and Plato (wt% maltose) as functions of density differ only by fractions of a percent in the ranges in which we are interested.
Please change this to:

A consequence of this is that wt% solutions of glucose, sucrose and maltose as functions of density are almost identical in the ranges in which we are interested.

Lyrebird_Cycles said:
The degree of polymerisation of malt derived dextrins varies with the mash profile, an average DP of approximately 6 appears to be typical of the maltodextrin fraction in ordinary worts.
Please change this to:

The degree of polymerisation of malt derived dextrins varies with the mash profile, a mean degree of polymerisation of 6-8 appears to be typical of the maltodextrin fraction in ordinary worts.

Thank you very much.
 

klangers

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I love this.

Two of my favorite things: physics and beer.
 

manticle

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Done on my phone while in a cab on the way to pints..
Let me know if I fucked anything up.
 

Lyrebird_Cycles

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Belatedly: Part 2. Armed with the theory, we can now try to make sense of the available data.

The relationship between refractive index and density for sucrose solutions is standardised, see for instance the first table in: http://faculty.weber.edu/ewalker/Chem2990/Chem%202990%20Refractive%20Index%20Readings.pdf

Getting values for maltose and other dextrins is a little harder. There’s a paper from the 1950s here: http://nvlpubs.nist.gov/nistpubs/jres/46/jresv46n3p165_A1b.pdf but somewhat bizarrely the solution concentrations are given in weight % of maltose hydrate, so we need to scale and interpolate to get meaningful data. Doing so gives pretty good agreement with the data given in this overview: http://chemistry.mdma.ch/hiveboard/rhodium/pdf/chemical-data/prop_aq.pdf .I can find no data for malt sugars of higher molecular weight, but armed with the information from this table:





We can interpolate.

Although the data relates to fructans not glucans*, if you followed the argument in post #1 above the relationship between different degrees of polymerisation within each class of oligosaccharide should be the same. Taking the data in the first and fifth columns the refractive index for maltotriose (DP=3) will be 0.117/0.128 = 91.4% of the value for maltose (DP=2), similarly maltotetrose (DP=4) will be 85.9% and malt dextrins will be approximately 77.3%.

In my opinion the easiest way to define the differences in the data is to take the average slope of the graph of the difference between the refractive index of the substance in question from zero to 10% wt / wt and the absolute refractive index of water at 20 degrees and 597 nm (1.3334)**, so the slope values in wt % for the various sugars become:

Sugar Slope % Sucrose response

Glucose .00143 99.3%

Sucrose .00144 100%

Maltose .00148 102.8%

Maltotriose .00135 93.9%

Maltotetrose .00127 88.3%

Malt dextrins .00111 77.1%

Since refractometers are routinely calibrated for sucrose (Brix), I have also shown the percentage response that would be expected for the different sugars. The value for Malt dextrins is a weighted average of the values for DP = 5 to 10.

I have done the same calculation for alcohol, but this time the value is scaled to ABV rather than wt% and since the curve is non-linear, I took the average to 5% ABV not 10 as it will be more representative of standard beers.

Alcohol (5%) .00048 33.6%

The first thing to notice is that maltose, the dominant sugar in wort, is almost 3% higher than sucrose, thus explaining some of the observed discrepancy when refractometers are used on wort and the need for a wort correction factor.

The second thing to notice is that the sugars which are the typical components of dissolved solids in attenuated worts (maltotriose and higher) are between about 77% and 94% of the sucrose value, thus explaining why using the wort correction factor on attenuated worts produces an error.

So how do we know what factor to use?

Well a while ago when I had access to an Anton Paar Alcoliser, an Anton Paar Density meter and my trusty Atago refractometer I measured all three parameters on a range of commercial beers:


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The value Alc D represents the expected equivalent Brix correction for the measured ABV using the standard value for alcohol obscuration of extract at 0.272 degrees Be / ABV and converting to Brix by multiplying by 1.8 (= 0.49 Bx / ABV). The next value is the corrected Brix by density. The value Alc R represents the expected equivalent brix correction for the measured ABV from the value in the table above. The next value is the corrected Brix by refractometry.

The last column shows the ratio between them, which is to say the ratio of the measured attenuated wort solids by refractometer to that measured by densitometer.

As can be seen all these beers fell in a fairly narrow range centred on a refractometer correction of about 0.9, so that seems to be a good value to use for now.

* Dextrins are a subclass of glucans.
** The value commonly used in literature is the relative refractive index of water in air = 1.3330.
 

Killer Brew

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Lyrebird_Cycles said:
As can be seen all these beers fell in a fairly narrow range centred on a refractometer correction of about 0.9, so that seems to be a good value to use for now.

* Dextrins are a subclass of glucans.
** The value commonly used in literature is the relative refractive index of water in air = 1.3330.
Thanks for this LC. Just coming back to it as haven't brewed since you put it together so this is the first chance I have had to try it out. So that I'm clear you are recommending a 0.9 correction factor regardless of the stage of the ferment (outside of OG obviously)?

To put that in a simple example to ensure I'm on the right track.

OG - reading 12P degrees; adjusted = 12P degrees or 1.048
24hrs - reading 10P degrees; adjusted = 9P degrees or 1.036
48hrs - reading 8P degrees; adjusted = 7.2P degrees or 1.029
72hrs - reading 7P degrees; adjusted = 6.3 degrees or 1.025

Okay?
 

Lyrebird_Cycles

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No.

I have not got a reliable handle on how to quantify the change as the various sugars ferment out.

For my own purposes I just calculate the expected end point using the 0.9 factor and work out the apparent extent of fermentation from the difference between initial wort concentration and this expected end point.

In your case: start reading 12 oP, correction is 1.04 so actual start conc is ~11.5.

Assuming your expected apparent FG (as measured by density) is around 3 oP, that should show as a reading of about 6.7 oP on the refractometer*, ABV will be around 5.2%.

In that case your reading at 10 oP is around (12 - 10) / (12 - 6.7) = 2 / 5.3 = 37% fermented so ABV is around 2%.




* I am not yet confident that the algorithm I used to derive this value is robust enough to publish. I am hoping to get access to some good instrumentation over the next little while and I may have more to report then.
 

Killer Brew

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Bugger. Thought that sounded too easy. Thanks for the response and work so far LC.
 

good4whatAlesU

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hmmm very interesting.

I just bought an Atago PAL 1 for work - (rockmelon and blueberry brix measurements). We look at the sugars under different treatments and see if there are significant differences in concentration (e.g. Blueberries grown above a black plastic weed mat, Blueberries grown above a white plastic weed mat)... I think it shall be coming home occasionally on weekends for "calibration" requirements.

Edit: The calibration certificate (report) that comes in the box says it was measured in:

1. Distilled water
2. "Sugar solution" 30%
3. "Sugar solution" 50%

I wonder what type of 'Sugar solution" they used to calibrate it? .. Could email ATAGO and find out.
 

Lyrebird_Cycles

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Anhydrous sucrose (which is basically ordinary sugar dried in an oven).

I rechecked the calibration on mine last week (it's eight years old) at 10 Brix and 20 Brix, still spot on. The zero point calibration is checked every time I use it.

I also checked my hydrometers, the 0 - 10 Brix one is fine, the 10 - 20 reads 0.2 Brix low.


Procedure was as follows:


Dry ~120 g of table sugar to constant weight +/- 0.1g in a 120 oC oven.

Weigh out 100.0 g dried sucrose, add 400.0 g of clean water (Melbourne tapwater is fine) = 20 Brix solution.

Take 200.0g of this solution, add 200.0g clean water = 10 Brix solution.
 

Lyrebird_Cycles

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BTW when using them on fruit: you will probably find a discrepancy between the sugar level as indicated by the refractometer and that indicated by densitometry, especially in under ripe fruit.

If you check the acid level, you will find a correlation between the acid and the discrepancy which in turn depends on the type(s) of acid present in the fruit. It's quite noticeable on underripe grapes (dominant acids are tartaric and malic), I don't know about blueberries.
 

good4whatAlesU

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Good info, thanks. Yes we are getting acidity tested too on the extracted juice but I'm not sure about type /speciation.. Some kind of ratio between acidity and sugars for my bosses paper..

If they can ripen fruit and get it to consumers early maybe a market advantage at certain times of year etc.
 
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