Zeta potential is a holistic property of particle and its environment.  Your question has no meaning for a powdered sample - you need to specify the system (pH etc) that the particle resides in.  That's why you'll see it always in liquid or colloidal suspension.  What are you trying to relate the charge on the surface to?  You can flow a known liquid over a solid system and measure a potential difference - is this what you're trying to do?

I am looking to measure at the surface of solid samples, such as a polymer sheet, in contact with particular solutions.  I am interested in measuring and comparing different solid samples, with hopefully negative surface charge, in contact with the same particular solutions.

the measurement you should consider is called "streaming potential". I cannot give you good advice on it as I have not usd it myself, but you will find a lot of information on  the web

We can measure surface potential with a special cell on our Zetasizer but this (and streaming potential measurements) does not fit your requirement of "While there are some instruments that would be useful, it would be cost prohibitive to purchase them.

Is there a simple and inexpensive measurement technique for determining zeta-potential and/or surface charge on solid samples?"

See for example: http://www.malvern.com/en/support/resource-center/application-notes/AN121220ZetaPotentialSurfacePTFE.aspx

and:

http://www.malvern.com/en/pdf/secure/AN130307IonicStrengthSurfaceZetaPotential.pdf

(Registration needed I think)

Forgot to add: The surface zeta potential cell is an accessory (ZEN1020) available for the Zetasizer Nano series of instruments for the measurement of the zeta potential of any flat surface

 Dear Daniel,

I think inexpensive may be hard to come by.  If you follow Roman's suggestion, then streaming potential is one conventional way to approach your question.  

• Many years ago I used the Anton Paar instrument  with an asymmetric clamping cell geometry (much more convenient than the symmetric system I thought).  Modern instrument is at:

http://www.anton-paar.com/us-en/products/group/surface-analysis/

• I have also used the ZetaSpin instrument 

https://www.andrew.cmu.edu/course/39-801/

I had a few more questions about how this one operates -- theory is "simple" and appealing as presented but mounting the samples to avoid potential artifacts was a little tricky for our sample system.  Some also object to some seeming aberrant values that the manufacturer frequently claim on reference mica surfaces using this instrument. But it functions fairly easy and maybe the inventing professor at CMU sells them more cheaply than the SurPass?!?

No doubt  there may be some "lab-made" examples discussed in the literature, but I am not up to date on this topic.

That's about the best I have for you, I fear.

Best regards,

Mike

Daniel, Please see the following paper on how to measure surface zeta potential ( in my case, intact shale).

~ Bez

Hi Daniel,

Currently I am facing the same issue as you did. Were you able to come up with a good solution? I would like to know.

Thanks,

Arputha

Hello,

I came across this video tutorial for surface zeta-potential by Malvern, I hope it helps!

https://www.brainshark.com/malvern/vu?pi=892751704&b=1&tx=120486&c1=22

Hi Daniel,

It's strange that I haven't seen this question. We have been doing measuring Zeta potential for surfaces. We have measured Zeta for both conductive and non-conductive surfaces.

I would agree to Mike Bender . SurPASS electrokinetic surface analyzer, manufactured by Anton Paar is a very good instrument when it comes to the measurement of Zeta potential. We have this instrument in our lab and we have used it to study many samples.

The measurement of Zeta potential for conductive or porous surfaces is very tricky, as surface conduction might trigger in. The most popular way of measuring zeta potential for surfaces is the streaming current method. But it gives wrong estimates (less in absolute value) for conductive or porous surfaces. The most straightforward and accurate method is the streaming current method, which we have used for our purpose.

did you solve this problem?

I recently look up some papers and comes up with two solutions in literatures.

1st Laser doppler electrophoresis method from Malvern, which requires a unique measurement kit.

2nd, Electrokinetic analyzer from Anton Paar SurPASS.