An alternative look at ink wetness

[LizEF]

22 minutes ago, InesF said:

Thank you @dipper!

 

Indeed pH and polarity of an ink changes its interference with the paper. ...

 

[lots of cool stuff]...

 

Most other effects can be explained by surface tension alone - but, some brand new measurement data are pointing towards a behaviour control by adding salt to an otherwise uncontrollable ink....

 

Wow!  That was fabulous.  This thread would make an amazing episode of [some science show on PBS¹ narrated by some dude with a British accent]!   Thanks for sharing your wealth of science-y knowledge, @InesF.

 

¹For those not familiar, PBS is a television station in the United States that tends to have lots of science-y / educational shows.

[Sholom]

Continuing to be a wonderful investigation. A couple of comments:

 

1) Of course, as far a wetness in a nib is concerned, surface tension is just an approximate proxy for interfacial tension between the nib, feed, and ink. Some probably otherwise as far as surface tension is concerned unremarkable inks are prone to nib creep. This means that they are better at wetting the nib metal than other inks. That may or may not be reflected in your surface tension measurements as the correlation between surface tension and interfacial tension is not perfect. As InesF has noted, paper is complex so again, we shouldn't be surprised to see some outliers in these correlations. The outliers may reflect the use of less common wetting agents, antifoams, or dispersants in the ink.

2) Paper can contain polymers, but they are generally easily separated from the cellulose fibers during recycling. Sizing agents (to control ink spreading) are generally relatively low molecular weight and often soluble in hot water or alcohol/water mixes. Gum Arabic is a common sizing agent for watercolor paper and is a natural polymer. Certain grades of polyvinyl alcohol polymer (a synthetic) are also used as sizing agents and are soluble in hot water but not cold.

3) Supposedly the quick dry feature of the ill-fated Parker Superchrome inks was a high pH that increased the rate of absorption. not sure where I heard that but highly likely it has been discussed on this forum in the past.

 

Looking forward to the conductivity measurements.

 

 

[InesF]

On 10/21/2021 at 11:37 PM, Sholom said:

Continuing to be a wonderful investigation. A couple of comments:

 

1) Of course, as far a wetness in a nib is concerned, surface tension is just an approximate proxy for interfacial tension between the nib, feed, and ink. Some probably otherwise as far as surface tension is concerned unremarkable inks are prone to nib creep. This means that they are better at wetting the nib metal than other inks. That may or may not be reflected in your surface tension measurements as the correlation between surface tension and interfacial tension is not perfect. As InesF has noted, paper is complex so again, we shouldn't be surprised to see some outliers in these correlations. The outliers may reflect the use of less common wetting agents, antifoams, or dispersants in the ink.

2) Paper can contain polymers, but they are generally easily separated from the cellulose fibers during recycling. Sizing agents (to control ink spreading) are generally relatively low molecular weight and often soluble in hot water or alcohol/water mixes. Gum Arabic is a common sizing agent for watercolor paper and is a natural polymer. Certain grades of polyvinyl alcohol polymer (a synthetic) are also used as sizing agents and are soluble in hot water but not cold.

3) Supposedly the quick dry feature of the ill-fated Parker Superchrome inks was a high pH that increased the rate of absorption. not sure where I heard that but highly likely it has been discussed on this forum in the past.

 

Looking forward to the conductivity measurements.

 

 

Thank you @Sholom for the well thought comments.

Indeed, surface tension does not fully describe surface wetability as it is dependent on the properties of the surface material.

 

And yes, there are outliers: inks with strange behaviour that do not (fully) follow the general rule. I have identified one such ink (see below). Unfortunately I do not have an electron microscope at hand to prove what I'm currently guessing about the composition of this ink.

 

More information below.

[InesF]

Todays update starts with new methods.

For measurement of electrical conductivity the instrument EC-11 from HORIBA (Japan) was used following the procedures of the user manual. The instrument has a built-in temperature sensor and calculates a compensation. The measurement sensor was equilibrated with the provided surfactant solution 10 minutes before the first measurement. The instrument was calibrated once per day using both calibration standards (1.41 and 12.9 mS/cm). The sensor was carefully rinsed with deionized water after each measurement.

The cavity of the sensor has a volume of 120 µL. After rinsing, a small volume of water remains adhered to the walls and the corners, diluting the next ink sample. Therefore the cavity was filled with ink, equilibrated for about 10 seconds, then the ink was removed and the sensor was filled again with a new volume of the same ink for the measurement.

The deionized water has an electrical conductivity of 0.008 mS/cm, local tap water has 0,513 mS/cm and measuring the calibration solutions as samples resulted in 1.39 to 1.43 mS/cm for the lower and 12.2 to 13.1 mS/cm for the higher standard – higher conductivity results have a slightly lower precision.

 

For statistical analysis the program R was used. Principal component analysis was calculated using the prcomp() command with data scaling, graphs were generated with the screeplot() and the biplot() functions.

The data pool for the principal components analysis had 32 cases (inks) with 16 variables each. There had been 34 inks measured for ink delivery. Unfortunately, the bottles of two of them were emptied before conductivity measurement could be done – these two inks had to be excluded from PCA analysis, with 32 remaining. The 16 variables are the four ink properties (surface tension, viscosity, pH-value and electrical conductivity), the four line widths, the four ink deliveries per line length and the four derivate values for ink delivery per paper surface area.

Reference for the program: R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

 

 

Measurements of previously identified outliers were repeated in the hope to eliminate them. In two cases the new data were more than 15% lower then before (strangely, never higher), in two more cases they were less than 10% different from before (higher and lower), in 1 additional case a calculation error and in another a typo (transposed digits) were identified. Because of the lastly mentioned findings, all previously measured data were re-calculated, but no more error was found. All together, six datasets with 8 data points were either changed (using mean values of both results) or corrected (replaced). Repeating all property measurements for Colorverse Quasar resulted in a minimal correction of its surface tension (from previously 59,2 to 58,6 mN/m), but not enough to bring it closer to the correlation line. Quasar remains an outlier and can be classified as ‘ink with strange behaviour’ – a classification that fits well to its name and to its strange surface contact behaviour.

 

Here the new condensed data table with the new conductivity measurements included.

 

Correlation of ink properties

In search for direct dependencies of data sets, all measured ink consumption / delivery results were correlated, one by one, with the other parameters. Only three such correlations were found: two strong between surface tension and in either ink delivery per line length or ink delivery per paper surface area. A weak correlation was found between ink line width and ink delivery per line length, valid only for absorbent paper. See both of these graphs below.

 

Note: correlating line width with ink delivery resulted in next to no correlation for 'ink friendly' paper while there is a weak correlation for absorbent paper.

 

PCR results

Importance of components:
	PC1	PC2	PC3	PC4	PC5
Standard deviation	3.170	1.1920	1.12333	0.94821	0.88508
Proportion of Variance	0.628	0.0888	0.07887	0.05619	0.04896
Cumulative Proportion	0.628	0.7168	0.79563	0.85183	0.90079

 

Discussion of the PCR Scree Plot

PC1 is dominating by explaining 63% of the total variance and only two more components are above the significance level: viscosity (9%) and conductivity (8%). Including the pH-value (6%), a total of 85% of all variances are explained. PC5 can not be related to a measured parameter.

 

 

 

Discussion of the PCR results (vector graph)

The numbers in the graph represent the following inks

1 Aurora / Black

2 Aurora / Purple

3 Colorverse / Quasar

4 deAtramentis / Atlantic Blue +0.7% G.A.

5 deAtramentis / Aubergine

6 deAtramentis / Aubergine +1% G.A.

7 deAtramentis / Ruby Red + 0.7% G.A.

8 deAtramentis / Sherlock Holmes

9 deAtramentis / Vienna +0.5% G.A.

10 deAtramentis / Virginia Woolf +0.3% G.A.

11 Diamine / Sargasso Sea

12 F.Schimpf / Gelassenheit

13 Ferris Wheel Press / Grape Ice Pop

14 Herbin / Rouge Grenat + 1% G.A.

15 Iroshizuku / Yama-budo

16 Lamy Crystal / Amazonite

17 Montblanc / Irish Green

18 Pelikan 4001 / Blue-black

19 Pelikan 4001 / Brilliant Black

20 Pelikan Edelstein / Aventurin

21 Pelikan Edelstein / Onyx

22 Pelikan Edelstein / Ruby

23 Pelikan Edelstein / Sapphire

24 Pelikan Edelstein / Star Ruby

25 Pelikan Edelstein / Topaz

26 Rohrer & Klingner / Alt-Bordeaux

27 Rohrer & Klingner / Alt-Goldgrün +2% GA

28 Rohrer & Klingner / Isatis tinctoria

29 Rohrer & Klingner / Verdigris

30 Waterman / Mysterious Blue

31 Waterman / Serenity Blue

32 Waterman / Tender Purple +0.6% G.A.

 

The surface tension vector points almost 180 degrees in opposite direction to ink delivery per line length and almost opposite to ink delivery per surface area. This indicates a strong invert correlation; in other words: ink delivery is almost solely dependent from surface tension of the ink and next to not from any one of the other three measured ink properties. The lower the surface tension, the more ink flows from the nib towards the paper!

 

The viscosity vector and to a smaller extent the conductivity vector, both point in opposite direction to the line width. This indicates a strong invert correlation; in other words: the ink line width is dominantly dependent from ink viscosity and to a lower extent from conductivity (and is minimally influenced by pH-value). However, nib width and paper type still have influence. For one nib and one paper type, a higher ink viscosity results in a more narrow line.

 

When comparing two inks with the same (or closely the same) surface tension but different viscosities, the ink with the higher viscosity forms thinner lines with either the same or even higher ink amounts laid down on the paper, resulting in a thicker ink film and in a more saturated colour!

 

Both, the electrical conductivity and the pH-value of an ink have only minor influence on ink behaviour. If any effect, the inks with higher conductivity or higher pH-value tend to result in thinner lines. Aside from the statistic indicators, the empirically observed effect is, that very acidic inks (low pH-value) that also have low surface tension show more feathering.

 

Combining statistics and observations

All those correlations, causalities and observed effects are more pronounced when writing on absorbent (low quality) paper and were comparably smaller for high quality paper – but always point in the same direction. Furthermore, all these correlations and causalities were the same for both fountain pens and strictly the same for the same paper type.

The differences in ink delivery amounts are best shown in the diagram: surface tension vs. ink delivery (see above). The correlations follow polynomial functions of second order with acceptable correlation coefficients. Please be aware that the PCA considers only linear dependencies and will therefore have a slightly decreased eigenvector (arrow length) along PC1 than the correlation coefficient of the polynomial function may suggest.

 

 

The near future

I will like to measure some more of my inks until I run out of this one specific batch of absorbent paper (will be around 42 inks – a number that gives me confidence for confirming the theory and finding the answer ;).

Later, I will focus on the question: What makes a fountain pen a wet writer?

 

It was a pleasure to discuss the measurements, the findings and all the subjective impressions with you!

Have a good time, stay healthy!

[InesF]

The new Grand Ink Wetness Theory

The following statements are strictly valid for writing with one pen at one paper type comparing different inks:

Higher surface tension reduces the amount of ink laid down to the paper

Higher viscosity reduces the line width and slightly increases the amount of ink laid down

Higher viscosity does NOT reduce ink flow of a fully functional fountain pen

Higher viscosity sharpens the edges of the ink line and lets it appear more crisp and more saturated

Higher conductivity (and higher pH-value) do(es) reduce the ink line width a little bit

Lower surface tension supports spreading and feathering of inks on absorbent paper

Inks with either lower surface tension or much higher viscosity appear to be wetter

 

Conclusion:

Ink wetness riddle solved!

The Universe is still a mystery!

👩‍🎓

[LizEF]

Wow, @InesF!  I gotta admit, a fair bit of your long post about PCR stuff went right over my head.   I'll try a second reading later, or even another day (today has a lot yet to be done).  But I'm thoroughly impressed by your dedication and knowledge.

 

Now (or rather, after re-reading / some study) I can go back to my thread on inky terminology for ink reviewers and see if I can come up with anything helpful for new reviewers...

 

And I'm looking forward to your study of pen wetness!

[inkstainedruth]

On 9/4/2021 at 2:06 AM, InesF said:

Ha, ha! I'm waiting for this! 

Me too!

Ruth Morrisson aka inkstainedruth

[inkstainedruth]

On 9/20/2021 at 2:51 AM, InesF said:

@LizEF, that's simply perfect! You got my face expression better than real life.

If you allow, I will print it and put it at my office wall, in front of me, always remembering me about the limited time left.

 

Hey, you're now going to be famous!  Well, at least as famous as my husband was one time a few years ago when some new-to-us people in the OTHER hobby were waxing enthusiastic about "the bakery down at Gulf Wars in Mississippi" at us, not realizing that we in fact knew ALL ABOUT the bakery -- which was my husband's mid-life crisis a few years ago....

No, he couldn't just go out and buy a 1960s Mustang to restore like a "normal" guy.  His reaction to being middle-aged (and worrying about maybe getting laid-off from his then job) was to start a sideline business.... 

Of course the joke is that there are some other people in the organization who only know HIM as being *my* husband and will call him "Mr. [name I use at events]", after years of me being recognized as *his* wife -- to the point that when I was being considered for an arts award (which he wasn't eligible for) I was APPARENTLY described in commentary as "being quiet and completely overshadowed by HIS accomplishments...."  Which, when I told that to some friends, one of them immediately said "Well obviously they didn't see the FINGERPRINT BRUISES in his back!" because at the time I was pushing for HIM to get that award....  Which is still better than the service equivalent, when on a couple of occasions people would come up to ME and say "Isn't it terrible that So-and-so doesn't have that award?" and I'd be going, "Yeah, I guess...." but THINKING, "Hey -- I've done more that that person and nobody is saying that to anyone about ME!  And why are they talking to ME about it anyway?  Do they think I already have the award?  Because I DON'T!"  And then when my name finally did come up for discussion, apparently everyone in the room apparently had a collective "V-8" moment....  And I got the award the following week....

You know, there's a definite perk to being in THIS hobby -- no "cookie" awards to collect.  Just bragging rights for being a "sumgai".... 

Ruth Morrisson aka inkstainedruth

[arcfide]

I'm am very, very contented reading these results. 

[InesF]

22 hours ago, LizEF said:

Now (or rather, after re-reading / some study) I can go back to my thread on inky terminology for ink reviewers and see if I can come up with anything helpful for new reviewers...

 

And I'm looking forward to your study of pen wetness!

Hi @LizEF, you're welcome! Thank you, I'm pleased by your willingness to translate some data for the review community!

 

Ah, the pen wetness! I'm still working on the measurement and evaluation concept.... 😅

[LizEF]

5 minutes ago, InesF said:

Hi @LizEF, you're welcome! Thank you, I'm pleased by your willingness to translate some data for the review community!

  Hopefully I can do it some justice...

 

6 minutes ago, InesF said:

Ah, the pen wetness! I'm still working on the measurement and evaluation concept.... 😅

Take your time.  I'm sure it'll be worth the wait.

[InesF]

19 hours ago, inkstainedruth said:

Hey, you're now going to be famous!  Well, at least as famous as my husband was one time a few years ago when some new-to-us people in the OTHER hobby were waxing enthusiastic about "the bakery down at Gulf Wars in Mississippi" at us, not realizing that we in fact knew ALL ABOUT the bakery -- which was my husband's mid-life crisis a few years ago....

No, he couldn't just go out and buy a 1960s Mustang to restore like a "normal" guy.  His reaction to being middle-aged (and worrying about maybe getting laid-off from his then job) was to start a sideline business.... 

Of course the joke is that there are some other people in the organization who only know HIM as being *my* husband and will call him "Mr. [name I use at events]", after years of me being recognized as *his* wife -- to the point that when I was being considered for an arts award (which he wasn't eligible for) I was APPARENTLY described in commentary as "being quiet and completely overshadowed by HIS accomplishments...."  Which, when I told that to some friends, one of them immediately said "Well obviously they didn't see the FINGERPRINT BRUISES in his back!" because at the time I was pushing for HIM to get that award....  Which is still better than the service equivalent, when on a couple of occasions people would come up to ME and say "Isn't it terrible that So-and-so doesn't have that award?" and I'd be going, "Yeah, I guess...." but THINKING, "Hey -- I've done more that that person and nobody is saying that to anyone about ME!  And why are they talking to ME about it anyway?  Do they think I already have the award?  Because I DON'T!"  And then when my name finally did come up for discussion, apparently everyone in the room apparently had a collective "V-8" moment....  And I got the award the following week....

You know, there's a definite perk to being in THIS hobby -- no "cookie" awards to collect.  Just bragging rights for being a "sumgai".... 

Thank you @inkstainedruthfor you comment - an interesting read!

 

Yes, there is definitely a difference between a recreational hobby and a job - and it is not only the money. For so many years I would not had called my use of fountain pens a hobby and never ever questioned the background. Fountain pens had been a tool and had to function, while I enjoyed being able to use funny colored inks. That's all.

It was only since the pandemic 'exilation at home' when I was bored, started to buy more inks, later some more pens and started to think about ink wetness. And all of a sudden, I felt the need to know the background!

To reveal a secret: I started the measurements to satisfy my own curiosity and later was happy about all the motivation I got from the forum members. In isolation, I may had stopped earlier.

 

Thanks again, looking forward to further discussions. 🙂

[Sholom]

Getting back to the PCA for a moment (I love PCAs but never worked on a project with enough data to make one worth doing; such is the life of an exploratory chemist). I was both pleased and a bit disappointed that the results make complete, intuitive sense. Actually, maybe a sense of relief? Thanks so much for doing this. I know it is a lot of work but that is why I never considered analytical chemistry as a career. Looking forward to more inks being tested as I use very few of these.

[InesF]

Hi @Sholom.

Yes, I thought similar at first, but was astonished about the not so intuitive correlation between viscosity and ink delivery per area and about the mysterious interaction of conductivity with line width.

 

Such surprises are salt and pepper (of otherwise sometimes boring) science! 😉

[InesF]

A short status report: six more inks were measured for consumption, 4 more to go when I run out of absorbent paper. An updated (and final) principal component analysis will be posted afterwards.

 

The initial drawing (page 2, my post from May 25th) needs an update. With respect to the new findings, please find the new description (the drawing itself is still valid) here.

 

Sketch A: The moving nib pulls the liquid ink film along the freshly drawn line. While h2 is bigger for inks with low surface tension, the height difference (h2 - h1) is dependent on ink viscosity and, to a much lower extent, on conductivity. An ink with higher viscosity has a smaller difference (comparably bigger h1), leaving more ink on the paper than another ink of the same surface tension with low viscosity.

 

Sketch B: Line width is influenced by the surface tension. w1 is the nib width directly in contact with the paper and w2 is the drawn line width. Inks with low surface tension form a broader meniscus (adding more width to w1).

 

Sketch C  The still wet line, after the nib has already been pulled further, broadens depending on paper type (absorbent or not) and on both, surface tension and viscosity. A low surface tension supports spreading, a high viscosity (and, to a much lower extent, high conductivity) inhibits it.

 

 

Next – and final – update in 2-3 weeks.

Stay healthy!

[LizEF]

Thanks for the update, @InesF.  I have no idea why this stuff is so interesting to me, but it is!  Maybe I should have taken a physics class and some more chemistry classes... 🤔

 

And I love that diagram.  Every time I see it I want to draw one like it, complete with arrows, measuring lines, subscripts, superscripts, legends, captions....  Only I can't think of anything brilliant to illustrate with said diagram.  Ergo, I need to send it to the back of my brain to come up with something creative (or at least mildly humorous).  (I've been feeding a few too many things to the back of my brain, though, and there seems to be a backlog...  Still, one day I'll wake up at 2:17 in the morning with a brilliant idea.  Hopefully I'll wake up enough to write it down...  )

[InesF]

On 11/14/2021 at 3:57 PM, LizEF said:

Only I can't think of anything brilliant to illustrate with said diagram. 

Veto, dear @LizEF!

If you draw Quins staff or Makhabeshs pendent or a magical hat, you may find plenty of opportunities to put measurement lines and arrows on it and to draw pointing lines to special ornaments and gemstones and explain their function....

😎

(oh, how would I love that!)

[LizEF]

30 minutes ago, InesF said:

Veto, dear @LizEF!

If you draw Quins staff or Makhabeshs pendent or a magical hat, you may find plenty of opportunities to put measurement lines and arrows on it and to draw pointing lines to special ornaments and gemstones and explain their function....

😎

(oh, how would I love that!)

  (Brilliant idea.)

 

As if my to-do list wasn't long enough already!   I actually already drew a very lousy sketch of Quin's staff, to help me describe it better.  Pretty sure that's in the trash now, but perhaps I'll try again.  @yazeh already drew Makhabesh's spider pendant, somewhere, but I could maybe give it a go.  It's about to get a new function - focused on a gemstone at its center.  I'll have to find pictures to draw from for that - I'm nowhere near good enough otherwise.

[LizEF]

6 minutes ago, LizEF said:

I'll have to find pictures

Holy overkill, Batman!

 

I'm thinking more like this, only this is upside-down:

 

[InesF]

On 11/17/2021 at 4:40 PM, LizEF said:

As if my to-do list wasn't long enough already!

Haha, always a pleasure to entertain you!

😇