Unappreciated materials (3): Paper

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paperSome materials catch headlines, are held in awe, but not all.  Some get little respect, despite having changed the world.  They have become commonplace, anonymous, ignored and (particularly if they are cheap) cast aside when no longer wanted.  If they had feelings, they would be hurt. This brief series of blogs is to draw attention to their plight.

Language has the capacity to absorb materials, assimilating their attributes as adjectives, adverbs and nouns to illustrate ideas: a leaden sky, and iron fist, a glassy look.   One material has been hijacked (honored?) in this way more than any other: paper.  Administration is paperwork.  A paper-thin excuse is insubstantial, but a paper-thin margin is something small but significant.  Defects can be papered-over to conceal them or exposed by publication in the paper.  Scientists reputation are built on their papers but beware the police if your papers aren’t in order.  Paper money is not money at all, but (at least in the UK) “…a promise to pay the bearer the sum of…”.

So what is paper? Something we receive, read, scrunch up, and throw away?  That is to overlook the potential of one of our most versatile materials.  There are at least 20 different sorts of paper.  Toilet tissue is soft, absorbent, and disintegrates in water.  Greaseproof and tar paper are stiff, waterproof, and durable.  Newsprint is cheap but yellows with age.  Rag papers retains its integrity and that of the writing or printing it carries.  Crepe paper is compliant; construction paper is stiff and ungiving.  Tracing paper is translucent; cardboard is totally opaque.

So lets ask  that question again – what is paper?  Most paper and paperboard (cardboard) is made by matting cellulose fibers.  The fibers come from fibrous plants – wood, ramie, kenaf, cotton or sisal – often with mineral fillers for whiteness, weight and absorbancy.  The fibers, extracted by crushing and leaching in caustic soda to free them from the lignin matrix, are typically 1 – 2 mm in length and 20 – 40 microns in diameter.  The fibers and fillers, suspended in water, are drained, callendered, and dried for form paper and paperboard, with a final porosity between 50 and 70%.

We use paper in quantities that exceed those of most other materials – 430 million tons in 2013 world-wide, and rising.  Some – about 12% of the total – is recycled; even this small fraction equates to 50 million tons per year.  Most is used for packaging and for printing, and for both these applications the density, stiffness and strength of the paper play a key role.  Packaging provides protection and here the need for strength is obvious.  All three properties influence the ability of paper to be fed through printing presses and copiers.  So how do paper-people describe them?

The density of paper products is measured as Grammage, R, its weight in grams per square meter, units g/m2, abbreviated to gsm.  It is related to the bulk density ρ in the usual units of kg/m3 by

 ρ =  R/t

where t is the thickness (“caliper”) of the sheet in millimeters.  The density of paper is almost as diverse as its uses:  as low as 150 kg/m3 (toilet paper) through 235 kg/m3 (Kleenex) to 780 kg/m3 (copier paper) peaking at 1,200 kg/m3 (glazed art paper).

Tensile stiffness St, units kN/m, is the slope of the force-per-unit-width versus tensile strain curveIt is related to the bulk Young’s modulus E (usual units, GN/m2) by

St  =  Et.

Tensile strength, less obviously, is measured as the Breaking length, BLIt is the length of a paper strip in meters that would just support its own weight if hung vertically from one end.  It ranges from 500 meters for extremely soft tissue to about 8,000 meters for strong Kraft bag-paper.  The breaking length is related to the bulk tensile strength σts  (usual units MN/m2) by

σts  = ρ g BL  = g BL (R/t),

where g is the acceleration due to gravity (9.81 m/s2).  The breaking lengths given above correspond to bulk tensile strength of  1.5 – 60 MPa.

You might think that these three properties were all that mattered about paper.  You would be wrong.  The coefficient of friction (typically 0.5) affects the way paper feeds through printers and presses.  The smoothness changes the way it accepts print.  The whiteness, color, gloss, opacity, and fluorescence all influence the appearance of the printed page.  Absorbancy is desirable in a paper towel but not wanted in a paper cup.  Permeability to water is a feature of filter paper, but one to be avoided in wrapping paper.  Paper can carry visible messages, but it can also carry messages that are less obvious – water marks, ultra-violet identiviers and metal threads in bank notes, the ability to change color with temperature or in the presence of poisons or pathogens.  The ability of paper to retain a fold is central to its everyday use in packaging and its artistic use in origami.  As cardboard and corrugated board paper becomes a structural material – even furniture can be made from it.

Paper is a truly remarkable material.  


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One thought on “Unappreciated materials (3): Paper

  1. Moro

    I am trying to plot an Ashyby diagram for bank note material selection. I need advice on performance index for bank note(eg. cotton paer) design.
    I used performance index,
    M = E/p (objective; increase stifness and reduce density) but I an not getting expected results..e.g cotton paper, PP etc
    Hope to hear from you. Are there any standard constraints for cotton paper bank notes design?.
    Thank you.


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