Polymer adsorption

Because the ability of a surface to adsorb molecules onto its surface depends on energies of interaction, thermodynamics of adsorption can be used to understand the driving forces for adsorption. To measure the thermodynamics of polymer surfaces, contact angles are often used to easily obtain useful information. The thermodynamic description of contact angles of a drop of liquid on a solid surface are derived from the equilibrium formed between the chemical potentials of the solid–liquid, solid–vapor, and liquid–vapor interfaces.

At equilibrium, the contact angle of a liquid drop on a surface does not change. Therefore, the Gibbs free energy is equal to 0:

${\displaystyle dG=0}$

The chemical potentials of the three interfaces must cancel out, producing Young's equation for the relationship between surface energies and contact angles:^[8]

${\displaystyle \gamma _{L}\cos \theta _{\mathrm {C} }\,=\gamma _{\mathrm {SV} }-\gamma _{\mathrm {SL} }-\pi _{\mathrm {e} }}$

where:

${\displaystyle \gamma _{L}}$ is the surface tension of the liquid

${\displaystyle \theta _{\mathrm {C} }}$ is the contact angle of the liquid

${\displaystyle \gamma _{\mathrm {SV} }}$ is the surface tension of the solid–vapor interface

${\displaystyle \gamma _{\mathrm {SL} }}$ is the surface tension of the solid–liquid interface

${\displaystyle \pi _{\mathrm {e} }}$ is the vapor pressure of the liquid at equilibrium.

However, this equation cannot be used to determine the surface energy of a solid surface by itself. It can be used in conjunction with the following equation to determine the relationship between contact angle and surface energy of the solid, as surface tension ≈ surface energy for a solid:^[1]

${\displaystyle \gamma _{\mathrm {SL} }=\gamma _{\mathrm {S} }+\gamma _{\mathrm {L} }-2{\sqrt {\gamma _{\mathrm {S,d} }\gamma _{\mathrm {S,d} }}}-2{\sqrt {\gamma _{\mathrm {S,p} }\gamma _{\mathrm {S,p} }}}}$

where

${\displaystyle \gamma _{\mathrm {S} }}$ is the surface energy of the solid

${\displaystyle \gamma _{\mathrm {L} }}$ is the surface tension of the liquid.

${\displaystyle \gamma _{\mathrm {S,d} }}$ and ${\displaystyle \gamma _{\mathrm {S,p} }}$ are the dispersive and polar components of the surface energy of the solid

Using these two equations, the surface energy of a solid can be determined simply by measuring the contact angle of two different liquids of known surface tension on that solid's surface.^[8]

For heterogeneous surfaces (consisting of two or more different types of material), the contact angle of a drop of liquid at each point along the three phase contact line with a solid surface is a result of the surface tension of the surface at that point. For example, if the heterogeneous regions of the surface form very large domains, and the drop exists entirely within a homogeneous domain, then it will have a contact angle corresponding to the surface tension of that homogeneous region.

Likewise, a drop that straddles two domains of differing surface tensions will have different contact angles along the three phase contact line corresponding to the different surface tensions at each point.

However, with sufficiently small domains (such as in those of a block copolymer), the observed surface energy of the surface approaches the weighted average of the surface energies of each of the constituents of the surface:^[8]

${\displaystyle \gamma _{polymer}=\sum _{i=1}^{n}f_{i}\gamma _{i}}$

where:

${\displaystyle \gamma _{polymer}}$ is the overall surface energy of the polymer

${\displaystyle f_{i}}$ is the fraction of the i^th component of the polymer's surface

${\displaystyle \gamma _{i}}$ is the surface energy of the i^th component

This occurs because as the size of the homogeneous domains become very small compared to the size of the drop, the differences in contact angles along different homogeneous regions becomes indistinguishable from the average of the contact angles.^[8]

The observed contact angle is given by the following formula:^[8]

${\displaystyle \cos \theta \ \mathrm {obs} =\sum _{i=1}^{n}f_{i}\cos \theta _{i}}$

where:

${\displaystyle f_{i}}$ is the fraction of i^th component

${\displaystyle \theta _{i}}$ is the contact angle i^th component

If the polymer is made out of only two different monomers, it is possible use the above equation to determine the composition of the polymer simply by measuring the contact angle of a drop of liquid placed on it:^[8][9]

${\displaystyle \cos \theta \ \mathrm {obs} =\ f\cos \theta _{1}+(1-f)\cos \theta _{2}}$

where:

${\displaystyle \theta \ \mathrm {obs} }$ is the observed contact angle

f is the area fraction of one component, and ${\displaystyle (1-f)}$ the area fraction of the other.

${\displaystyle \theta _{1}}$ and ${\displaystyle \theta _{2}}$ are the contact angles of the first and second components of the polymer.

One of the defining features of polymer surfaces and coatings is the chemical regularity of the surface. While many materials can be irregular mixtures of different components, polymer surfaces tend to be chemically uniform, with the same distribution of different functional groups across all areas of the surface. Because of this, adsorption of molecules onto polymer surfaces can be easily modeled by the Langmuir or Frumkin Isotherms. The Langmuir equation states that for the adsorption of a molecule of adsorbate A onto a surface binding site S, a single binding site is used, and each free binding site is equally likely to accept a molecule of adsorbate:^[1]

${\displaystyle {\ce {A + S <=> A - S}}}$

where:

A is the adsorbate

S is the surface binding site

${\displaystyle A-S}$ is the bound adsorbate/binding site pair

The equilibrium constant for this reaction is then defined as:^[1]

${\displaystyle k_{ad}={\frac {[A-S]}{[A][B]}}}$

The equilibrium constant is related to the equilibrium surface coverage θ, which is given by:^[1]

${\displaystyle \theta \ ={\frac {k_{ad}[A]}{k_{ad}[A]+1}}}$

where:

θ is the surface coverage (fraction, 0 is empty, 1 is fully covered)

${\displaystyle k_{ad}}$ is the adsorption equilibrium constant

Because many polymers are composed of primarily of hydrocarbon chains with at most slightly polar functional groups, they tend to have low surface energies and thus adsorb rather poorly. While this can be advantageous for some applications, modification of polymer surfaces is crucial for many other applications in which adhering a substrate to its surface is vital for optimal performance. For example, many applications utilize polymers as structural components, but which degrade rapidly when exposed to weather or other sources of wear.^[10] Therefore, coatings must be used which protect the structural layer from damage. However, the poor adhesive properties of nonpolar polymers makes it difficult to adsorb the protective coating onto its surface. These types of problems make the measurement and control of surface energies important to development of useful technologies.

The Gibbs energy of adsorption, ${\displaystyle \Delta G_{ad}}$, can be determined from the adsorption equilibrium constant:^[1]

${\displaystyle \Delta G_{ad}=-RT\ln K_{ad}.}$

Because ${\displaystyle \Delta G_{ad}}$ is negative for a spontaneous process and positive for a nonspontaneous process, it can be used to understand the tendency for different compounds to adsorb to a surface. In addition, it can be divided into a combination of two components:^[1]

${\displaystyle \Delta G_{ad}=\Delta G_{p}+\Delta G_{c},}$

which are the Gibbs energies of physisorption and chemisorption, respectively. Many polymer applications, such as those which use polytetrafluoroethylene (PTFE, or Teflon) require the use of a surface with specific physisorption properties toward one type of material, while being firmly adhered in place to a different type of material. Because the physisorption energy is so low for these types of materials, chemisorption is used to form covalent bonds between the polymer coating and the surface of the object (such as a pan) which holds it in place. Because the relative magnitudes of chemisorption processes are generally much greater than magnitudes of physisorption processes, this forms a strong bond between the polymer and the surface it is chemically adhered to, while allowing the polymer to retain its physisorption characteristics toward other materials.^[10]

Experimentally, the enthalpy and entropy of adsorption are often used to fine-tune the adsorption properties of a material. The enthalpy of adsorption can be determined from constant pressure calorimetry:^[1]

${\displaystyle Q=-\Delta H_{ad}N,}$

where:

${\displaystyle Q}$ is the heat exchanged,

${\displaystyle \Delta H_{ad}}$ is the integral molar enthalpy of adsorption,

${\displaystyle N}$ is the number of moles adsorbed.

From the enthalpy of adsorption, the entropy of adsorption can be calculated:

${\displaystyle \Delta S_{ad}={\frac {\Delta H_{ad}}{T}},}$

where:

${\displaystyle \Delta S_{ad}}$ is the integral molar entropy of adsorption,

${\displaystyle T}$ is the temperature in kelvins.

Together, these are used to understand the driving forces behind adsorption processes.

Protein adsorption influences the interactions that occur at the tissue-implant interface. Protein adsorption can lead to blood clots, the foreign-body response and ultimately the degradation of the device. In order to counter-act the effects of protein adsorption, implants are often coated with a polymer coating to decrease protein adsorption.

Polyethylene glycol (PEG) coatings have been shown to minimize protein adsorption in the body. The PEG coating consists of hydrophilic molecules that are repulsive to protein adsorption.^[11] Proteins consist of hydrophobic molecules and charge sites that want to bind to other hydrophobic molecules and oppositely charged sites.^[12] By applying a thin monolayer coating of PEG, protein adsorption is prevented at the device site. Furthermore, the device's resistance to protein adsorption, fibroblast adhesion and bacteria adhesion are increased.^[13]

The hemocompatability of a medical device is dependent upon surface charge, energy and topography.^[14] Devices that fail to be hemocompatabile run the risk of forming a thrombus, proliferation and compromising the immune system. Polymer coatings are applied to devices to increase their hemocompatability. Chemical cascades lead to the formation of fibrous clots. By choosing to use hydrophilic polymer coatings, protein adsorption decreases and the chance of negative interactions with the blood diminishes as well. One such polymer coating that increases hemocompatability is heparin. Heparin is a polymer coating that interacts with thrombin to prevent coagulation. Heparin has been shown to suppress platelet adhesion, complement activation and protein adsorption.^[13]

Advanced polymer composites are used in the strengthening and rehabilitation of old structures. These advanced composites can be made using many different methods including prepreg, resin, infusion, filament winding and pultrusion. Advanced polymer composites are used in many airplane structures and their largest market is in aerospace and defense.

Fiber-reinforced polymers (FRP) are commonly used by civil engineers in their structures. FRPs respond linear-elastically to axial stress, making them a great material to hold a load. FRPs are usually in a laminate formation with each lamina having unidirectional fibers, typically carbon or glass, embedded within a layer of light polymer matrix material. FRPs have great resistance against environmental exposure and great durability.

Polytetrafluoroethylene (PTFE) is a polymer used in many applications including non-stick coatings, beauty products, and lubricants. PTFE is a hydrophobic molecule composed of carbon and fluorine. Carbon-fluorine bonds cause PTFE to be a low-friction material, conducive in high temperature environments and resistant to stress cracking.^[15] These properties cause PTFE to be non-reactive and used in a wide array of applications.