Developer Temperature Compensation Formula

Discussion in 'B&W: Film, Paper, Chemistry' started by schwefel, Jul 15, 2008.

  1. schwefel

    schwefel Member

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    I did some searching, on here and am not finding much.

    I am looking for the formula for determining the temperature compensation for developers. Based on what I remember from chemistry class, I came up with the following formula:

    (10th root of 2)^ΔT for Celcius.

    [10th root of 2 raised to the differece in temperature]

    When looking at some of the charts I found online, it does not match up.

    Anyone out here know the formula?

    Thanks,

    Jason

    Jason
     
  2. Photo Engineer

    Photo Engineer Subscriber

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    Jason;

    There is no rule AFAIK for adjusting development time with temperature. Kodak has published curves for time vs temp for several film and developer combinations. Some are posted on their web site.

    PE
     
  3. Paul Verizzo

    Paul Verizzo Member

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    As they say, "It depends!"

    Developers with one agent can have a defined delta, but each agent is different, although most of the common ones are pretty similar. Developers with two agents, with the ususal hydroquinone as one, is valid only in a narrow range. HQ changes activity at four times the rate of Metol, for instance (IIRC). Therefore, the negative characteristics will change with any significant change in temperature.
     
  4. johnnywalker

    johnnywalker Subscriber

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    Ilford has a chart on their website as well.
     
  5. Lee L

    Lee L Member

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    There's another recent thread on this is at: http://www.apug.org/forums/forum37/50284-how-accurate-using-time-compensate-temp.html

    I posted a .pdf chart there for D-76 time vs temp data from Kodak for multiple films. I've seen some formulae posted by Michael Covington and by others here on APUG, and also ran a regression recently to find out what made the Kodak Darkroom Dataguide development time vs temp wheel work. I got formulae, but if you look at the various specific manufacturer's time vs temp charts, you'll find that the formulae and curves found lying around are mostly generic, and designed to be close for most films and developers, and are probably close to exactly correct in a few cases.

    P.E. and others have the answer, there's not a single answer/formula for all films or all developers.

    Lee
     
  6. RobC

    RobC Member

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    The Ilford film datasheets each have a chart from which you can read off temp/time equivalents. But I guess they will all be based on ID11.
     
  7. df cardwell

    df cardwell Subscriber

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    Here are Kodak's contrast curves for good old 35mm / 120 Tri X.
    Some have a similar slope, some do not.

    Kodak publishes a LOT of good info like this.

    Older data shows the effect of temperature.
     

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  8. Tom Hoskinson

    Tom Hoskinson Member

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    Yes, Jason: The Arrhenius Rate Law is applicable
    Rate = A exp(-B/T)

    The constants A and B in the Arrhenius rate law are empirical and differ from one reaction to another. However, the empirical values of B are found to be similar for many chemical reactions. One result of this similarity is the useful generalization that for many reactions which occur near room temperature, a temperature increase of 10oC approximately doubles the rate of the reaction.

    Reference: http://www.ualberta.ca/~jplambec/che/p102/p02151.htm

    I use algebra to obtain the necessary constants from the published Kodak, Ilford, etc time and temperature development data for specific films and developers.
     
  9. Paul Verizzo

    Paul Verizzo Member

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    Or use Diafine! :D
     
  10. ic-racer

    ic-racer Member

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    For years I used this equation with a 'room temp.' method. The equation is taken from the Kodak darkroom dataguide. I remember using my first computer (Commadore 65) to decode the Kodak wheel back in the 80s. Later I put the equation into an Excel spreadsheet.

    New Decimal Time=((X_Constant*($B$6-(Temp * Y_Constant))/(1+(Temp * X_Constant)))+Y_Constant)*(LOG(A9))+($B$6-(Temp * Y_Constant))/(1+(Temp * X_Constant))


    x_constant =-0.6205672
    y_constant = -0.576929
    $B$6 = base time (min)
    Temp = base temp (degrees)
    A9 = new temp

    To convert to minutes and seconds:

    Minutes and seconds =INT(decimal time[-1]) + ((decimal time[-1]-INT(decimal time[-1])))*0.6


    (working spreadsheet available to anyone who asks)
     
  11. Photo Engineer

    Photo Engineer Subscriber

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    The problem with the Kodawheel is that it has a different "constant" to be applied to each film-developer combination that causes an offset unique to the wheel which is non-linear. So, the above equation in post #10 will only work for one unique combination from a table of constants that is a 7 x 23 matrix of offsets. I'm sorry, but I would not trust that equation for general use.

    PE
     
  12. Tom Hoskinson

    Tom Hoskinson Member

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    I agree, P.E. Using an Arrhenius chemical reaction rate equation as a model, each film/developer combination would be be expected to have a unique pair of empirical constants:

    1. The activation energy for the chemical reaction.
    2. The pre-exponential factor (also called the frequency factor).

    Thus Rate = A exp(-B/T) where T is the Developer temperature in °C+273, B is the Activation energy and A is the frequency factor



    Thus the rate of a chemical reaction increases exponentially as the absolute temperature increases.
     
  13. Photo Engineer

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    Add into that any synergy between the developing agents and all bets are off.

    I explained that at Kodak we had begun to exploit electron transfer agents in development. This offset all of this again and is used in the Liquidol developer that Bill Troop and I designed. I suspect it would behave in a very non-linear fashion, but since the use temperature is 20 C, I have never tested it above that.

    Kodak used to publish tables for film developer temperature combinations, but I guess much of that is a thing of the past. I have looked up a few of the ones I have, but they are mostly meaningless as many relate to discontinued products.

    I have the 2 page matrix and "wheel" sitting next to me. It is a marvel of engineering that works out all possible non-linear combinations of time and temp from 60 to 80 F for B&W films. That took a lot of lab work.

    PE
     
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  15. fschifano

    fschifano Member

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    Sure thing. I like spreadsheets. Can you post it to this thread as an attachment?
     
  16. Photo Engineer

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    Why? It may not work!

    PE
     
  17. ic-racer

    ic-racer Member

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    Here it is. It follows the "12-74-IX Minor Revision, (c)1974" datawheel exactly. In this version of the wheel, all developer/film combos behave the same ON THE WHEEL. Those green, red and blue boxes have nothing to do with temp. response. That is, all 8min/20C film/dev. combos have the same temp. response ACCORDING TO THIS WHEEL. They don't really in real life so.....
     

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  18. ic-racer

    ic-racer Member

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    T-Max

    When T-max came out in the 80s I modified the equation, again using Kodak's data. This one follows the time-temp info that came with the 1980s T-max film pretty closely. I follows Kodak's consumer data for rotary processing T-max 400 in T-max developer. I used these two sheets (originally generated on the C64) for about 15 years until I got a temp. controlled Jobo.
     

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  19. ic-racer

    ic-racer Member

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    To use the spreadsheet, just put your baseline time and temp at the top of a column and the new time/temp data will fill in the column below.
     
  20. fschifano

    fschifano Member

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    Thanks. I'll compare it to what Ilford has on their compensation chart.
     
  21. Photo Engineer

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    Kodak has published a modern revised edition of the B&W Darkroom Dataguide with modern film and developer recommendations including time and temperature information.

    This sixth edition has 8 pages of time/temp information.

    PE
     
  22. ic-racer

    ic-racer Member

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    All the equations are in the spreadsheets, so you may be able to fiddle with it to get a good fit with the Ilford data.

    If you like math and are curious how I came up with the equation, I just plotted the time/temp data with the C64 and then manipulated the x and y axis values (ie log, square, square root, etc) until I found a combination that produced the lowest standard deviation for the line (ie, the straightest line). This was not very difficult, as I had to write my own line-plotting program, and distorting the axes was easy. I think if I were to do it again today I would use some software I have been using to fit polynomials to H&D curves. The only problem I have with that is once I have the polynomial equation, I don't have good way to solve it.

    Not sure if PE was implying the Manufacturers temp compensation data is good or not. I always used their temp compensation data. I figured it was like ISO testing; that is, I am not likely to have equipment accurate or sensitive enough to dispute the Manufacturer. Is there any value to test and generate a 'personal temp compensation index,' (like doing your 'personal exposure index')? I don't know, but I am always open to ideas. I just figure the thermal properties of mater are similar between my darkroom and the Manufacturer's lab.
     
  23. Photo Engineer

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    I was pointing out that you have one set of constants for the entire equation, but Kodak points out that the wheel must be adjusted in a non-linear fashion and they give a matrix as I described, of different constants for each film and developer. I was wondering how your formula could do that, as it seemed not able to take into account all of the Kodak constants.

    PE
     
  24. df cardwell

    df cardwell Subscriber

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    From a table by J.M. Eder,
    published many times,
    taken here from “Developing”,
    by CI Jacobson,
    13th edition, Focal Press, 1955.

    “The increase in speed of develpoment with an increase of 10˚ Centigrade is taken as the Temperature Coefficient of the developer. For example, if we find that a certain developer works twice as quickly (at 25˚ as it did at 15˚), then we say it has a Temperature Coefficient of 2."

    While I think this is only useful as a guide, it IS helpful to see the factors in play.

    Temperature Coefficients of Various Developers
    Metol-Soda 1.5
    Metol-HQ 1.7-1.9
    HQ-Soda 2.2-2.6
    Pyro-Soda 2.2-2.4
    Rodinal 2.0
    Glycin-Potash 2.5-2.7
    Pyrocatechin-Potash 2.8

    This should illustrate why a single correction curve for all developers is invalid. FURTHER, films play a factor. In Kodak published curves,
    you can see that D-76 and Microdol-X are sometimes, but not always, parallel.

    While a single correction factor is a good estimator,
    so is an experienced hunch. A notebook usually is much better .

    Rodinal, whose times should double from 59 to 77 degrees F, comes close with some films, but depending upon the degree of development (gamma, or CI). Here are three AGFA curves, for 3 well-missed films. See that the the lines curve, and are seldom parallel. Two Rodinal dilutions are shown, as well as Studional/Rodinal Special.
     

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  25. ic-racer

    ic-racer Member

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    Ok, I think I see what you are saying, my wheel may now be outdated. My 1974 Kodak wheel has a table with numbers in the 30s to 40s, but there is nothing that interacts with the wheel function. For example, in the table in front of me, all 4 film/developer combos that have number 38.5 all have a baseline time of 9 min at 20c and about 10.5 min at 18c based on the wheel. There is no notation that one would spin the wheel farther or differently for each of the 4 different combinations. I agree with you 100% that those different film/dev. combos probably won't respond the same, but my wheel says they do, and the equation follows the wheel exactly. The best thing as you are saying would be a separate equations for each combination, but as far as I knew Kodak never provided this until I saw the T-max literature, at which time I deciphered it to come up with a new equation.
     
  26. Photo Engineer

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    DF has shown it well. IC, note that in that table, you are talking about 3 films in 4 different developers and the fact that they may have the same coefficients is merely coincidence. So, in that table, Royal X pan in Polydol behaves like Super XX in HC110 B. In DK-50, these two films are a 34 and a 36 which would be quite far apart. And as the above charts show, behavior is non-linear.

    PE