Activity of developing agents as a function of temperature

[Romanko]

I vaguely remember seeing a figure showing activity of developing agents as a function of temperature. It looked somewhat similar to the density vs. pH plot below. I can't remember where I saw it. It must have been in one of the old books. Any help is much appreciated.

(The curves are: 1 - metol, 2 - pyrogallol, 3 - hydroquinone, and 4 - paraphenylenediamine)

 

[Raghu Kuvempunagar]

This pH dependence graph is taken from here:

Fundamentals of Photographic theory, by T. H. James [and] George C. Higgins.

You can perhaps browse the book and find out if there is a similar graph for temperature.

 

[Romanko]

there is a similar graph for temperature

Thanks a lot! It is on page 123 of this book.

 

[Romanko]

Also in The Theory of Photographic Process by Kenneth Mees, 1942.

 

[albada]

The Zone VI temperature-compensating development-timer would compensate for temperature by making each "second" shorter or longer. It had a switch on the front for "paper" or "film", and I've always wondered what exponent or formula it used for both. I put such a timer in my LED controller, and chose to use the exponent from Ilford's temperature-compensation table, which is an 8.8% time-change per degree-change (in C). Most developer formulations nowadays contain two developers working in concert, so I'm afraid one will need to measure temperature-vs-time by experiment with those. Or use 8.8% and hope that's close enough. If you use Metol alone, as in D-23, the graph above says the constant is 10 ^ (log(2/1.07) / 5) = 1.133 which is 13.3% per degree C.

 

[Romanko]

Most developer formulations nowadays contain two developers working in concert, so I'm afraid one will need to measure temperature-vs-time by experiment with those.

The data above is for individual developer agents. If you have a developer with two (or more) superadditive agents you need to know the curve for this developer/film combination. You can use the following approximation:
dev_time = exp(a + b * T)
where a and b are film- and developer-specific constants that can be found by linear regression using three data points provided by the developer/film manufacturer. Here's an example for Tri-X in HC-110(B). I would use this curve only for temperatures between about 15 and 25 degrees. For extreme conditions you have to do tests, of course. Kodak does not recommend development times shorter than 4 minutes in HC-110, anyway.

 

[albada]

Mees-James, 3rd edition (1966), page 371, says:

The temperature-dependence on the rate of development can be expressed roughly in terms of the temperature coefficient. This coefficient is the ratio of the rate at a particular temperature to the rate at a temperature 10 [degrees] lower on the Centigrade [...] scale.​

A table of coefficients follows. For example, the coefficient of D-76 is 2.8, which is 1.108/degree, or 10.8%/degree. That means for each degree rise in temperature, development rate increases by 10.8%. Coefficients vary widely, from 3.9 for Windisch 665 down to 1.9 for Agfa 15.

 

[Romanko]

Mees-James, 3rd edition (1966), page 371, says:

The temperature-dependence on the rate of development can be expressed roughly in terms of the temperature coefficient. This coefficient is the ratio of the rate at a particular temperature to the rate at a temperature 10 [degrees] lower on the Centigrade [...] scale.​

A table of coefficients follows. For example, the coefficient of D-76 is 2.8, which is 1.108/degree, or 10.8%/degree. That means for each degree rise in temperature, development rate increases by 10.8%. Coefficients vary widely, from 3.9 for Windisch 665 down to 1.9 for Agfa 15.

This is a more convenient way of calculating the development time, especially if you don't have a computer at hand or can't be bothered with regression analysis. Also, it requires only one data point (development time; temperature) and the temperature coefficient which according to Mees is independent of the film.

 

[snusmumriken]

If you use Metol alone, as in D-23, the graph above says the constant is 10 ^ (log(2/1.07) / 5) = 1.133 which is 13.3% per degree C.

Would you be kind and explain how you got that from the graph?

 

[snusmumriken]

Would you be kind and explain how you got that from the graph?

It's OK, I think I've worked it out. Had to scrape away some adult brain sludge to rediscover school maths.

You read the time values for the relatively straight line segment from 17 to 22 deg C, which are respectively 2 and 1.07 units on the y-axis. Although the y-axis is plotted logarithmically, the numbers shown are not log values (misleading description!). Development time at 17 deg must be 2/1.07=1.87 times greater than at 22 deg. You take the log of 1.87 to get it into the same x-y space as the plotted curve. It's a 5 deg range, hence you divide that log value by 5 to get the log change per degree. Take the antilog (10 to the power of ...) of the result, and you have a multiplication factor per degree for times in ordinary units. A multiplication factor of 1.133 is the same as 113.3% or an increase of 13.3% for every degree.

Have I got that right?

 

[snusmumriken]

This is a more convenient way of calculating the development time, especially if you don't have a computer at hand or can't be bothered with regression analysis. Also, it requires only one data point (development time; temperature) and the temperature coefficient which according to Mees is independent of the film.

Presumably this is like working out compound interest?

In the metol example, the graph data show that you need to increase development time by a factor of 1.87 (i.e. 87% increase) if your temperature is 17 deg rather than 22. If you mistakenly took 5 times 13.3%, you'd increase it by only 1.665 (i.e. 66.5% increase). If development time is (say) 4 minutes at 22 deg, that's the difference between 7 min 29 sec (correct) and 6 min 40 sec (11% too short) at 17 deg.

To be correct, you need to calculate t x coefficienttemp diff for a lower temperature, or t / coefficienttemp diff for a higher temperature. Is that right?

 

[Romanko]

To be correct, you need to calculate t x coefficientdifference in temperature for a lower temperature, or t / coefficientdifference in temperature. Is that right?

Almost. Choose the sign of your temperature difference, for example positive temperature difference means you are developing at at temperature (t) lower than the temperature (t_ref) for which the development time is known (Time_ref). Then the equation is

Time = Time_ref * coefficient^(t_ref - t)

If the difference is negative (development at higher temperature) the same equation is used. It is equivalent to Time = exp(a + b*t) that I used to plot the curve.

 

[snusmumriken]

Almost. Choose the sign of your temperature difference, for example positive temperature difference means you are developing at at temperature (t) lower than the temperature (t_ref) for which the development time is known (Time_ref). Then the equation is

Time = Time_ref * coefficient^(t_ref - t)

If the difference is negative (development at higher temperature) the same equation is used. It is equivalent to Time = exp(a + b*t) that I used to plot the curve.

Great, thanks. So what I was heading towards was to make an Ilford-style time-temperature chart for a metol-only developer. I think this is right, but it would be kind if someone would check it.

 

[albada]

It's OK, I think I've worked it out. Had to scrape away some adult brain sludge to rediscover school maths.

You read the time values for the relatively straight line segment from 17 to 22 deg C, which are respectively 2 and 1.07 units on the y-axis. Although the y-axis is plotted logarithmically, the numbers shown are not log values (misleading description!). Development time at 17 deg must be 2/1.07=1.87 times greater than at 22 deg. You take the log of 1.87 to get it into the same x-y space as the plotted curve. It's a 5 deg range, hence you divide that log value by 5 to get the log change per degree. Take the antilog (10 to the power of ...) of the result, and you have a multiplication factor per degree for times in ordinary units. A multiplication factor of 1.133 is the same as 113.3% or an increase of 13.3% for every degree.

Have I got that right?

That's exactly right (assuming I got it right).
And yes, it's like compounding interest, as @Romanko showed in his formula in posting #12.

 

[Romanko]

I was heading towards was to make an Ilford-style time-temperature chart

The family of curves is for different films or developer concenrations, right?
The plots look correct to me, should be straight lines if you make your time axis logarithmic. (Linear time scale is easier to use, so don't do this).
I like this idea. It might be worthwhile to get the HC-110 data sheet and plot development times in this fashion.

 

[albada]

Great, thanks. So what I was heading towards was to make an Ilford-style time-temperature chart for a metal-only developer. I think this is right, but it would be kind if someone would check it.
View attachment 322934

It appears that your base temperature is 22 degrees, and that the curves represent the base times of 2, 3, 4, 5, 6, 7, 8. By looking at the topmost curve, I estimated that your temperature coefficient is 1.13, which agrees with an earlier posting. Looks good to me.
I suppose a good test is to develop a strip at 19.5 degrees for 4 minutes, and another at 25 degrees for 2 minutes, and verify that their densities are equal.

 

[snusmumriken]

The family of curves is for different films or developer concenrations, right?

Not exactly. If you know your dev time at a given temp, you find that point on a curve, then trace it along to the temp you want. To make the curves I started with whole numbers of minutes at 22 deg. As Ilford do, I’ve not over-cluttered the graph, as it’s easy to imagine intermediate curves.

 

[snusmumriken]

It appears that your base temperature is 22 degrees, and that the curves represent the base times of 2, 3, 4, 5, 6, 7, 8. By looking at the topmost curve, I estimated that your temperature coefficient is 1.13, which agrees with an earlier posting. Looks good to me.
I suppose a good test is to develop a strip at 19.5 degrees for 4 minutes, and another at 25 degrees for 2 minutes, and verify that their densities are equal.

Yes, but I’ll have to leave that to someone else as I don’t have a densitometer.

 

[Romanko]

Not exactly. If you know your dev time at a given temp, you find that point on a curve, then trace it along to the temp you want. To make the curves I started with whole numbers of minutes at 22 deg. As Ilford do, I’ve not over-cluttered the graph, as it’s easy to imagine intermediate curves.

Yes, we are talking about the same thing here. If you shoot a different film your known development time will be different for the same temperature of 22 degrees. You pick a curve closest to your time and trace along this curve to the desired temperature. Thus, each film will have its own curve. The same is true for developer concentrations.

If someone compiles the datasheets from major developer and film manufacturers this could be a pretty neat online calculator. I am not sure how practical it is, though. Most photographers shoot just several films they know and would establish their own development process. So who would need such resource?

 

[albada]

Yes, but I’ll have to leave that to someone else as I don’t have a densitometer.

High precision is not needed for this test, so you could hold both strips before a lampshade or on a light table, and judge their equality by eye. I would feel uneasy relying on a temperature coefficient that was determined over 50 years ago.

Actually, you do have a densitometer: Your light meter. Hold each strip over the meter's sensor with a bright light nearby, subtract the readings and multiply that by 0.3. That's the density difference.

 

[snusmumriken]

So who would need such resource?

I’ve got a decent darkroom now, and find it easy to raise my chemicals to a standard 22deg C. That wasn’t always the case - I often had to process at ambient temperature.

I would feel uneasy relying on a temperature coefficient that was determined over 50 years ago.

Fair caution, although as it happens I am currently favouring Double -X and a version of the Leitz 2–bath developer, both of which were developed over 50 years ago!

Surely it’s equally unwise to rely on a universal time-temperature chart if in fact there are significant differences between developing agents? I had no idea of that before this thread started.

Actually, you do have a densitometer: Your light meter. Hold each strip over the meter's sensor with a bright light nearby, subtract the readings and multiply that by 0.3. That's the density difference.

Great idea, thanks! Not sure that I need any maths, do I? All I need is to determine what dev time at (say) 17 deg gives me the same density as the reference time and temperature, as you suggested a couple of posts back. I will try this in due course and report back.

 

[Romanko]

I would feel uneasy relying on a temperature coefficient that was determined over 50 years ago.

You determine your temperature coefficient from the development times at three temperatures (technically two is sufficient, but the third gives you some estimation of the quality of fit). This data is provided in the film and developer datasheets.

 

[albada]

You determine your temperature coefficient from the development times at three temperatures (technically two is sufficient, but the third gives you some estimation of the quality of fit). This data is provided in the film and developer datasheets.

Good idea! I didn't think of that. For best accuracy, I suppose one should select two temperatures that are far apart to compute the coefficient, and use the intermediate temperatures to check it.
For the fun of it, from Kodak's instructions, I just computed the coefficient for XTOL and TMAX-400; it's 3.2 (12.3% rate-gain per degree).

 

[Alan Johnson]

I just cut out and use the Ilfordphoto chart, seems to be close enough for most developers.
Films changed a lot since 1942, post 4.

https://www.ilfordphoto.com/amfile/file/download/file/1829/product/551/

 

[Romanko]

I just computed the coefficient for XTOL and TMAX-400; it's 3.2 (12.3% rate-gain per degree).

I used the development times of 7.25, 6.5, 6.25, and 5.25 mins for temperatures of 18, 20, 21 and 24 degrees, respectively, for XTOL full strength solution and TMAX-400 at EI 400 developed to CI=0.56.

XTOL datasheet

The development time at 15 degrees is 8:31. What is your development time at 15 degrees?