top-down, bottom up and all together (was Re: Could someone summarize that gum up or down discussion?)

So here's the result from absorption model analysis.

1. If the UV-density is mostly built by the binder and pigment, "all
   together" hardening would require dichromate concentration profile
   to be in the form of c exp (x/r) where x is depth and c and r
   constants. Bottom up hardening would require steeper increase of
   dichromate concentration as x increases. This is highly unlikely to
   happen in reality.

2. If the UV-density is mostly built by dichromate (i.e. the binder
   and pigment are UV-transparent), then "all together" hardening
   would require dichromate concentration profile to be in the form of
   c / (a - x) and the material cannot be thicker than the constant a,
   which can be quite large if the UV irradiation is strong. Bottom up
   hardening would require dichromate concentration profile that is
   steeper than this. This may be potentially possible in reality,
   given that the UV exposure is sufficiently strong and the coating
   is sufficiently thin.

Here, "all together" condition is such that the amount of UV absorbed
by dichromate is constant regardless of the depth x. The solutions for
this condition can be readily obtained from simple differential
equations (freshman calculus level). In condition 1, dichromate has to
be more concentrated as the depth x increases because the amount of
available UV exponentially decreases as x increases due to the UV
absorption by material other than dichromate. In condition 2, the
dichromate has to be more concentrated as the depth x increases
because the available UV is decreased as x increases, because some of
the UV is already absorbed by dichromate between surface (x=0) and the
point in question.

Of course, the condition 1 is the most favorable condition for
top-down, and condition 2 is the most favorable condition for
bottom-up. In condition 1, bottom-up is very unlikely. In condition 2,
bottom-up may be possible if:

* binder and pigment are relatively UV-transparent, compared to the UV
  density of dichromate
* the coated layer is sufficiently thin

The UV density of dichromate decreases with exposure time, since 370nm
absorption is due to Cr(VI) and some of this Cr(VI) is reduced to
lower oxidation states. This is practically relevant in condition 2,
but not in condition 1.

Therefore, two measurements of UV densities, one for gum+pigment only,
and another for gum+pigment+dichromate, can determine whether the
actual dichromate coating is close to the condition 1 or 2, and from
there, we get much better insight as to whether gum printing can be
bottom-up due to possible dichromate concentration gradient questioned
by Mike Ware.

From: Ryuji Suzuki <rs@silvergrain.org>
Subject: Re: Could someone summarize that gum up or down discussion?
Date: Fri, 14 Apr 2006 18:52:42 -0400

> On Fri, 14 Apr 2006 22:22:07 +0000, "Marek Matusz"
> <marekmatusz@hotmail.com> said:
> > Perhaps we could test some of the hypotheis put forward. For example: the
> > light penetration of the gum layer. With some assumption one could
> > calculate
> > if the light penetrates to the paper interface or not. Anybody still
> > remember their freshman chemistry or physiscs. If I get bored enough with
> > gum transfer experiments I might do the calculations as well. For the
> > very
> > thick, heavily pigmented gum layers that I am using for back printing
> > there
> > is no visible ligt passing through and since carbon absorbs everything
> > indiscriminately no UV passes through as well. I will test that to make
> > sure.
>
> I proposed such a model yesterday, describing exponential decay. It is a
> simple differential equation that appears in many aspects of science and
> engineering.
>
> Assuming a uniform layer, the UV light intensity falls as the depth
> increases in the form of exp(-x/c) where x is the depth (surface is at
> x=0) and c is depth constant. In other words, c is the thickness of the
> layer which gives UV density of 0.43, which is log exp -1. In this
> sense, the rate at which the UV is attenuated is described by one number
> and it can be compared across different solutions, etc. This is very
> analogous to power loss that occues when RF signal is transmitted over a
> long coaxial cable (or any constant-impedance transmission line for that
> matter), to help understanding of radioheads.
>
> Since Mike Ware mentioned a possibility that dichromate concentration is
> not necessarily homogeneous in the coated layer, I suggest to make two
> measurements. One is UV-optical density of gum plus pigment at any known
> thickness, and another is that of gum, pigment and dichromate at any
> known thickness. This way, we can calculate two depth constants. Those
> numbers should be measured from films made on nonabsorbent support, and
> may be measured with the support or measured as a film peeled off from
> it. By using these two numbers, we can easily conclude for any given
> coating thickness of actual dichromated gum material, how much UV would
> reach the "bottom" if the dichromate is uniformly distributed, or if all
> dichromate is absorbed by the paper substrace and available only at the
> gum-paper interface.
>
> There are three factors that people didn't mention, though.
>
> 1. The UV-optical density of dichromated gum will change during the
> course of UV exposure. (This is a real problem.)
>
> 2. There _may_ be significant scattering of light at the gum-paper
> surface.
>
> 3. The number of crosslinking necessary to render the macromolecule
> insoluble depends on the MW and other factors. When the gum can
> crosslink with the sizing layer (which would be the case with
> glut+gelatin sizing).
>
> This is an interesting question, but I am not set up to do UV
> densitometry so I'll have to leave it to someone else.
>
> For one case where much of the UV-density is built by the binder and
> pigment, I think there is little question for top-down theory. If, in
> such situation, one wants to make a uniform "all-together" hardening, it
> would require that the dichromate concentration would be in the form of
> exp(+x/c) and, and it is unlikely that actual dichromate concentration
> is anything like this. If pigment and the binder are both
> UV-transparent, then the situation is a bit better for bottom hardening.
>
> Some of you might have been bothered by the term UV here, but if it
> helps, read "monochromatic 370nm light" or something like that.
>
Received on Sat Apr 15 20:12:34 2006