Fundamental Study of the Initial Agglomeration of Lithium Soap Thickener in Lubricating Oil

Fundamental study of the initial agglomeration of lithium soap thickener in lubricating oil

Paul Shiller1, Nikhil Prasad1, and Gary Doll1

1The University of Akron Contents

1 Introduction 4 1.1 How does the grease thickener structure form? ...... 5 1.2 Model of grease bleed? ...... 6 1.3 What is the relation of grease bleed to lubrication? ...... 7

2 Motivation 7

3 Testing 8 3.1 Grease Formulation ...... 8 3.2 Rheology ...... 8 3.3 Dynamic Light Scattering ...... 9 3.4 Atomic Force Microscopy ...... 10 3.5 Size Exclusion Chromatography ...... 10

4 Modeling 11 4.1 Geometry ...... 11 4.2 Theory ...... 14 4.2.1 ASED Theory ...... 14 4.3 Density Functional Theory ...... 16 4.3.1 Molecular Dynamics Theory ...... 17 4.3.2 Micelle Formation Theory ...... 18

5 Results 18 5.1 ASED modeling of interatomic forces ...... 18 5.1.1 Separation Distance ...... 18 5.1.2 Growth of Micelles ...... 19 5.2 Rheology ...... 19 5.2.1 Rheology: Oscillating Stress Sweep ...... 19 5.2.2 Rheology: Frequency Sweep ...... 21 5.3 Dynamic Light Scattering Results ...... 23 5.4 Atomic Force Microscopy ...... 24 5.5 Size Exclusion Chromatography ...... 24

6 Discussion 25

References 27

A Grease making procedure 29

B Rheology testing procedure 31

List of Figures 1 Continuum of micelle structures over water, oil, and surfactant (soap) concentrations. 4 2 Storage and loss moduli plotted against angular frequency of oscillation showing the relative intensity. Scaling is identical for both y-axes. The storage modulus is greater than the loss modulus at 20% grease and above which is an indication that it is still grease-like...... 5

1 3 Picture of the TA Instruments AR-G2 Rheometer as setup in the lab...... 9 4 Dynamic light scattering graphs comparing calcium sulfonate and lithium complex greases...... 10 5 Structure of grease as seen through AFM...... 11 6 Structure of Li 12-hydroxystearate...... 11 7 Stylized view of soap thickener molecule for calculating interactions. Image shows center and direction vector. Blue areas are negatively charged and associated with oxygen atoms. Red area is positively charged and associated with the Li ion . . . . . 12 8 Orientation of two thickener molecules in space...... 13 9 Energy vesus separation in the z-direction and ﬁt to Lennard-Jones 6-12 potential. . 19 10 Image of LiHSA from molecular dynamics calculation...... 20 11 Cone and Plate Rheometry of 3% LiOH grease in oil showing Oscillatory Stress vs Modulus ...... 20 12 Cone and Plate Rheometry of 4% LiOH grease in oil showing Oscillatory Strain rate vs Modulus...... 21 13 Cone and Plate Rheometry of 5% LiOH grease in oil showing Oscillatory Stress vs Modulus...... 21 14 The discrete relaxation spectra of the Time-Temperature superposition of 3% LiOH . 22 15 The discrete relaxation spectra of the Time-Temperature superposition of 4% LiOHs. 22 16 The discrete relaxation spectra of the Time-Temperature superposition of 5% LiOH. 23 17 Raw DLS results for 3% LiOH...... 24 18 Raw DLS results for 4% LiOH...... 24 19 Raw DLS reults for 5% LiOH...... 24 20 AFM results for 3% and 5% Li 12HSA grease...... 25 21 Size exclusion chromatography results for 3% and 5% Li 12HSA grease...... 25 22 Graphical representation of grease making recipe...... 29 23 Screenshot of software setup for test procedure...... 32

List of Tables 1 Crossover points...... 21 2 Grease recipe calculations...... 30 3 Parameters for rheological testing ...... 31 4 Parameters for Oscillating Stress Sweep (OSS) ...... 31 5 Parameters for Frequency Stress Sweep (FSS) ...... 32

2 Summary

Lithium 12-hydroxystearate (Li 12HSA) forms fibrous structures. The thickening properties are developed at the critical micelle concentration which has been found to be around the 4% to 5% soap concentration. – This is supported by rheological measurements, atomic force microscopy, and dynamic light scattering. Atomistic modeling shows that London dispersion forces drive the Li HSA into a fibrous structure. – The forces are strongest along the axis of the Li HSA – Infrared analysis suggests the molecules interact along an axial direction (fibers) rather than side-by-side (spheres). Two Li-12HSA molecules can interact in a few different structures. – The most stable is with the Li and O in a planar structure and the tails pointing away from each other. – This structure is supported by infrared analysis – The tails have a repulsive interaction of about 0.9 eV which is in the range of Van der Waals forces. Molecular dynamics calculations show that Li 12-HSA molecule adsorb along the length of the micelle bundle and be aligned with the long axis. – The growth of the fibers due to London dispersion forces makes them thicker. – The repulsion due to the ionic head groups coupled with the hydroxy groups staggers the placement making the fibers longer.

3 1 Introduction

Grease thickeners are most often compared to sponges holding oil instead of water. This idea is very helpful for designs using soap thickeners. This idea may not be so helpful for other thickener systems. Soap thickeners form reverse micelles in oil, see Figure 1.

Figure 1: Continuum of micelle structures over water, oil, and surfactant (soap) concentrations.

Other thickeners like alkyl benzene sulfonates may also form similar micelle structures. Micelle creation comes from the head (hydrophilic) and tail (lypophilic) structure. Polymer thickeners (polyurea) and solid thickeners do not have this same structure. The mechanism of bleed will be diﬀerent based on the type of thickener used so there may not be a “universal” mechanism. The structure of grease is complex and determined by the type of thickener. The interactions are governed by Van der Walls forces between the surfactant and the oil and between surfactant molecules themselves. There is also a physical entanglement occurring between the surfactant molecules and the lubricating oil molecular chains. There are chemical and mechanical interactions that make up the oil thickener matrix. Soap thickeners and perhaps the sulfonate thickeners form worm-like reverse micelle structures. The tails solubilized in the oil phase. In aqueous micelle formation the heads of fatty acid surfactant molecules form anions and the counter cation is solubilized by water molecules. This mechanism is absent in oil mixtures due to the very low concentration of water; i.e. there is no ionization of fatty acid soap molecules in grease. This is fortuitous with the heads crowded together if they were ionized the electrostatic repulsions would destabilize the micelle. This may be the mechanism of degradation when water gets into grease at higher concentration. Polymer thickeners can operate in a number of ways. Polyethylene and all long chain polymer additives can thicken simply by mechanical interaction with other polymer additives and the oil. Polyurea thickeners consist of short chain dimers and tetramers. Polyurea chains have both a carbonyl and a secondary amine group. These may interact through a hydrogen bonding interaction to make the chains act longer. Solid particle thickeners depend on the interaction with the lubricating oil resulting in the oil wetting the surface. Clay thickeners must be treated with surface active agents to increase the

4 interaction between the particles and the oil. Other solid thickeners must be matched with the oil type to provide enough interaction to provide thickening.

1.1 How does the grease thickener structure form? In order to determine how grease bleeds it is necessary to understand how the grease thickener matrix forms. The idea of a reverse micelle will be used as a starting point to understand grease formation. Micelle formation in aqueous solutions only happens after a critical micelle concentration (CMC) is reached. Grease thickeners also require a critical concentration for matrix formation.[21] The first task will be to measure the CMC for grease formation. Grease formation introduces a nonlinear component to the rheology of the mixture. Rheological testing will be used to determine when the grease first forms. Using a cone on plate rheometer the storage and loss moduli can be measured under oscillating motion. The method here will involve small angle oscillatory shear (SAOS). Under these conditions the goal is to measure the rheological properties without disturbing the thickener matrix. Multiple tests can be performed since the grease should not be significantly disturbed. Repeats and replicates will determine if this is indeed the case. Storage modulus is related to a “solid” material while the loss modulus is related to a “liquid” material. A rubber band has a large storage modulus with no loss modulus. Lubricating oil has a large loss modulus with no storage modulus. CMC will be the point when the storage modulus is larger than the loss modulus; i.e. the mixture is more solid than liquid, see Figure 2. Concentration will be altered by diluting fully formulated grease. This may require manufacturing laboratory quantities of grease with differing concentrations of thickener.

Figure 2: Storage and loss moduli plotted against angular frequency of oscillation showing the relative intensity. Scaling is identical for both y-axes. The storage modulus is greater than the loss modulus at 20% grease and above which is an indication that it is still grease-like.

[ht] Rheological measurements will get close to the critical micelle concentration but tells us nothing about the matrix formulation. Structure elucidation requires more precise measurements of the

5 interactions. Conventional analytical techniques like NMR can be used to investigate the interaction of the oil with the thickener. This will give information in the changes in the electronic environment of the atoms as they interact. There are also optical means of determining when the thickener agglomerates. Fluorescence polarization has been used to study micelle formation. Before agglomeration the molecules are free to move about giving a small polarization. As the molecules agglomerate and begin to form the thickener matrix the polarization increases. The change in polarization is what is measured. The interaction between the thickener molecules and the oil can also be modeled. The modeling can give the energy of interaction and some structural information. There has been some modeling of micelle formation in aqueous solutions, which can be extended here for non-aqueous solutions. Surface interactions are also well studied and will be extended to investigate the oil solid thickener interactions. The interaction with the least background will be the polyurea thickener interactions. These may not form micelles but may agglomerate through dipole-dipole interactions and hydrogen bonding. Thickener mixtures in oil act in a manner similar to proteins in an aqueous environment. This is deduced from the use of Maxwell and Kelvin models for both aqueous and non-aqueous mixtures as well as the similarity of normal or reversed “worm like” micellar structures. If the grease is modeled after an aqueous gel mixture like Gluten dough it is possible to develop a similar analytical methodology. These dough mixtures are network formers and develop their properties during mixing as the Gluten proteins unfold due to the shearing action of the mixing. Thickeners in oils can be visualized as performing similarly as the thickener unfolds exposing the chains more to the oil solvent. The proteins in dough mixtures crosslink through interactions of the disulfide bonds and interact with the solvent through hydrogen bonding. These forces are much stronger than in lubricating oil mixtures where the interactions are mostly from London dispersion forces. Disulfide bridges in protein crosslinking can only occur where there are sulfur atoms so the crosslinking can be destroyed by overly mixing (shearing) the mixture. If the thickener crosslinks are not site dependent they may survive excessive shearing. This would be an important property of lubricants. Testing of network formation and the investigation of the network interactions can follow similar testing and analyses developed by McKinley, Ewoldt, and Hosoi who used a Fourier transform rheological approach to analyzing the data from Large Angle Oscillatory Shear (LAOS) tests. This methodology will allow us to obtain a “rheological fingerprint” of the material through a strain stiffening ratio and the temporal evolution of thixotropy. The rheological fingerprint should be able to differentiate between the network formation of different thickeners.

1.2 Model of grease bleed? Once the mechanism of grease thickener formation is understood it will be possible to understand how the grease thickener matrix bleeds oil. Oil bleed is the mechanism most discussed as the mechanism for grease lubrication in loaded contacts. Bleed is variable among grease types with polyurea-thickened grease bleeding only slightly through soap thickened grease to solid thickened grease that bleed the most. For grease there is a static bleed and a dynamic bleed. A container of grease that is opened and oil was found pooled on the top is an example of static bleed. Dynamic bleed is found when pumping grease and the oil is pushed out from the thickener or oil separation is seen in a bearing contact.

6 Static bleed rate is relatively easy to measure using the cone bleed test or the pressure bleed test. These tests simply measure the amount of oil that is released from a grease sample for a given time at a given temperature. The cone bleed test (ASTM D-6184) exposes the grease to 100 °C for 30 hours. The pressure bleed test (ASTM D-1742) exposes the grease to 25 ◦C for 24 hours with 0.25 psi air pressure. Models of oil bleed consider either permeability or capillary ﬂow. Both are governed by Darcy’s Q k ∆p equation: A = ν L . Where the total discharge is proportional to the pressure drop divided by the viscosity. Cone bleed follows Darcy’s equation with ∆p equal to ρg. By measuring the viscosity as a function of thickener concentration we can arrive at a value of the proportionality constant, k. These proportionality constants will depend on how the viscosity changes with respect to thickener concentration and thickener type so the models should show a diﬀerent proportionality constant for each thickener system.

1.3 What is the relation of grease bleed to lubrication? Grease bleed is important in lubrication and usually manifests in fretting wear conditions. Tests have shown that rolling contact tests are more sensitive to grease bleed than sliding tests. Test- ing the relation of grease bleed on lubrication will involve testing under rolling or rolling sliding conditions as in the micro-pitting rig (MPR). We will also test full size rolling element bearings in a lubrication evaluation machine (LEM). Both tests will yield friction curves for the samples. Testing different grease thickeners at the same bleed will give an indication of how the bleed relates to friction. Sliding contacts generally are more sensitive to surface-active additive packages than to bleed. However; under short sliding distances for short times there may be an effect of bleed. This project will investigate the onset of wear under sliding conditions with short stroke length for short times. This testing has been performed in TESL to investigate chemical wear of surfaces and has shown some differences.

2 Motivation

The common understanding of how grease lubrication thickeners work is a “sponge” analogy. It is difficult to determine when this analogy started but in 1951 Bondi et al. stated the consistency of grease is due to the thin fibrous shapes of the soap forming a latticework that holds the oil by capillary forces.[4] In 1954 Boner reviews the literature discussion between syneresis and bleed.[5] Syneresis is the expulsion of liquid as the gel structure collapses and bleed is due to defects in the gel network. These terms are used interchangeably but are related to the effects of pressure on the lubricating grease; i.e. a sponge. The fibrous structure of lithium soap thickener in grease was known from about that time through electron micrographs produced by Brown, Huddson, and Loring.[6] Grease, as we know it today, is a three dimensional network of thickener particles. These thickener particles adhere to each other and the oil matrix through chemical and physical forces. The pores of this network are filled with oil possibly held by the addition of capillary forces. The sponge-like ability of grease is measured by the bleed property. Saatchi et al. developed a relationship between grease bleed and thickener particle shapes.[20] The bleed property is related to the shape of the thickener particles and the thickener particle shapes are in turn determined by the chemistry of the thickener. So at this time grease performance as measured by bleed is determined by the chemistry

7 of the thickener. If the shape of thickener particles can be made independent of teh chemistry then the grease can be better tailored to the applications. The key to make grease thickener shapes independent of chemistry is to ﬁrst determine how the thickener shapes initially form. This initial formation is determined by the intermolecular forces between thickener molecules. If it can be determined how thickener particle shapes initially form then by controlling those conditions other shapes might be achieved. If that is the case then the bleed properties can be controlled independent of the chemistry. This project is designed to determine how lithium 12-hydroxystearate thickener particles form into ﬁbrous structures.

3 Testing

3.1 Grease Formulation Rheological testing was performed on a TA ARG-2 rheometer using a cone with a 40 mm 2° base angle. Two types of rheological analysis were performed. Small angle Oscillating Stress Sweeps (SAOS) and Frequency Stress Sweeps (FSS). Table 2 and 3 in the appendix have the parameters for the tests. The Loss modules (G”) and Storage modules (G’) were obtained by the by the software and plotted, the crossover point of the two was used to see the critical micelle formation. The greases used in this project were formed using an ISO VG 10 base oil, 12-hydroxystearic acid, and LiOH. The greases were synthesized by heating the base oil to 150 °F and adding 12-hydroxystearic acid in a Kitchen Aide mixer ﬁtted with a controlled heater. After the 12- hydroxystearic acid melted and dissolved the temperature was raised to 200 °F and lithium hy- droxide and water solution was added. The temperature was increased to 250 °F. Llithium 12- hydroxystearate soap forms and the water is allowed to evaporate. While the temperature of the system was at 250 °F measurements were taken every 30 minutes to check water levels using a DL39 water Titrator conﬁgured for Karl Fisher titration. The mixture was left to cool without control.

3.2 Rheology A number of different greases were formulated with varying thickener concentrations to determine where the grease forms. Three different concentrations of grease 3%, 4% and 5% bracket the grease formation point and will be used to study the rheology changes as the grease forms. To test the grease micelle structure, a cone and plate TA AR G-2 rheometer was utilized with the TA Rheology Advantage instrument control and data analysis software. The cone was a 40 mm 2° cone. The rheometer was set up as shown in Figure 3. The grease was tested in an Oscillating Stress Sweep experiment at 40 °F and a frequency of 1 Hz with the stress ranging from 0.1 Pa to 1000 Pa. The loss (G”) and storage (G’) moduli and tan(δ) (the phase difference between the input and output frequencies) were measured using the rheometer software package. The point at which the loss modulus equaled the storage modulus is the point at which micelle structures forms. Three additional greases were synthesized with the following concentrations: below critical micelle concentration, at critical micelle concentration, and above critical micelle concentration. Oscillating frequency sweeps (OFS) were performed on the rheometer to calculate the discrete relaxation spectrum (DRS) of the grease structure. The DRS was calculated using time-temperature superposition (TTS) methods from the data collected from the OFS experiments over four temperatures ranging from -15 to 18 ºC. Lithium 12-hydroxystearate thickened greases were tested at 40,

8 Figure 3: Picture of the TA Instruments AR-G2 Rheometer as setup in the lab.

25, 10, and 5 ºC. OFS experiments measured the storage and loss moduli of the grease from 1-100 Hz at a strain of 0.1%. The low strain allowed for the assumption that the grease operated in the linear viscoelastic regime and the structure was not deformed during the test [10]. TTS analysis is part of the data analysis software. This calculation used the 40-degree curve as a reference curve and other OFS temperature results were shifted to create a master curve [23]. A discrete relaxation spectrum calculation was performed and results recorded. These curves were generated three times for each grease with the thickener structure below the critical micelle concentration, at the critical micelle concentration, and above the critical micelle concentration.

3.3 Dynamic Light Scattering Dynamic light scattering was performed on a Brookhaven Research Goniometer and Laser Light Scattering System. Dynamic light scattering of the samples was used to determine the size and shape of the particles. Light scattering experiments are performed by passing a laser beam through the sample and measuring the light that is deflected from the original path. The angle and intensity of the deflected light is used to determine the size and shape of the particles. Grease is difficult to determine because samples tend to be opaque. The samples need to be diluted to allow the beam to pass through. The risk is that the size and shape changes as the sample is diluted. Multiple samples diluted to different concentrations and measured did not see significant differences in particle size or shape. While performing DLS noise is a big concern, therefore, to prepare the samples the greases were serially diluted and then filtered through a 5mm nylon mesh to remove any large agglomerations. Hydrodynamic radius was obtained from all the sample to see how the micelles were forming at the different concentration. It is clear how the amplitude of the deflected light can be used to determine the size of the particles but how is shape information determined? Particles of different shape will scatter the light differently. Figure 4 shows the comparison of calcium sulfonate and lithium complex greases in a dynamic light scattering experiment. The top plot shows the scattering from calcium sulfonate thickened grease at angles of 50, 70, 90, and 100 degrees. The scattered light intensity curves have the peaks in the same position indicating spherical structures. A lithium complex grease in the lower plot at 60, 70,

9 Figure 4: Dynamic light scattering graphs comparing calcium sulfonate and lithium complex greases. and 90 degrees have the scattered intensity light peaks shifted. Calculations based on these shifts give a form factor that is the same as that of rods or ﬁbers.

3.4 Atomic Force Microscopy Atomic force microscopy was performed on a Bruker Dimension Icon AFM on tapping mode was used with a spring constant of 50 N m−1. Samples were prepped by dabbing disks of flat Germanium gently on their respective greases to smear it on the surface. After which the disks were washed with petroleum ether and dried with air. A metal tip is moved across the sample and the height is monitored. This gives an extremely precise measurement of the surface heights of the sample. There have been a number of experiments that were performed to visualize the thickener structure in grease. Recently atomic force microscopy (AFM) was used to look at the thickener structures. Cyriac, Lugt, Bosman, Padberg, and Venner published images (See Figure 5) showing the different types of thickener structures: fibrous, spherical, and platelet.[8]

3.5 Size Exclusion Chromatography Size exlcusion chromatography (SEC) is a method of measuring the molecular weight distribution of samples. Typically used for polymer samples. This method was used to determine if teh size of the agglomerated thickener would show up as a peak in the chromatogram. The samples were dissolved in a suitable solvent and injected onto the chromatographic column. The column separates the materials by molecular size which is related to the molecular weight eluting the larger molecules ﬁrst.

10 Figure 5: Structure of grease as seen through AFM.

4 Modeling

4.1 Geometry Any agglomeration of materials within a solvent matrix requires that they come into contact. Lithium 12-hydroxystearate (LiHSA) used as a thickener in lubricating greases has a tubular structure with a hydrophobic (lipophilic) tail and a hydrophilic (lipophobic) head. The head group consists of a lithium cation and an organic acid functional group. The organic acid functional group is a resonance structure with the charge distributed over the oxygen atoms. This is a classical structure used in modeling micelle structures in water. In lubricating oils the structures are reverse micelles. Modeling the interaction of two LiHSA molecules requires that the separation and relative angle of the molecules is known. LiHSA has the structure:

O− Li+

Figure 6: Structure of Li 12-hydroxystearate.

This structure can be simpliﬁed to a spherocylinder with charged areas on the surface. The center of this cylinder will be mean of the coordinates of the atoms. The direction of the spherocylinder is given by the unit vector along the center of the molecule pointing towards the Li atom. The center, (xc, yc, zc), of a molecule with n atoms is given by:

Σx Σy Σz (x , y , z ) = ( i i i ) (1) c c c n n n

11 The unit vector along the center of the molecule is more diﬃcult to calculate. For the purposes here only the carbon backbone will be used to determine the direction. Calculation of the direction vector starts with calculating the vectors of the carbon atoms from the center of the molecule:

hx, y, zii = (xi − xc, yi − yc, zi − zc) (2)

The vectors are then converted to unit vectors:

hx, y, zii hx, y, zii = (3) q 2 2 2 xi + yi + zi

Calculating the vectors of the carbon atoms in this manner yields vectors pointing in diﬀerent directions because some carbon atoms are on one side of the center and others are on the opposite side. The molecule positioned more or less along the x axis so the vectors were rotated so the x component was positive.

( hx, y, zii, if xi ≥ 0 hx, y, zii = (4) h−x, −y, −zii, otherwise

Then the mean of the vectors is computed:

1 hx, y, zi = Σhx, y, zi (5) n i The spherocylindrical shape of the soap thickener molecule then can be visualized by:

Center

Direction Vector

Figure 7: Stylized view of soap thickener molecule for calculating interactions. Image shows center and direction vector. Blue areas are negatively charged and associated with oxygen atoms. Red area is positively charged and associated with the Li ion

The separation and orientation of two thickener molecules can be related through a separation distance, the angular separation of the direction vectors, and a rotation about their axes. For this to be accomplished more easily lets set the center of one of the thickener molecules at the origin of the coordinate system with the direction vector lying along the x-axis. The thickener molecules are not symmetric because of the hydroxy group and the lithium carboxylate group. The separation of two thickener molecules is deﬁned as the separation of their respective centers:

p 2 2 2 d = ((x1 − x2) + (y1 − y2) + (z1 − z2) ) (6)

12 The orientation of the molecules is deﬁned as the angular separation of their respective direction vectors. This is easily calculated from the dot product of the vectors. Recall that the direction vectors are unit vectors so their magnitude is equal to 1.

~v · ~v cos φ = 1 2 (7) | ~v1|| ~v2|

= ~v1 · ~v2 (8) −1 φ = cos ( ~v1 · ~v2) (9)

There are two more variables that need to be specified to fix the orientation of one thickener molecule with respect to another. The separation distance gives the separation in the z direction but the molecules can move laterally in the x direction. This distance can be specified as the lateral distance, l. Because the molecules are not atomically cylindrical, there is a bend at the lithium carboxylate group, a spin angle around the molecular axis needs to be specified. The reference plane for the rotation can be set by placing the plane described by the axis of the molecule and the position of the lithium atom parallel to the xy plane of teh coordinate system. The spin angle then will be the angle between the reference plane and the plane of the molecule defined as above. These orientation variables are shown in Figure 9

Lateral Separation Spin Angle Separation Distance

Angular Rotation

x z y

Figure 8: Orientation of two thickener molecules in space.

The lubricant molecules can be visualized in the same manner but without the charged areas. LiHSA has an 18 carbon chain so an oil solvent of 18 carbons will have the same dimensions as the LiHSA. It follows that a 36 carbon chain would be twice the length and 9 carbon chain would be half the length. The size of the molecules can be obtained using Petitjean’s numerical algoritm for ﬁnding the smallest enclosing cylinder.[18] Petitjean provides a program that utilizes his algorithm for calculating the minimum enclosing cylinder.[17] Using this program yields a radius of the cylinder as 2.50 A¦ with a length of 22.38 A.¦

13 4.2 Theory 4.2.1 ASED Theory Determining the agglomeration of the thickener molecules requires calculating the interaction forces of the molecules as they approach each other. This interaction has three components: 1. an attractive force at long distances, 2. a repulsive force at close distance, and 3. a columbic force between the negatively charged areas and the positively charged areas. The forces and energies can be found by mapping the potential energy of the molecules as they move respective of each other in space. The distances should be large enough that electronic interactions requiring Hartree-Fock or Denity Functional methods are not necessary. This will ease the burden on the computational effort. Molecular mechanic methods can calculate the energies but it may be impossible to separate out the attractive, repulsive, and columbic energies. The method of choice will be a semi-empirical method. A method that has worked well in calculating structures and reaction mechanisms is Anderson’s modification of the Extended Hückel Method.[1] The Hückel method was described by Hückel in a series of papers in the early 1930’s.[13], [12], [14] The Hückel method uses the Linear Combination of Atomic Orbitals (LCAO) approximation to construct the wave functions for the eigenvalue problem from the atomic basis sets. So, given a normalized basis n set of atomic orbitals {φi}i=1 a wave function is constructed:

ψg = N(c1φ1 + ··· + cnφn) (10) Hψˆ (i) = Eψ(i) (11)

The normalization factor N and the coeﬃcients ci need to be determined such that:

Z ∗ ψg ψgdV = 1 (12) R3 The derivation proceeds to give the following equation, which, when solved, yields the molecular orbitals and orbital energies.

n X cj(Hij − ESij) = 0 (i = 1, ··· , n) (13) j=1

Here Sij is the atomic overlap integral and Hij is the exchange integral or the overlap and Hamil- tonian matrices, respectively. They are given by:

Z ∗ Sij = φi φjdV (14) R3 Z ∗ ˆ Hij = φi HφjdV (15) R3

14 The overlap integral is calculated in a straightforward manner but the Hückel method neglects differential overlap so off diagonal elements are zero and the diagonal elements are 1. The Hij are parameterized as:

 α, i = j;  Hij = β, i, j adjacent; (16) 0, otherwise.

α and β here are relative to the ionization potential of the carbon 2p orbital, approximately −11.4 eV. Hoffmann in 1963 introduced the Extended Hückel Theory (EHT) to more fully account for overlap, include s and p orbitals, and better define the parameterization.[11] EHT does not neglect differential overlap but calculates the overlap Sij pairwise between atom. Slater type orbitals are used. The diagonal Hamiltonian matrix elements, Hii, are the valence state ionization potentials of the orbitals obtained from Skinner and Pritchard.[22], [19] The off diagonal Hamiltonian matrix elements are given by:

Hij = 0.5K(Hii + Hjj)Sij (17)

Hoffmann set the value of K to equal 1.75 to reach a compromise between experimental energy barriers and stability of results.[11] The EHT method does not give reasonable bond lengths so can not reasonably map the potential energy surface between two atoms or two molecules. Anderson and Hoffmann attempted to correct this situation by adding a two-body electrostatic interaction to the calculation.[3] Anderson and Hoffmann started with the electronic charge density between two atoms given as:

ρ(Ri, ~r) = ρj(~r) + ρi(Ri − ~r) + ρNPF (Ri, ~r) (18)

The origin of the coordinate system is on nucleus j and ρi and ρj are the charge densities centered on the nuclei and follow the motions of the nuclei; these are repulsive forces. ρNPF is a charge density correction and is ”Non-Perfectly-Following” the nuclei; this is an attractive force. The Hellmann-Feynman formula is used to calculate the energies from the forces on the atoms. The Energies are given by:

W (Ri) = Wj(Ri) + WNPF (Ri) (19) Z −1 −1 Wj(Ri) = Zi[ZjRi − ρj(~r |Ri − ~r | dr] (20)

Z Ri Z 0 d 0 −1 0 WNPF = −Zi ρNPF (Ri, ~r ) 0 |Ri − ~r | drdRi (21) ∞ dRi

The Poisson equation is derived from the Laplacian of the energy giving the force constant of the bond.[2]

15 2 ke = ∇Ri W (Ri) (22) 2 = ∇Ri Wj(Ri) (23) = 4πZiρj(Ri) (24)

Because this equation gives a good approximation to k then ∇2 W (R ) is approximately zero e Ri NPF i −1 at the equilibrium position. This implies the NPF energy is attractive and proportional to Ri . This attractive force can be thought of as charge density being concentrated between the molecules through an induced dipole interaction. Feynman suggested this source of attractive forces as the attraction of a nucleus to its own distorted charge distribution leading to a 1/R7 force.[9] Taking this two-body repulsion into effect modifies the Hamiltonian matrix through simple addition.[1] α The diagonal matrix elements of the Hamiltonian on atom α, Hii , are still the valence state ion- α ization potentials explicitly shown as energies, Ei . The off diagonal matrix elements are the sum of the Hückel type matrix elements slightly modified and the two-body repulsion energy.

1 Hαβ =∼ K(Eα + Eβ)Sαβ + E Sαβ (25) ij 2 i j ij R ij

EHT sets the value of K to 1.75 but must be increased to a value of 2.25 in this method. Although bond lengths and force constants are predicted well the binding energy curves give higher energies. 1 α β αβ αβ −δR To improve the predictions from this method 2 K(Ei +Ej )Sij +ERSij is multiplied by e where δ = 0.13A˚−1. LiHSA is has an ionic headgroup and, as Anderson suggests, the energy curves may be improved (deepened) by adding a point-charge attractive energy to the total energy.[1]

4.3 Density Functional Theory Density functional theory or DFT is a method of computing the energy of a molecular structure. It is an ab-initio method in that the only information needed is the coordinates and types of the atoms in the molecule. The energy is calculated by solving Schr¨odinger’sequation:

HΨ = EΨ (26) where H is the Hamiltonian operator and E are the energy eigenvalues. Ψ is a wavefunction describing the positions of the electrons in the molecule. There are two main methods of solving this equation: choose a model wavefunction (molecular orbital theory) or choose the electron density (density functional theory). But what does the term “functional” mean? Normally we think of a function as an operation that maps one number to another; i.e. f(x) = y. A functional maps a set of functions to a number; i.e. g{f(x)} −→ R. This is essentially a function of functions. The Hamiltonian operator is simply the potential and kinetic energy operator of the electrons and nuclei of the molecule but it is the interactions of all of the particles that complicate the form. Mathematically the Hamiltonian is given by:

H = Te + Tn + Ve−e + Vn−n + Ve−n (27)

16 where the T are the kinetic energy operators of the electrons and nuclei, respectively. V are the potential energy operators of the electron – electron interactions, the nucleus – nucleus interactions, and the electron – nucleus interactions. When constructing the Hamiltonian using the Born-Oppenheimer approximation keeps the atomic nuclei stationary so Tn is zero and Vn−n is constant. Ve−n can be considered as an external field of the nucleus charge acting on the electron. What is left, Te + Ve−e is approximated in the various DFT methods. The approximations are given by functions of the electron density, ρ(~x). In DFT functionals are chosen that fit calculated energies of a test set of molecules with known energies. The most popular functional is designated the B3LYP functional and is popular because it gives good energy calculations in a reasonable computational time. B3LYP combines a correlation functional with an exchange functional. The B3 is a 3 parameter functional for the electron exchange developed by Becke. LYP is a correlation functional developed by Lee, Yang, and Parr. There are other functionals that are used in different chemical structures and charge distributions. In 1965 Kohn and Sham suggested an implementation of DFT to compute the energies. Their method was similar to the wavefunction method and relied on a linear combination of basis sets X Ψj(~r) = cj,αfα(~r) (28) α and a diagonalization of a matrix composed of the Hamiltonian and energy operators acting on the basis sets. Because the wavefunction method requires the calculation of electron-electron interactions but the DFT method accounts for this with the density functional so the electron-electron interactions do not need to be calculated it is very much simpler. For this project a set of Gaussian type orbitals (GTO) are used as the basis set and are designated as 6-31++G(d,p). This shorthand notation indicates that the orbitals on a heavy atom (anything heavier than H) is composed of a group of 6 GTOs for the S orbital, two groups of 3 GTOs and 1 GTO for the SP orbitals. The ++ adds additional P and D GTOs to polarize the orbitals. The (d,p) adds additional D and P GTOs to create larger orbitals that diffuse the electron density. These additions are used to increase the accuracy of the calculated energy. Density functional theory uses functionals of electron density to approximate the two-electron interaction when constructing Schrödinger’sequation. Wavefunctions comprised of a linear combination of basis sets are used to solve Schrödinger’sequation based on the Kohn-Sham method to calculate the energy of a molecule given the coordinates of and types of atoms.

4.3.1 Molecular Dynamics Theory The ASED theory above is used to ﬁnd the energy between two molecules. Studying the initial agglomeration requires the model to have many molecules both thickener molecules and solvent molecules. The energy of these models will be found by molecular dynamics calculations. Molecular dynamics diﬀers from quantum mechanics in that it uses classical equations of motion to evolve the system over time. The potential energy of a system of point charges is a summation of all of the energy of the point charge interactions divided by 2. The division is from counting the energy of interaction of atom 1 and atom 2 as well as atom 2 and atom 1. The equation is given by:

17 N N(j6=i) 1 X X qj U = k q (29) E 2 C i r i=1 j=1 ij

The attractive forces and repulsive forces are usually calculated as a Lennard-Jones 6-12 potential.[16][15] The Lennard-Jones equation can be simpliﬁed and given as:

A B E(r) = − (30) r12 r6 where A and B are values relating to the zero crossing energy and the bonding energy of the molecules. These will be found through a least squares procedure. The r−12 portion is considered the attractive component while the r−6 portion is the repulsive component. The minimum energy of the curve can be calculated from taking the derivative and setting that equal to zero. This yields:

r 2A r = 6 (31) min B

4.3.2 Micelle Formation Theory Micelle self-assembly in aqueous mixtures has been discussed thoroughly in the literature. The structures formed predicted by a packing parameter, v0/aIo with v0 the volume of the surfactant, a the area of the ionic head group, and I0 the length of the hydrophobic tail. This packing parameter places the micellar structure as spherical, cylindrical, or bilayer. Micelle formation in non-aqueous mixtures is not as well studied. The solubilities of the hydrophilic end of the micelle and water is vastly diﬀerent from the solubilities of the lipophilic end in oil. The mobility of water through water is much faster than the mobility of the larger oil molecules through oil. Because of this the micelles in oil are not as compact and well structured as micelles in water.

5 Results

5.1 ASED modeling of interatomic forces 5.1.1 Separation Distance Two thickener molecules as described above and considered rigid were moved relative to each other along the z direction; i.e. the separation distance. This calculated the potential energy surface. The data collected were fitted to a Lennard-Jones 6-12 potential.[16] The fitted curve gave a value ¦ of A= 33716293 and a value of B=1790.52 giving a calculated minimum distance of rmin =5.79 A. ¦ The fitted value of rmin is close to the iterated value from the ASED computations of 5.68 A. The results are shown in Figure 9.

18 Translation energy for motion in z-direction

From Theory From LJ 6-12 2.5 ·10−2 2

2 0

−2 1.5 5 5.5 6

Energy (eV) 1

0.5

4 5 6 7 8 9 10 Separation Distance (A)˚

Figure 9: Energy vesus separation in the z-direction and ﬁt to Lennard-Jones 6-12 potential.

5.1.2 Growth of Micelles Constructing a model of 13 LiHSA in a cube 60 A¦ on a side. The oil in this model consists of 197 hexatriacontane (C36H74), which yields about a 4% by weight mixture. A molecular dynamics calculation shows a self-assembly of the LiHSA into a tubular structure as shown in Figure 10 The calculated van der Waals interaction energy is 6.5 eV per molecule (627 kJ mol−1) which is close to that calculated for the two molecules interacting. These calculations were carried out using Biovia’s Molecular Studio suite of programs. One program can survey the potential energy surface to determine the most likely adsorption sites. The calculations show that the next LiHSA molecule will adsorb along the length of the micelle bundle and be aligned with the long axis. The growth of the ﬁbers due to London dispersion forces makes them thicker. The repulsion due to the ionic head groups coupled with the hydroxy groups staggers the placement making the ﬁbers longer.

5.2 Rheology 5.2.1 Rheology: Oscillating Stress Sweep OSS data was obtained from 3 diﬀerent concentrations: 3%, 4% and 5%. Figures 3, 4 and 5 show the modulus vs percent strain. The crossover points where the storage modulus (G’) was less than the loss modulus (G”) is the region where the behavior of the grease is that of a liquid

19 Figure 10: Image of LiHSA from molecular dynamics calculation. rather than a solid. We can see a significant difference amongst the crossover points between the 3 concentrations. Although there are no complex micelles forming at 3% there is still some stiffness that is observed at pressure less than 1 Pascal, this can be explained by the small concentrations of thickener molecules sticking to each other to form random and haphazard structures.

Figure 11: Cone and Plate Rheometry of 3% LiOH grease in oil showing Oscillatory Stress vs Modulus .

20 200 Pa to 300 Pa

Figure 12: Cone and Plate Rheometry of 4% LiOH grease in oil showing Oscillatory Strain rate vs Modulus.

Figure 13: Cone and Plate Rheometry of 5% LiOH grease in oil showing Oscillatory Stress vs Modulus.

5.2.2 Rheology: Frequency Sweep Frequency stress sweeps were performed on 3%, 4% and 5% grease on a range of temperatures from 10 °C to 70 °C. The discrete relaxation spectra (DRS) were plotted and compared. DRS were utilized to determine the crossover points listed in Table 1, i.e. points at which the storage and the loss moduli are equivalent. In other words, the points at which the grease transformed from either a solid to a liquid or a liquid to a solid. These crossover points can be seen in the master curves and relaxation spectra of each of the tested greases. Master curves are data generated from the TTS software and are the superposition of the frequency sweep curves translated in temperature. The master curves are ﬁtted to a generalized Maxwell model.

Table 1: Crossover points.

Concentration Soap Frequency (hertz) Modulus (pascal) 3% 75.5 7.7 4% 0.9 2195 5% Not Found Not Found

21 n 2 2 X Giτ ω G0 = i (32) 1 + ω2τ 2 i=1 i

n X ηiω G” = (33) 1 + ω2τ 2 i=1 i where n is the number of crossover points, ω is the frequency, τ is the relaxation time, and η is the grease viscosity. An example of the DRS calculated at 40 °C from the OFS tests performed at 10, 25, 40, and 65 °C is shown in Figure 3. The solid lines are the ﬁtted DRS curve representations. The positioning of the crossover points can be diﬃcult to visualize from Table 1. Figures 4 and 5 display the crossover points and thickener concentrations for each of the greases. In the only crossover point for the lithium hydroxystearate grease, the thickener concentration (3%) below the CMC had the lowest frequency and highest modulus crossover value, while the thickener concentration (5%) above the CMC had the highest frequency and lowest modulus crossover value. Sensibly, the thickener concentration (4%) at the CMC value had a frequency and modulus between the 3% and 5% samples.

Figure 14: The discrete relaxation spectra of the Time-Temperature superposition of 3% LiOH .

Figure 15: The discrete relaxation spectra of the Time-Temperature superposition of 4% LiOHs.

22 Figure 16: The discrete relaxation spectra of the Time-Temperature superposition of 5% LiOH.

The relaxation time for the system occurs at the crossover point. In Figures 14, 15, and 16 frequency increases left to right across the x axis. Relaxation time is the reciprocal of the frequency so relaxation time increases right to left. The relaxation time is shortest for the 3% concentration and longer for the 4% concentration. No relaxation time is found for the 5% concentration under the conditions of this test. How can these results be interpreted? Thinking about the crossover point in frequency at low frequencies of motion (left side of the plot) the material has time to respond and move out of the way. As the frequency of motion increases a point is reached where the motion is faster than the material can respond so it seems more solid. Like slowly moving your hand through water versus slapping the water. At 3% concentration the relaxation time is short which is indicative of smaller particles. At 4% concentration the relaxation time increases which is indicative of larger particles. There are also two peaks in the curve which may be due to different modes of interaction. This is the initial thickener agglomeration showing grease characteristics which for soap thickeners is the formation of fibrous structures. These fibrous structures not only get bigger (longer) but can also entangle leading to longer relaxation times (lower frequency). The peak at 3% is near a frequency of 100 Hz. 4% has a peak at 100 Hz and about 1 Hz. 5% has its peak at about 1 Hz. This is the initial formation of the fibrous structures captured in the rheological response.

5.3 Dynamic Light Scattering Results This results of dynamic light scattering for 3, 4, and 5% concentrations of Li 12-HSA show some interesting trends that compare favorably with the idea that the grease structure forms around the 4% concentration range. The size distributions for the 3% and 4% mixtures are bimodal with a region of small size and a region of large size. This changes radically at the 5% where the large particles disappear entirely leaving only a small agglomerate of very narrow size distribution. The size covers about 90% of the particles and is between 1400 and 1800 nm. The composition of the large particles in the 3% and 4% concentrations is unknown further investigation would resolve the issue.

23 Figure 17: Raw DLS results for 3% LiOH.

Figure 18: Raw DLS results for 4% LiOH.

Figure 19: Raw DLS reults for 5% LiOH.

5.4 Atomic Force Microscopy Atomic force microscopy was used to measure the 3% and 5% concentration samples, see Figure 20. We found the 3% sample devoid of surface structure. The 5% sample shows short but ﬁbrous like structures.

5.5 Size Exclusion Chromatography Would the formation of agglomerates maintain their structure and possibly show up as a peak in a size exclusion chromatogram. Figure 21 shows the chromatograms for 3, 4, and 5% Li 12-HSA

24 Figure 20: AFM results for 3% and 5% Li 12HSA grease. along with the chromatogram of the base oil. Very little diﬀerence is seen in the chromatograms indicating the agglomerates may not act as a single component or the structure is destroyed under the conditions of chromatography.

Figure 21: Size exclusion chromatography results for 3% and 5% Li 12HSA grease.

6 Discussion

Regardless of micelle concentration, all greases at lowest frequency show a higher loss modulus than a storage modulus. This would be where the greases have the longest relaxation time to flow, and as such, it is sensible that they would behave more like a viscous liquid than an elastic solid. As the relaxation times get shorter (frequency increases), then the greases should behave increasingly like an elastic solid as there is less time for oil to flow. This is in accordance with commonly accepted viscoelastic theory regarding time-temperature superposition [7]. This project was designed to determine the initial formation of grease which in turn is the initial agglomeration of thickener particles. This happens at about 4% thickener concentration of Li 12- HSA. The soap thickener forms fibrous structures which is supported by rheological studies, atomic force microscopy, dynamic light scattering, and modeling. The fibers grow in diameter due to

25 London dispersion forces and lengthwise due to ionic head group interaction. The head group interaction is supported by a combination of computational chemistry and infrared analysis. The computations were performed on molecules with short “tails” so the full attraction of the hydrocarbon tails and the eﬀects of the hydroxy group. So for a short tail without hydroxy groups there is a repulsive force. A longer tail with a hydroxy group yields an attractive force. Motivation for this project was to determine the forces involved in the initial agglomeration of grease thickener particles. This information then can be used to determine if the shape of the agglomerate can be controlled and manipulated to produce other shapes like spheres or platelets. If that can be accomplished then the combinations of thickener chemistry and bleed due to the shape can yield grease with novel properties.

26 References

[1] A. Anderson. Derivation of the extended hückel method with corrections: One electron molecular orbital theory for energy level and structure determinations. J. Chem. Phys., 62:1187, 1975. [2] A. Anderson. Vibrational potentials and structures in molecular and solid carbon, silicon, germanium, and tin. J. Chem. Phys., 63:4430, 1975. [3] A. Anderson and R. Hoffmann. Description of diatomic molecules using one electron configu- ration energies with two-body interactions. J. Chem. Phys., 60:4271, 1974. [4] A. Bondi, J. P. Caruso, H. M. Fraser, J. D. Smith, S. T. Abrams, A. M. Cravath, R. J. Moore, W. H. Peterson, A. L. Smith, F. H. Stross, E. R. White, and J. N. Wilson. Developments in the field of soda base greases. In Proceedings of the 3rd World Petroleum Congress. World Petroleum Congress, World Petroleum Congress. [5] C. J. Boner. Manufacture and application of lubricating greases. Reinhold Publishing Corpo- ration. [6] J.A. Brown, C.N. Huddson, and L.D. Loring. Lithium compounds—electron microscope study of lithium greases. 15(11):8. [7] R. M. Christensen. Theory of Viscoelasticity. Dover Publications, 2 edition, 2003. [8] F. Cyriac, Pieter Martin Lugt, Rob Bosman, Clemens J. Padberg, and Cornelis H. Venner. Effect of thickener particle geometry and concentration on the grease ehl film thickness at medium speeds. Tribology letters, 61(2):1–13, 2016. Open access. [9] R. Feynman. Forces in molecules. Physical Review, 56:340, August 1939. [10] W. M. Findley, J. S. Lai, and K. Onaran. Creep and Relaxatino of Nonlinear Viscoelastic Materials. Dover, 1976. [11] R. Hoffmann. An extended hückel theory. i. hydrocarbons. The journal of Chemical Physics, 39(6):1397, September 1963. [12] E. Hückel. Quanstentheoretische beiträge zum benzolproblem ii. quantentheorie der in- duzierten polaritäten. Zeitschrift für Physik, 72(5-6):310–337, May 1931. [13] E. Hückel. Quantentheoretische beiträgezum benzolproblem. i. die elekfronenkonfigurafion des benzols und verwandfer verbindungen. Zeitschrift für Physik, 70(3-4):204–286, March 1931. [14] E. Hückel. Quantentheoretische beirägezum problem der aromatischen und ungesättigten verbindungen. iii. Zeitschrift fürPhysik, 76(9-10):628–648, September 1932. [15] J. E. Lennard-Jones. Cohesion. Proc. Phys. Soc., 43:461, 1931. [16] J. E. Lennard-Jones and S. Chapman. On the determination of molecular fields. —ii. from the equation of state of a gas. Proceedings of the Royal Society of London. Series A, 106, October 1924. [17] M.Petitjean. http://petitjeanmichel.free.fr/itoweb.petitjean.freeware.html#cyl. [18] Michel Petitjean. About the algebraic solutions of smallest enclosing cylinders problems. Ap- plicable Algebra in Engineering, Communication and Computing, 23(3-4):151–164, 2012.

27 [19] H. O. Pritchard and H. A. Skinner. The concept of electronegativity. Chem. Rev., 55:745, 1955. [20] A. Saatchi, P. J. Shiller, S. A. Eghtesadi, T. Liu, and G. L. Doll. A fundamental study of oil release mechanism in soap and non-soap thickened greases. 110:333–340. [21] P. Shiller. Measuring the ”worms” in grease. NLGI Spokesman, 74(6):18–26, 2011. [22] H. A. Skinner and H. O. Pritchard. The measure of electronegativity. Trans. Faraday Soc., 49:1254–1262, 1953. [23] M. Williams, R. Landel, and J. Ferry. The time dependence of relaxation mechanisms in amorphous polymers and other glass forming liquids. page 3701, 1955.

28 A Grease making procedure

1. Pour 1000 g of the base oil into the mixing bowl. Make sure that the mixing bowl has a thermocouple attached to its base. 2. Attach the bowl to the mixer and ﬁt the heating mantle under it. Add a ceramic block under the mantle to make sure the mantle is ﬂush against the surface of the bowl. 3. Attach a secondary thermocouple to the handle of the bowl. 4. Add the required amount of 12-hydroxystearic acid as needed for the concentration given by Table 2. 5. Turn on the heating elements to 150 °F and set the stir speed to the lowest setting. 6. Once the 12-hydroxystearic acid has dissolved add the solution of LiOH in deionized water and turn the temperature to 200 °F 7. After 10 mins turn the temperature to 250 °F to evaporate the water. 8. Check the water content by using the DL39 water Titrator every 30 mins. When the water level is suitably low about 100 ppm, remove the heating element. Care must be taken to keep stirring as it cools down to prevent bubbling and burning. 9. Transfer the grease to a clean, airtight container for storage.

Figure 22: Graphical representation of grease making recipe.

29 Table 2: Grease recipe calculations.

3% soap Assume oil 1000 g then 1030.9278 g total weight then 30.9278 g Li 12HSA or 0.1006 mol Li 12HSA or 0.1006 mol LiOH and 0.1006 mol 12HSA giving 2.4093 g LiOH and 30.2295 g 12HSA

4% soap Assume oil 1000 g then 1041.6667 g total weight then 41.6667 g Li 12HSA or 0.1355 mol Li 12HSA or 0.1355 mol LiOH and 0.1355 mol 12HSA giving 3.2459 g LiOH and 40.7259 g 12HSA

5% soap Assume oil 1000 g then 1052.6316 g total weight then 52.6316 g Li 12HSA or 0.1712 mol Li 12HSA or 0.1712 mol LiOH and 0.1712 mol 12HSA giving 4.1000 g LiOH and 51.4433 g 12HSA

30 B Rheology testing procedure

1. Switch on the rheometer and make sure the base plate and cone are clean, if not clean the surface of the plate and the head of the cone with hexane and Kim wipes. 2. Attach the base plate to its mount, plugging in the red plug and pump connectors to the rheometer. Switch on the pump. 3. Open the software and click on Tab 1 and set the initial temperature to 40 °C. 4. Calibrate the instrument inertia. Options Instrument Inertia Calibrate Make sure to observe that the cone is not attached and click Finish 5. Take the 40 mm 2° cone and attach it to its mount by sliding it in and turning the knob on the top to engage it. 6. Return to the software and click on Tab 2 to calibrate the Geometry Inertia. Options Instrument Miscellaneous Calibrate Bearing Friction 7. Set the Zero Gap Tab 1 Zero gap icon Set Gap Continue Raise head 8. Set Rotor Mapping Rotor Mapping Pop Out Perform Mapping 9. Set the sample on the plate making sure there is enough to cover the head of the cone. Go to Geometry depth 10. Click on Tab 3 and set the experiment parameters as seen in Table 3 and Figure 23. Make sure to click the check marks of Event Temperature and Perform Equilibrium 11. Set the Post-Experiment temperature to 25 °C 12. Name the ﬁle and start the experiment.

Table 3: Parameters for rheological testing

Sweep Oscillating Stress (Pa) Range 0.1 Pa to 100 Pa Mode Log Points per decade 20 Frequency 1 Hz

Table 4: Parameters for Oscillating Stress Sweep (OSS)

Temperature (°C) 40 Frequency (Hz 1 Stress Range (Pa 0.1 to 500

31 Figure 23: Screenshot of software setup for test procedure.

Table 5: Parameters for Frequency Stress Sweep (FSS)

Temperature (°C) 10 to 70 Frequency (Hz 1 to 100 Stress (Pa 70