The non‐steady‐state or transient technique records a measurement during the heating process. The method determines thermal conductivity properties by means of transient sensors. These measurements can be made relatively quickly, which garners an advantage over steady‐state techniques. For this reason, numerous solutions have been derived for the transient heat conduction equation by …
Low surface energy materials
Certain polymeric substrates are difficult to bond. The main reason that these materials present problems is their low surface energy which is unlike metals, ceramics, and most other polymers.
The low surface energy simply prevents conventional adhesives from making intimate contact (wettability) with the substrate surface and this reduces adhesion.
Image 1: a) Surface Free Energy(1) b)High and Low surface energy materials vs wettability (1)
From Image 1-A and B it can be observed that, in the bulk material each atom/molecule is surrounding by atoms/molecule and the interactions (force) is equilibrated or compensated by the surrounding atoms/molecule. In the surface of the solid, the forces are not compensated and intermolecular interactions occurs at an interface, i.e., London dispersive force, Debye inductive force, Keesom orientational forces, hydrogen bonding, Lewis acid–base interactions, and energetically homogeneous and heterogeneous interactions 
Surface free energy or interfacial free energy or surface energy quantifies the disruption of intermolecular bonds that occurs when a surface is created. The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk:
Image 2: High and Low surface energy materials vs wettability (2)
On the other hand, depending on the forces of the solid and the liquid at the interface (see Image 2), a balance of forces is created where it can occur:
- If the interactions between the solid molecules are stronger than those between the liquid molecules themselves (cohesive force), then the liquid spreads over the solid surface. This is called ‘the wetting process’.
- On the contrary, if the intramolecular interactions between the liquid molecules are stronger than those between the solid and the liquid molecules, the liquid will not spread and will remain as a droplet on the solid surface.
The forces acting in the line of three phase contact were for the first time described by Thomas Young. It relates surface free energy of solid being in equilibrium with the liquid vapor γsv, liquid (surface tension) γlv, interfacial solid/liquid free energy γsl, and the contact angle θ
γSV = γSL + γLV cos θ
As it can be observed in the next image, depending on the contact angle θ, it can be predict the wettability of the surface or the hydrophilic-hydrophobic behavior:
Image 3: a) Evolution of contact angle depending on the wettability of the surface (3) b) Evolution hydrophilic-hydrophobic behavior(4)
How is a Contact Angle Measured?
To measure the contact angle Goniometer is used. The measurement process is as follows:
- The stage is flattened, so that the droplet does not move during deposition.
- A droplet of liquid is deposited on to the stage.
- The droplet is illuminated from behind, and an image is recorded by the camera.
- The image is analysed using code or software, and a contact angle measurement is determined.
Image 5: Schematic measurement overview (5)
Contact angle and surface roughness
The Young equation assumes that the surface is chemically homogenous and topographically smooth. This is however not true in the case of real surfaces, which instead of having one equilibrium contact angle value exhibit a range of contact angles between the advancing and receding ones.
Image 6: Contact angles and surface roughness(6)
The relationship between roughness and wettability was defined in 1936 by Wenzel 
cos θm = r · cos θY
- θmis the measured contact angle,
- θYis the Young contact angle
- ris the roughness ratio.
When the liquid does not penetrate into the grooves, the Wenzel equation does not apply. In this case the Cassie equation  is used:
cos θm = x1 · cos θY1 + x2 · cos θY2
Surface roughness is a measurement of surface texture. It is defined as a vertical deviation of a real surface from its ideally smooth form. Roughness plays an important role in various processes such as friction and adhesion and is widely measured
This parameter is especially useful in wettability studies since it can be used to calculate the roughness ratio r, according to equation below.
r = 1 + Sdr ⁄ 100
Methods of solid Surface tension measurement
There are no methods for direct determination of solid surface free energy like some of those used for liquids surface tension (surface free energy) determination. Therefore to determine the energy for a solid surface various indirect methods are used. Thus the energy can be determined from:
- Wetting contact angles
- Adsorption isotherms of liquid vapors on solid surface
- Heat of wetting
- Heat of adsorption
- Solid solubility parameters
The most often used methods are that based on the contact angle measurements. Based on the contact angle measurements, four different approaches are mainly used for determining the energy of rigid solid substrates
1-Critical Surface Tension 
Using a series of homologous nonpolar liquids of differing surface tensions a graph of cos θ vs. γ is produced. It will be found that the data form a line which approaches cos θ = 1 at a given value of γ. This value, called the critical surface tension, can be used to characterize your solid surface.
Image 7: Zisman plot (contact angle vs liquid surface tension)(7)
2-Geometric Mean (Extended Fowkes)
3-Harmonic Mean (Wu)
4-Acid-Base (van Oss et al.)
In this method, also the contact angle and surface free energy can be defined according to the Washburn theory. According to the Washburn theory, when a porous solid is brought into contact with a liquid the rise of the liquid into the pores of the solid will obey the following relationship:
T = [η ⁄ C · ρ^2 · γ · cos θ] · M^2
T — time after contactThe terms are defined as follows:
η — viscosity of liquid
C — material constant characteristic of solid sample
ρ — density of liquid
γ — surface tension of liquid
θ — contact angle
M — mass of liquid adsorbed on solid
A time/mass graph should give a straight line whose slope is:
η ⁄ C · ρ2 · γ · cos θ
If viscosity, density and surface tension are known, the only two variables unknowns are contact angle and C parameter. To obtain the C value, first it is necessary to perform an experiment in which the contact angle is assumed to be zero with a liquid with very low surface tension . When the experiment is performed, the material constant for the solid may be solved for:
η ⁄ C · ρ2 · γ
Factors affecting C
- Porous Solids
Image 8: Powder Wettability by the Washburn theory (8)
Surface Treatment Processes to Optimize Interface
Many industrial and consumer systems required a good adhesion to plastic surfaces but the inherent low energy of plastics would make the process difficult without some form of pre-treatment  .
The different types of polymer surface pre-treatment are carried out in order to:
– Remove the surface contamination (surfactant, plasticizer, etc.);
– Enhance the surface energy of plastics (initial non-polar hydrophobic surface);
– Lower the contact angle, improve wetting, and increase work of adhesion;
– Surface activation (introduction of functional groups, improve adhesion).
‘Clean’ smooth plastic surfaces are difficult to maintain in industrial processes and in environment – contaminants create the weak boundary layers (WBL) that should be removed from the surface
The surface pre-treatment can be classified depending on the mechanism of action:
- A) Solvent pre-treatments
Removal of weak boundary layer/contaminants, increased surface roughness/bond area and plasticization of surface to aid the diffusion process.
- B) Mechanical pre-treatments
Removal of weak boundary layer/contaminants, increased surface roughness/bond area and increased possibility of mechanical keying
- C) Oxidative pre-treatments
(e.g. with chromic acid, ‘flame’, ‘corona discharge’ to improve bonding of low-density polyethylene):
Removal of contaminants and additives, change in topography e.g. surface roughness (+ or). Alter surface chemistry (introduction of functional groups) to affect wetting and adhesion by modifying the forces of attraction between plastic surface and other component.
- D) Surface ‘etching’ with ‘chromic’ acid:
There are differences between the material removed (etch rate), the depth and the extent of oxidation of various polyolefin following chemical oxidation.
In the next
‘Corona’ discharge treatment (CDT) as the most widely used technique in industry, is suitable for continuous treatment of plastic film at atmospheric pressure. Directing a high frequency discharge at the plastic surface from close-range simply disrupts the molecules by oxidising it. The discharge splits the carbon molecules and breaks the oxygen into iones, some of which enter the surface layer of the plastic and improve the bonding, while others form into ozone that needs to be extracted.
The mechanisms of surface modification: change from C-C and C-H into C-N and C-O species. Corona treatment affects only the surface layer of the plastic, to a depth of 0.01 micron, and does not change its appearance or strength.
Image 9: Corona discharge treatment (9)
Plasma treatment – much research with a wide variety of polymers have been made. Power is applied to a gas or a monomer (air, oxygen, nitrogen, argon etc.) in a low vacuum chamber and a plasma formedconsisting of ions, electrons, atoms and free radicals does produce a more uniform surface oxidation of plastics compared to CDT. Various mechanisms of surface modification: ablation of small molecules, cross-linking or introduction of carbonyl and amine groups, possible grafting to the polymer surface with monomers.
Image 10: Plasma treatment (10)
Flame treatment is preferable for treating ticker plastic objects (e.g. PE bottles prior to printing/labelling) as a surface oxidation method which relies on temperature (the gas-burners with 10% oxygen excess to that for complete combustion as hydrocarbon gas mixture). The exact mechanisms of flame-treatment is not known: mixture of processes- thermal oxidation as a chain-reaction free radical attack, surface oxidation and incorporating of oxygen and nitrogen groups.
Image 11: Flame treatment (11,12)
In the table 1 (adapted from special.chem), shows a summary of the different technologies for modifying the surface of the solids as well as the mechanism by which modification occurs.
Table 1: Effect of the Treatment Processes on the Surface (1)
PhD. Chemical Engineer
Innovation I+D Manager NTC (Nuevas Técnicas de Coloración)
(7) Abhinandan Agrawal, Surface Tension of Polymers, Massachusetts Institute of Technology, 2005
(10) Corona treatment vs Plasma treatment, Pillar Technologies 2014
 Soo-Jin Park, Min-Kang Seo, Chapter 2 – Solid-Gas Interaction, Interface Science and Technology, Volume 18, 2011, Pages 59-145
Wenzel: R. N. Wenzel, ‘Resistance of solid surfaces to wetting by water’, Industrial and engineering chemistry 28 (1936) 988.
Cassie: A. B. D. Cassie and S. Baxter, ‘Wettability of porous surfaces’, Transactions of the Faraday Society 40 (1944) 546.
 Abhinandan Agrawal, Surface Tension of Polymers, Massachusetts Institute of Technology, 2005
 Vera Kovacevic , International Workshop on Advanced Polymer Science and Turbulent Drag Reduction: Surface and Interface Phenomenon in Polymers, 2008
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