[harryn]

sigma John,

Sorry not to key on the DOE (not Dept. of Energy) trial thing. I've been busy trying to solve a riduculously annoying but simple software problem in the paying portion of my life for the last week or so.

In general, I would consider the aggregate problem to be solved. Given any mixture of aggregate, I can say within less than 3% what the packing density Phi will be after taking a Beta measurement on each component. (I'm using estimated beta values right now and thus my results are only relative to one another right now). The French Researcher, de Larrard, whose models I have implemented spent about 10 years validating them with data and has published many papers and the book I am working from. I have shown that I can duplicate the numbers published in his book.

Given that the aggregate packing density Phi can be calculated to within 3% for the model, My engineering judgment tells me the DOE experiment design doesn't need to account for individual aggregate types but should instead specify Phi values. Phi goes from 0 percent (all epoxy) by volume to about 92% (8% epoxy) by volume.

It is known from the rule of mixtures model that modulus follows a uniformly increasing nonlinear curve with percentage of aggregate. It is also known that eventually there is a point where the modulus becomes zero with increasing aggregate content due to insufficient epoxy to bind the material.
The minimum amount required to fill all of the empty space in the solid is 1-Phi. Any less than that and the mixture doesn't contain enough epoxy to hold itself together. More epoxy than 1-Phi that causes the particles to be fully encapsulated by epoxy in model terms.

So, I would say the first unknown is what the optimal amount of epoxy for maximum modulus is. Of course this assumes that all mixtures with the same Phi value are equally good for modulus. This assumption is true according to the rule of mixtures but there could be effects related to the quality and type of aggregate that cause fractures which affect the result.


Here is the summary of factors,likely effects on modulus, and range is as below:

Packing Density of Particles: positive linear: 0----92% by volume aggregate
Epoxy volume percentage in composite: negative linear: (100% - Phi)----50% by volume aggregate
Titanate Concentration: concave down parabolic: 0----1% by weight aggregate
Silane Concentration: concave down parabolic: 0----5% by weight aggregate
Cobalt Acetyl Acetonate Concentration: positive linear: 0----1% by weight epoxy
Epoxy to Hardener Mix Ratio: concave Down Parabolic: 2.1-----2.5 w/w for 37-127/37-606
Well Dispersed Nanomaterial Concentration: positive linear: 0----10% by weight epoxy

Once the gross problems like bad choice of hardener etc have been worked out, a DOE trial of the above factors would be a good way of getting the optimal material.

Regards all,

Cameron

Hi Cameron - I think your variable set, range, and potential result is getting closer. I will suggest a slightly different way to view it which might be entirely wrong, but here it is anyway.

a) The first testing set
- Modeling is great, but obviously, we are getting to the point where the theoretical models need some baseline testing - if for no other reason, than to see if they are not just figments of our imagination.
- At this stage, we have so little experimental information on the "real" effects, that we should concentrate on getting a baseline on likely first order effects in the general mix range that is plausible.
- It should also be assumed that the first DOE experiment will be botched. That is not a criticism, it is just simple reality - science is messy, especially wet lab science. Keep it simple.

b) Phi - essentially void space as a variable in the DOE.
- My perception is that this is not a good item to select as a variable, even though it is a calculable variable and subject to some reasonable experimental control.
- Even if you have an extremely well controlled bulk value for Phi, locally, this will have wide variation no matter how well we are able to mechanically mix.
- The smaller the agr. size, the more difficult it will be to mix, making Phi even less reliable as an indicator.
- Once the minimum size agr takes on an (unknown) layer thickness of epoxy, the Phi value becomes almost lost in the noise.

b) Minimum agr size as a variable
- My suggestion is to use the presence or absence ( 0 - 100 %) of your smallest agr. as a variable and see if the needle moves enough to keep it in as a first order effect compared to other factors.

c) Epoxy concentration
- This one is more obvious 10 - 20 % range
- If the real need becomes 25 %, then the first DOE will tell us to go that direction anyway.

d) Hardener
- Type - I would guess there is an effect, but this is not a variable that can easily take on a 3 "level" effect for the DOE, especially the first round.
- Qty of hardener - this is more easily fit into a DOE.

e) Cure Temperature
- Likely first order effect

f) Cure Time
- Likely first order effect

Keep everything else steady.

That is more than enough variables for a a first trial. JMHO.