Rheological Behavior of Surface Modified Silica Nanoparticles

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Rheological behavior of surface modified silica nanoparticles dispersed in Partially Hydrolyzed Polyacrylamide and Xanthan Gum solutions: Experimental measurements, mechanistic understanding, and model development Laura M. Corredor-Rojas, Abdolhossein Hemmati Sarapardeh, Maen M. Husein, Prof. Mingzhe Dong, and Brij B. Maini Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b02658 • Publication Date (Web): 20 Sep 2018 Downloaded from http://pubs.acs.org on September 22, 2018

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Energy & Fuels

Carboxylic acid

O R

Modified silica NP

Silica +

OH

+

+H

R

C

Si

-OH

R

C OH

OH

OH

OH

+

H

Silica

O

+

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OH

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R

OH2

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Si

-H

OH

-H2 O

O

+

+

O Si

Si

Modified silica NP R1 CH2 CH

Silane

R1 Silica surface H

O Si HO

OH

O

H

H

H

O

O

O

Si

Si

Si OH

O

OH

OH

2

OR

+ R O Si OR H2C OH

R1

n

Si O HO

OH

O

O

ACS Paragon Plus Environment

Si

Si

Si OH

O

O

O

Si

n

+ 3ROH

n

Si

O

OH

O

OH

OH

O Si

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Rheological behavior of surface modified silica nanoparticles

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dispersed in Partially Hydrolyzed Polyacrylamide and Xanthan

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Gum solutions: Experimental measurements, mechanistic

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understanding, and model development

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Laura M. Corredor-Rojasa, Abdolhossein Hemmati-Sarapardehb,*, Maen M. Huseina,*, Mingzhe Donga, Brij B. Mainia

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a

9

b

Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive Northwest, Calgary, Alberta T2N 1N4, Canada Department of Petroleum Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

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ABSTRACT

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Polymer solutions are designed to develop a favorable mobility ratio between the injected polymer solution and the oil-water bank being displaced by the polymer. Subsequently, a more uniform volumetric sweep of the reservoir is produced. Chemical and mechanical degradation of the polymer solutions, on the other hand, reduce their viscosity which significantly affects their performance. The primary objective of this study is to investigate the effect of surface modification of silica nanoparticles (NPs) on the effective viscosity of partially hydrolyzed polyacrylamide (HPAM) and xanthan gum (XG) solutions at different NP concentrations and temperatures. The chemical functionalization of SiO2 NPs with carboxylic acids and silanes was confirmed by FTIR measurements. The experimental results showed that the addition of SiO2 NP increased the viscosity of XG solutions due to the formation of three-dimensional structures between the silica NPs and the polymeric chains. The thickening effect of HPAM was improved by the addition of silica NPs modified with 3-(methacryloyloxy)propyl] trimethoxy silane (MPS), octyl triethoxy silane (OTES), and oleic acid-method A (OAA). In addition, the HPAM and XG nanopolymer sols of modified silica NPs showed more temperature and brine tolerance than that of unmodified silica NPs. A model was developed based on multilayer perceptron (MLP) neural network for predicting viscosity of nanopolymer sols using 9900 data points. The MLP model was trained by Bayesian Regularization (BR), Levenberg-Marquardt (LM), Resilient Backpropagation (RB), and Scaled conjugate gradient (SCG) algorithms. The results revealed that the BR-MLP model outperformed the three other models and could predict all the viscosity data with an average absolute relative error of 2.46% and R2 of 0.999.

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Keywords: surface modified, nanoparticle, HPAM, XG, viscosity, polymer flooding, MLP

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*Corresponding authors: A. Hemmati-Sarapardeh ([email protected]) and M. Husein

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([email protected]) 1 ACS Paragon Plus Environment

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1. Introduction

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Polymer flooding results from adding a high-molecular-weight water-soluble polymer to the

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injected water in a waterflood to reduce the mobility ratio by increasing water viscosity and

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reducing the formation permeability.1 The reduced mobility ratio, defined as the ratio of the

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displacing fluid mobility to the displaced fluid mobility, results in an increase in the volumetric

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sweep efficiency compared to water flooding. This effect is particularly significant in highly

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heterogeneous reservoirs and reservoirs with poor vertical sweep efficiency due to gravity. The

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viscosity-increasing feature of polymers is derived from the repulsion between polymer

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molecules and between the segments of the same molecule.

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The two types of polymers primarily used in polymer flooding are synthetic polymers and

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biopolymers.2 HPAM is the most-used synthetic polymer to date. Its performance depends on its

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molecular weight and its degree of hydrolysis. The typical molecular weight of HPAM used is

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within the range of 2 - 20 × 106 Dalton and the degree of hydrolysis is within 25% - 35%. HPAM

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solutions often suffers from viscosity loss due to conditions as high temperature, high pressure,

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and presence of other chemical substances in the oil reservoirs.

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XG is the most widely used biopolymer for polymer flooding, but its current use is low

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compared to HPAM, in part due to its higher cost. The viscosity of the XG solutions is relatively

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insensitive to the salinity of the brine solvent and mechanical shearing, but it is quite susceptible

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to biological degradation.3

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Recent studies have shown that the addition of silica NPs to polyacrylamide solutions increases

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their mobility control ability, temperature tolerance, and salt-tolerance1,4,5 and consequently,

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increases the oil recovery. Silica NPs have received more attention due to their well-defined

2 ACS Paragon Plus Environment

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ordered structure, high surface area, cost-effective production, and the ease of surface

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modification.6

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Maghzi et al.4 found that the addition of 0.1 wt.% of nanosilica in polymer solution increased

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polyacrylamide (PAM) viscosity to 2-4 times, and the pseudoplasticity behavior of the solution

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was improved only at low and medium shear rates. They concluded that it could be a reason for a

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10% increasing oil recovery during flooding test by nanopolymer sols in comparison with

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polymer flooding. Maurya and Mandal1 reported that PAM got adsorbed on the surface of silica

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by virtue of hydrogen bonding and the silica particles acted as physical cross-linker between the

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polymeric chains resulting in improvement of viscosity of the displacing fluid. The decrease in

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viscosity in case of silica/PAM suspension was less than that in case of the PAM solution in

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presence of salt. Also, the results indicated that the viscosity of both silica/PAM suspension and

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PAM solution is strongly dependent on temperature. For both systems, the viscosity decreased as

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the temperature increased. However, the viscosity of silica/PAM suspension was at least 1.5

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times higher than that of PAM solution at all temperatures. Kennedy et al.7 studied the rheology

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of XG, locust bean gum and mixed biopolymer gel with nanosilica. These results showed that

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nanosilica changed the rheological behavior of XG, including enhanced viscosity and elasticity.

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It is well known that the best performance of these nanopolymer sols can be obtained when the

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silica NPs are uniformly dispersed in the polymer solution. Good extent dispersion can be

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achieved by altering the silanols of the surface of silica NPs with organic functionality, either

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physically or chemically by covalent bonding.6 The modification of silica particles leads to better

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hydrophobic interactions with the polymer when compared to unmodified hydrophilic fillers.8

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On the basis of chemical interaction, the silylation of hydroxyl groups using organoalkoxysilanes

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is the most commonly used method for surface modification of silica particles .9–15 Other


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modifiers have been proposed to avoid some drawbacks accompanying the silylation reaction as

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some silanols groups of the coupling agent might remain in the product causing further

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condensation reactions during the period of storage and usage of the formed nanopolymer sol.

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Those modifiers include alcohols16, carboxylic acids17, and polymers. 6,18–26

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All those surface modification techniques have been widely studied for producing

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polymer/silica nanocomposites that have potential application as coatings, sensors, proton

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exchange membranes, etc.27, but they have not been studied for enhanced oil recovery (EOR)

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applications.

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In this study, the silica NPs are treated by chemical grafting with carboxylic acids and silanes to

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generate different interfacial interactions. To this end, two polymers are used and also eight NPs

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are synthesized. The expected effects are: (i) hydrophobicity of the NPs is increased, facilitating

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silica NPs/polymer miscibility and a more uniform dispersion of the NPs; (ii) the interaction

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between the treated NPs and the polymer can be tailored by changing the species of the coupling

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agents to improve the mobility and control the ability of polymer solutions for polymer flooding.

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A model is developed based on multilayer perceptron (MLP) neural network for predicting

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viscosity of nanopolymer sols (9900 data points). The MLP model is trained by Bayesian

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Regularization (BR), Levenberg-Marquardt (LM), Resilient Backpropagation (RB), and Scaled

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conjugate gradient (SCG) algorithms. Statistical and graphical error analyses are conducted to

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evaluate the performance of the developed models.

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1. Materials and Methods 2.1 Materials. Dodecanedioic acid (DDDA, 99%), stearic acid (C18H36O2, 95%), oleic acid (C18H34O2,

90%),

3-(Methacryloyloxy)propyl]

trimethoxy


silane

(MPS,

98%),

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Octyl(triethoxy)silane (OTES, ≥97.5%), sulfuric acid (H2SO4, 95-98%), ethanol (EtOH, 99%),

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hydrochloric acid (ACS reagent, 37%), sodium dodecyl sulfate (SDS, ≥98.5%), formaldehyde

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solution (37 wt.% in water, contains 10-15% of methanol as stabilizer), sodium chloride (NaCl ,

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99%), fumed silica powder (0.007 µm) were all obtained from Sigma-Aldrich (USA). Acetic

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acid (99.5%), cyclohexane (99.5%), and ammonium hydroxide (28-30 wt.% solutions of NH3 in

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water) were obtained from Fisher Scientific. Xanthan gum (XG, MW>2.106 Dalton) was

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obtained from MP Biomedicals and FloopamTM 3630s (HPAM, hydrolysis degree 30-35%, MW>

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20.106 Dalton) was obtained from SNF Floerger, USA). All chemicals were used as received.

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2.2

Synthesis. Synthesis of SiO2 NPs modified with dodecanedioic acid (DDDA). A mass of 4

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g of SiO2 NPs was dispersed into 100 mL of acetic acid using an ultrasound bath for 1 h. Then, 1

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g of DDDA and 0.1 mL of H2SO4 were added to the dispersion which was stirred at 150 rpm for

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another hour at 70°C using a magnetic stirrer. Afterward, the acetic acid was recovered using a

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rotary evaporator. The dispersion was neutralized with 5 mL of 28-30 wt.% aqueous ammonia

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solution while agitation continued for 1 h. The mixture was centrifuged at 2500 rpm for 30 min.

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The precipitate was washed three times with 20 mL of 1/1 EtOH/water (V/V) solution to remove

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excess DDDA. The precipitate was dried in an oven at 90°C for 24 h to yield 2.02 g of modified

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SiO2-DDDA powder.

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Synthesis of SiO2 NPs modified with oleic acid. The surface functionalization of SiO2 NPs with

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oleic acid was carried out by using two different procedures. For the first procedure, a mass of 3

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g of SiO2 NPs was dispersed into 100 mL of cyclohexane using an ultrasound bath for 3 h. Then

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1.5 mL of oleic acid was added to the dispersion which was stirred at 150 rpm for 1 h at 75°C.

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The cyclohexane was recovered using a rotary evaporator. Then, 5 mL of 28-30 wt.% aqueous

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ammonia solution was added to the solution. The solution was stirred for 1 h at 80 rpm and 45°C.


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The mixture was centrifuged at 2500 rpm for 30 min. The precipitate was washed three times

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with 25 mL of 1:1 EtOH/water (V/V) solution to remove the excess amount of oleic acid. The

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precipitate was dried in an oven at 60°C for 24 h to yield 2.17 g of modified SiO2-OAA powder.

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The second modification was performed following a procedure proposed by Mahdavian et al.19.

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A mass of 3 g of SiO2 NPs was dispersed into 90 mL of deionized water (DI) using an ultrasound

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bath for 3 h. Then 1.5 mL oleic acid was added into the dispersion which was stirred at 150 rpm

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for 90 min at room temperature. Then, 5 mL of 25 wt.% aqueous ammonia solution was added

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into the solution while agitation continued overnight. The dispersion was neutralized with 30

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wt.% aqueous HCl solution. The mixture was centrifuged at 2500 rpm for 30 min. The

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precipitate was washed three times with 15 mL of 1:1 EtOH/water (V/V) solution to remove the

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excess amount of oleic acid. The precipitate was dried in an oven at 50°C for 24 h to yield 2.51 g

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of modified SiO2-OAB.

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Synthesis of SiO2 NPs modified with stearic acid. The surface functionalization of SiO2 NPs

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with stearic acid was carried out using two different procedures. For the first procedure, 1 g of

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stearic acid was dissolved in 100 mL of cyclohexane at 45°C under magnetic stirrer (80 rpm).

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Then, 4 g of SiO2 NPs and 0.2 mL of H2SO4 were added to the solution and agitation continued

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for another hour. Afterward, the temperature was increased to 75°C while agitation continued for

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2 h. The cyclohexane was recovered using a rotary evaporator. The precipitate was dispersed

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with 100 mL of 1/1 EtOH/water (V/V) solution and 5 mL of 28-30 wt.% aqueous ammonia

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solution. The mixture was centrifuged at 2500 rpm for 30 min. The precipitate was washed three

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times with 25 mL of 1:1 EtOH/water (V/V) solution to remove excess stearic acid. The

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precipitate was dried in an oven at 90°C for 24 h to yield 3.14 g of modified SiO2-SAA powder.


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For the second procedure, the same steps were followed except that H2SO4 was not added to the dispersion. A mass of 3.28 g of modified SiO2-SAB powder was obtained.

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Synthesis of SiO2 NPs modified with MPS and OTES. A mass of 4 g of SiO2 NPs was dispersed

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into 80 mL of cyclohexane by using an ultrasonic bath for 1 h. Then, 1.6 mL of MPS or 2.09 mL

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of OTES was added to the dispersion. The dispersion was stirred for 12 h at room temperature.

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Then, it was centrifugated at 2500 rpm for 30 min. The precipitate was washed three times with

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EtOH. The precipitate was dried in an oven at 70°C for 24 h to yield 3.44 g of modified SiO2-

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MPS powder and 3.29 g of SiO2-OTES.

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2.3 Characterization of the NP. A Fourier transform infrared spectrometer, FTIR (model

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IRaffinity-1s, Shimadzu, Japan) was used to analyze the NPs. Each spectrum was recorded over

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the range of 4000–400 cm−1. Dry KBr was used for running the background spectrum. Scanning

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electron microscopy coupled with energy dispersive X-ray, SEM-EDX (Phenom proX scanning

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electron microscope, ThermoFisher scientific, Canada) was used to identify the elemental

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composition of the surface modified silica NPs.

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2.4

Nanopolymer sols preparation. Three different concentrations of SiO2 NPs (0.5, 1.0 and

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2 wt.%) were used to prepare the nanopolymer sols. At first, SiO2 NPs were dispersed in DI

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water and ultrasonicated for 1 h. A concentration of 0.1 wt.% of sodium dodecyl sulfate (SDS)

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was added and the dispersions were stirred for 30 min. To prepare the HPAM nanopolymer sols,

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0.4 wt.% of HPAM were added to the dispersions which were gently stirred for 48 h. To prepare

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XG nanopolymer sols, 0.4 wt.% of XG were added to the dispersions which were stirred for 1 h

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at 45°C. Finally, 1.0 wt.% of NaCl was added to each sample.

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2.5 Viscosity of the nanopolymer sols. The viscosities were measured at 25°C and 70°C on a

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Thermo Scientific™ viscometer (HAAKE RotoVisco 1, USA). The viscosity measurements


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were conducted at shear rate from 5.0 to 100 s−1. Each measurement was repeated at least three

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times to confirm the reproducibility, with the uncertainty found to be in the order of ± 1 to 7% of

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the reported value.

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3. Model Development

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3.1. Multilayer perceptron neural network

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One of computational intelligence systems is artificial neural networks (ANNs), which are

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inspired form biological nervous systems. ANNs are widely used to find complex relationships

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among outputs and inputs of a systems. Generally speaking, ANN has different elements

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including weights, biases, nodes (neurons), transfer functions which help to find the unknown

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relationships among the independent variables and the desirable output. Weights and biases are

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interconnections which provide connections among processing elements, neurons

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the proposed ANN models, Multilayer Perceptron (MLP) is recognized as the most commonly

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used network in different areas such as petroleum engineering, chemical engineering, etc. This

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type of network includes several layers in which the first layer is assigned to the inputs, while the

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last layer is the desired output. The layers between the input and output layers are known as

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hidden layers. Hidden layers establish the relationship between the output and inputs. 28–30

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Each layer has a certain number of neurons; the number of neurons in the first layer is equal to

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the number of input variables, where the last layer has only one neuron, which is the output of

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the model. The number of neurons in the hidden layers are normally determined using a trial and

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error procedure. Transfer functions are used in the neurons of hidden layers and output layer to

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help the network providing more accurate results. Weights connect neurons in different layers to


28–30

. Among

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each other and each neuron in the hidden layers and output layer has also a bias. The value of a

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neuron is passed through an activation/transfer function. In previous studies, we have completely

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described mathematical formulation of the MLP networks. 31,32

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The output of an MLP model having two hidden layers with logsig and purelin activation

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functions for the two layers, respectively, and tansig for output layer is calculated as follows: Output = tan sig (w3 × ( purelin(w2 × (log sig ( x) + b1 )) + b2 ) + b3 )

(1)

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In this formula, b1/b2/b2 are bias vectors of the first hidden layer/the second hidden layer/the

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output layer. Furthermore, w1/w2/w3 are the weight matrices of the first hidden layer/the second

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hidden layer/the output layer. Different methods can be used to train the MLP networks using

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actual data. Normally, Levenberg-Marquardt (LM) is used for training such networks, while in

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this study we used four different methods namely Scaled conjugate gradient (SCG), Bayesian

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Regularization (BR), Resilient Backpropagation (RB), and Levenberg-Marquardt (LM) for

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training neural networks, principle of which can be found in our previous publication32. The

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proposed models based on these algorithms were called SCG-MLP, BR-MLP, RB-MLP, and

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LM-MLP, respectively.

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3.2 Preprocessing of the data for modeling

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Each neural network model uses a set of inputs to calculate the desirable output. Selecting the

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proper inputs for a model plays a key role in efficiency of the developed model. In fact, inputs

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should cover all of affecting parameters on the output and also be independent. The aim of this

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part is to find all of the affecting parameters/properties on the viscosity of nanopolymer sols.

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Therefore, viscosity is regarded as the output of our proposed models. The affecting parameters 9 ACS Paragon Plus Environment

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on the viscosity include shear rate, type of NP, type of polymer, temperature, and concentration

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of NPs. In this study, we only used a certain amount of SDS and NaCl in all experiments;

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therefore, these parameters should not be selected as inputs as they are the same in all systems. It

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should be noted the input of the model should quantitative rather than qualitative. To This end,

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we assigned a number for the type of NP and polymer. For polymers, instead of using the name

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of polymers as inputs, we used 1 for HPAM and 2 for XG. For NPs, we used 0 for SiO2

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(unmodified), 3 for SiO2-SAB, 4 for SiO2-SAA, 5 for SiO2-OAB, 6 for SiO2-OAA, 7 for SiO2-

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DDDA, 8 for SiO2-MPS, 9 for SiO2-OTES, and 10 for the systems without any NPs. In

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summary, viscosity is regarded as a function of type of polymer, type of NP, concentration of NP

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(%), temperature (Celsius), and shear rate (s-1). = , , . % , , ℎ 2

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4. Results and Discussion

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3.1 FTIR and SEM-EDX results. Figures 1 and 2 show the FTIR spectra of unmodified and

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modified silica NPs after normalization of the peak area. Unmodified silica shows peaks at 3745

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and 3367 cm−1 which are assignable to (Si-OH) isolated groups and (Si–OH) stretching

228

vibration.33 The peaks at 1627 and 1130 cm−1 correspond to (O–H) bending vibration of

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adsorbed molecular water and asymmetric stretching vibration of (Si-O-Si band). The peaks at

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806 and 469 cm−1 are assigned to (Si-O-Si) symmetric bending vibration and (Si–O) rocking

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vibration33, respectively.

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The characteristic peaks of MPS are 2951 and 2481 cm−1 which are assigned to the asymmetric

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and symmetric (C-H) stretching vibrations, and the peaks at 1703, 1456 and 1406 cm−1

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correspond to the stretching vibration of (C=O), methylene (C–H) and vinyl (C–H) bending

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vibration of MPS34, respectively. The identification of these peaks and the peaks at 970 and 1274 10 ACS Paragon Plus Environment

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cm-1 ascribed to Si-C bond35 in the IR spectrum of the modified SiO2 (Figure 1), proves the

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bonding of MPS in the silica surface.

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The characteristics peaks of OTES are 2926 and 2858 cm-1 which show very intense

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asymmetric and symmetric (C-H) stretching vibrations. These bands are more intense than those

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shown by MPS due to the large number of -CH2 groups in the octyl group36. These peaks are

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identified in the IR spectrum of the SiO2-OTES NPs. Also, two more peaks are identified in this

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spectrum. The peak at 1392 cm−1 which is assigned to the asymmetric deformation vibration of

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(C-H) shown a slight substitution of the octyl groups in place of the -OH groups37 and the peak at

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960 cm-1 which is ascribed to (Si-C) bond. The identification of all these peaks in the IR

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spectrum of the modified SiO2 (Figure 1), proves the bonding of OTES in the silica surface.

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Figure 1. IR spectrum of SiO2, SiO2-MPS, and SiO2-OTES.

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The characteristic peaks of the carboxylic acids (DDDA, SA and OA) are ~2927 and ~2851

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cm−1 which are assigned to the asymmetric and symmetric (C-H) stretching vibrations of -CH3 or

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-CH2 groups, ~1690 cm-1 which correspond to the stretching vibration of (C=O), 1446 cm-1

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which is ascribed to the symmetric stretching of (COO-)38, and 1400 cm-1 which is ascribed to 11 ACS Paragon Plus Environment

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the (C–H) bending vibration. The identification of these peaks in the IR spectrums of SiO2-OA,

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SiO2SA, and SiO2-DDDA (Figure 2), proves the bonding of the carboxylic acids in the silica

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surface.

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Figure 2. Infrared spectroscopy of (a) SiO2-DDDA, (b) SiO2-OAA and SiO2-OAB, and (c) SiO2-SAA and SiO2-SAB. 12 ACS Paragon Plus Environment

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The chemical modification of the silica surface with all these compounds is confirmed through SEM-EDX results presented in Table 1. Table 1. Elemental analysis per EDX results.

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Sample SiO2 SiO2-SAA SiO2-SAB SiO2-OAA SiO2-OAB SiO2-DDDA SiO2-MPS SiO2-OTES

Concentration, wt.% O Si C 58.72 36.39 4.89 60.46 26.47 13.07 46.91 46.3 6.79 54.82 38.07 7.11 33.49 43.98 22.53 58.52 34.41 7.07 48.23 43.99 7.79 40.66 54.23 5.11

262

263 264 265 266

3.2 Effect of NP concentration and temperature on the viscosity of the HPAM nanopolymer sols. The results of HPAM solutions and HPAM nanopolymer sols are presented in Figure 3 and 4, respectively.

267

It is known that electrolytes tend to suppress the pseudo-plasticity of HPAM solutions.26,39–41

268

When HPAM is dissolved in water, the groups COO- of the molecular chain repel each other

269

causing its structure to remain extended. This feature gives the molecular chain a higher

270

hydrodynamic volume, increasing the viscosity of the polymer solution. When salt is added, the

271

cations of the salt neutralize the intrinsic electrical charges on the polymer particles. The charge

272

shielding effect causes the chains of the polymer to coil up into roughly spherical coils exposing

273

the minimum surface to the water which decreases the interactions between polymer chains.

274

Also, the polymer chains hydrate poorly so that the effective size of the swollen polymer

275

molecules decreases. Both effects cause the solution viscosity and its dependence on the shear


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Energy & Fuels

276

rate to decrease (Figure 3). On the other hand, the apparent viscosity of the HPAM solutions did

277

not significantly decrease with temperature.

278 279 280 281

Figure 3. Effect of salt and temperature on the viscosity of the HPAM solutions at constant polymer (0.4 wt.%), SDS (0.1 wt.%) and salt concentration (1 wt.%), whenever applicable.

282

It is observed from Figure 4 that the addition of untreated silica to the HPAM solutions has a

283

positive effect on the viscosity values at all concentrations. The same effect was observed for

284

silica modified with both silanes and OAA. The viscosity increase is attributed to adsorption of

285

the polymer molecules at the silica surface via hydrogen bonding between the oxygen or nitrogen

286

from HPAM and the hydrogen from the SiO2 surface (SiO-H ּ◌···N-H or SiO-H ּ◌···O-CNH2) or

287

between the hydrogen from the HPAM and the oxygen of the SiO2 surface (SiO···HNH-CO-C)42–

288

44

289

modifier molecules. In both cases, the silica particles act as physical cross-linker between the

290

polymeric chains.

or the hydrophobic interaction between the hydrocarbon backbone of the polymer and the

291

It has been demonstrated that despite the unfavorable electrostatic interactions between the

292

anionic polymer and the negatively charged silica particles, polymer adsorption does occur. 14 ACS Paragon Plus Environment

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293

Otsubo and Watanabe45 reported that during the adsorption process, polymeric chains can be

294

attached to more than one particle at a time and a number of polymeric chains can be attached to

295

the surface of one particle. Upon adsorption, only a portion of the polymer chain is in contact

296

with the NP surface (at single or several points), while the rest extend away from the silica

297

particle. This free chain can be adsorbed onto different silica particles, leading to the formation

298

of a three-dimensional network of flocs.46 The network structure is controlled by five parameters

299

that include polymer size, NP size, NP surface coverage, thickness of the adsorbed polymer

300

layer, and the interparticle repulsion range.47

301

When the silica particles concentration increases the viscosity of the nanopolymer sol increases

302

because of insufficient coverage of the particle surface with polymeric chains. This in turn

303

promotes the bridging of the polymer among more silica particles. This network is stable and not

304

easily broken by the irreversible adsorption of the polymer. Polymer adsorption is irreversible

305

because the polymeric chains may not be able to desorb simultaneously from all attached sites.

306

Desorption is determined by several factors, such as the charge density of the polyion, the nature

307

and charge of the surface, the concentration and molecular weight of the polymer, the salt

308

concentration in the solution, and the non-electrostatic interactions of the macromolecules with

309

each other and with the surface.43

310


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Energy & Fuels

T = 25°C

T = 70°C

a

b

c

d

e

f

311 312 313 314

Figure 4. Viscosity of the HPAM nanopolymer sols with (a-b) 0.5 wt.%, (c-d) 1.0 wt.%, and (ef) 2.0 wt.% NP concentration at 25°C and 70°C.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

315

The reduction in viscosity values caused by the addition of SAA, SAB, and OAB modified

316

silica NPs into the HPAM solutions suggests that the amount of polymer adsorbed at the silica

317

surface is high. It appears that the polymer molecule attaches to the particle at multiple points,

318

which promotes coiling of the polymer chain. Such adsorption at the silica surface reduces the

319

bridging of polymer with different silica particles and reduces the hydrodynamic size of the

320

polymer molecule which results in a lower viscosity than the HPAM solution. Sedeva et al.48

321

studied the adsorption of modified PAM on gold substrates with different degrees of

322

hydrophobicity and found that both the adsorbed amount of polymer and the adsorption rate

323

increase with the hydrophobicity of the gold substrates. The EDX analysis (Table 1) shows that

324

the silica NPs modified with SAA, SAB, and OAB are more hydrophobic than the silica NPs

325

modified with OAA and silanes. This suggests that polymer adsorption occurs via hydrophobic

326

interaction between the R-CH3 chain on the silica surface and the polymer backbone (-CH2-CH2-

327

).

328

Adsorption of the polymer molecules at the silica surface in case of the HPAM-DDDA

329

nanopolymer sols can occur via hydrogen bonding between carboxyl groups of the HPAM and

330

the COOH of the silica surface. The reduction in viscosity can be attributed to the low interaction

331

between NPs and polymer chains caused by the formation of the hydrogen bonding between the

332

carboxyl groups of the NPs. The increase of the concentration of the silica NPs modified with

333

SAA, SAB, DDDA, and OAB in HPAM solutions did not dramatically affect the viscosity,

334

contrary to what was expected. It suggests that the polymer adsorption mechanism is

335

predominant in the viscosity reduction.

336 337


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338 339 340 341

Energy & Fuels

3.3 Effect of NP concentration and temperature on the viscosity of the XG nanopolymer sols. The results of XG solutions and XG nanopolymer sols are presented in Figures 5 and 6, respectively.

342 343 344 345

Figure 5. Effect of salt and temperature on the viscosity of the XG solutions at constant polymer (0.4 wt.%), SDS (0.1 wt.%) and salt concentration (1 wt.%), whenever applicable.

346

The XG polymer and nanopolymer sols exhibited non-Newtonian flow and shear-thinning

347

behavior due to the uncoiling and partial alignment of the polymer chains in the high shear rate

348

region (Figure 5). The addition of 1 wt.% salt made the viscosity higher than that of a salt-free

349

solution. This effect was previously studied by Wyatt and Liberatore.49 They reported that the

350

effect of salt concentration on the viscosity change is highly dependent on the polymer

351

concentration. For polymer concentrations below the critical concentration (CC~ 2000 ppm), the

352

viscosity dramatically decreases upon addition of salt. The addition of salt neutralizes the

353

charges on the XG molecules, therefore the elongated molecules (disordered conformation state)

354

are transformed into helix molecular conformation (ordered conformation state), which occupy 18 ACS Paragon Plus Environment

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355

smaller hydrodynamic volume. When the concentration is > CC, the interaction among the

356

intermolecular bonds increases, and its effect on solution viscosity is relatively more important

357

than the effect caused by the change in the hydrodynamic volume of the molecules.

358

As observed in Figure 5, XG solutions viscosity decreased at 70°C. The change in viscosity is

359

attributed to a conformation transition of the backbone from helix (ordered) to elongated

360

molecules (disordered) with progressive decrease of the rigidity of the (1-4)-β-D-glucan chain as

361

temperature increases.50

362

Addition of unmodified silica cannot mitigate the viscosity reduction when the temperature

363

increases from 25 to 70°C. However, the nanopolymer viscosity is higher than that of the XG

364

solution at low shear rates. The significant viscosity reduction can be attributed to the decrease in

365

the number of cross-linkers in the network formed by the NPs and the polymeric chains caused

366

by the reduction in the adsorbed amount of polymer onto the SiO2 surface. Also, the increase in

367

viscosity with the addition of silanes, SAA, OAA, OAB, and DDDA-modified silica can be

368

attributed to the crosslinking between the NPs and the polymeric chains through hydrogen

369

bonding or hydrophobic interaction. For silica modified with silanes, SAA, OAA, and OAB, the

370

crosslinking occurs via hydrophobic interaction between the R-CH3 chain on the silica surface

371

and the XG backbone. For XG-DDDA nanopolymer sols, the crosslinking can occur via

372

hydrogen bonding between the carboxylate groups on the trisaccharide side chains of the XG and

373

the COOH groups of the DDDA molecules attached to the silica surface. The viscosity reduction

374

caused by the increment of temperature from 25 to 70 °C is attributed to the weakening of the

375

hydrogen bonds and the hydrophobic interactions between the modified NPs and the XG chains.

376


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Energy & Fuels

T = 25°C

T = 70°C

a

b

c

d

e

f

377 378 379 380

Figure 6. Viscosity of the XG nanopolymer sols with a-b) 0.5 wt.%, c-d) 1.0 wt.%, and e-f) 2.0 wt.% of NP concentration at 25°C and 70°C.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

381

3.4. Evaluation of the viscosity models of the nanopolymer sols

382

An efficient and reliable model for accurate predicting the viscosity of the nanopolymer sols is

383

developed based on the experimental data. To this end, MLP neural network was selected which

384

has been widely used in many industries. The data points were randomly divided into two sets

385

including training (80%) and testing sets (20%). A four layer MLP model was designed to

386

accurately predict the large number of viscosity data. The first layer corresponds to inputs which

387

have five neurons and the last layer is assigned to output (viscosity) which has one neuron, as

388

stated earlier. The optimum architecture for the hidden layers was found to be 10 neurons for

389

both hidden layers, and tansig and logsig activation functions for the first and second hidden

390

layers, respectively. Purelin was selected as the activation function of the output layer.

391

For finding the optimum structure, different number of neurons in the first and second hidden

392

layers were considered and the networks were trained with Bayesian Regularization (BR),

393

Levenberg-Marquardt (LM), Resilient Backpropagation (RB), and Scaled Conjugate Gradient

394

(SCG) algorithms. The performance of each network depends, not only the number of neurons in

395

hidden layers, but also on the initial weights and biases which were randomly assigned to the

396

network. To find an appropriate number of neurons in the hidden layers, different number of

397

neurons in the hidden layers were tried and 10 neurons for both hidden layers were found a good

398

structure using all training algorithms after running the networks 20 times. Afterward, 10

399

neurons in each hidden layer were considered, and each model was trained a 100 times using

400

random initial weights and biases and the best model for each of the four algorithms, based on

401

statistical error analysis, were selected. Instruction for using the models is reported in the

402

Supplementary File. To evaluate the performance of each model, some statistical parameters;

403

including average absolute relative error (AARE%), average relative error (ARE%), standard


Page 22 of 30

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Energy & Fuels

404

deviation (SD), root mean square error (RMSE), and R2 were used. Formulations and definitions

405

of these parameters can be found elsewhere32. The aforementioned statistical parameters for the

406

developed models are reported in Table 2 for training, testing, and whole data sets. As can be

407

seen in Table 2, all of the developed models have acceptable performance and could predict

408

viscosity of the nanopolymer sols with satisfactory accuracy in all sub sets. Nevertheless, BR-

409

MLP model has higher accuracy followed by LM-MLP, SCG-MLP, and RP-MLP. BR-MLP

410

model predicts all the data with an average absolute relative error of 2.47% and R2 of 0.9996. It

411

is interesting to note that the statistical parameters in training and testing sets are close to each

412

other, suggesting that overfitting was not an issue during model training. In addition, the average

413

relative error in all models is close to zero, illustrating no overestimation or underestimation in

414

the models.

415 416

Table 2. Statistical errors of the proposed models for predicting viscosity of nanopolymer sols Model

BR-MLP

LM-MLP

SCG-MLP

Set

ARE%

AARE%

RMSE

SD

R2

Train

-0.12

2.45

0.0029

0.0014

0.9996

Test

-0.20

2.52

0.0036

0.0015

0.9994

Total

-0.14

2.46

0.0031

0.0014

0.9996

Train

-0.22

3.99

0.0047

0.0046

0.9991

Test

-0.25

3.88

0.0051

0.0040

0.9987

Total

-0.23

3.96

0.0048

0.0045

0.9990

Train

-1.24

7.78

0.0147

0.0134

0.9916

Test

-0.98

7.78

0.0143

0.0141

0.9910

Total

-1.19

7.78

0.0146

0.0135

0.9915


Energy & Fuels

RP-MLP

Train

-1.28

10.37

0.0183

0.0237

0.9874

Test

-1.38

10.64

0.0177

0.0274

0.9844

Total

-1.30

10.43

0.0182

0.0244

0.9869

417

2.5

2.5

2

2 Predicted Viscosity, Pa.s

Predicted Viscosity, Pa.s

418

1.5

1 BR-MLP 0.5

1.5

1 LM-MLP 0.5

Y=X

0

Y=X

0 0

0.5 1 1.5 2 Experimental Viscosity, Pa.s

2.5

0


2.5

419 2.5

2.5

2

2

1.5

1 SCG-MLP 0.5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 30

1 RP-MLP 0.5

Y=X

0

Y=X

0 0

420 421 422 423

1.5


2.5

0


2.5

Figure 7. Crossplot of the proposed MLP models for predicting the viscosity of the nanopolymer sols.


Page 25 of 30

424

The performance of the developed models was further checked graphically. For this purpose,

425

crossplot of all the models is depicted in Figure 7. In this figure, the predicted valued by the

426

proposed models were plotted against their corresponding experimental data. Figure 7 clearly

427

shows that the data points in all the models are close to the unit slope line, suggesting good

428

performance of the developed models. Nevertheless, the dispersion of the data around the unit

429

slope line is less in BR-MLP model followed by LM-MLP model. These graphical results are in

430

good agreement with statistical parameters, which attests to the superiority of the BR-MLP

431

model. It is noticeable that the RP-MLP model underestimates the viscosity data at high values.

432

To further graphically compare the performance of the developed models, the cumulative

433

frequency of the data versus their absolute relative errors was plotted in Figure 8. The proximity

434

of the model prediction to the vertical axis shows a higher model accuracy. Figure 8 again

435

confirms that the proposed BR-MLP model has the best performance among the developed

436

models and could predict 50% of the data with an absolute relative error of less than 1.35% and

437

80% of the data with an absolute relative error of less than 4.4%.

438 1

Cumulative Frequency

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.8

0.6 BR-MLP

0.4

LM-MLP 0.2

SCGMLP

0 0

5

10

15

20

Absolute Relative Error,%

439 440 441

Figure 8. Cumulative frequency versus absolute relative error of the proposed MLP models for predicting viscosity of nanopolymer sols 24 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

442 443

Conclusions

444

The steady shear viscosity of HPAM nanopolymer sols exhibited shear-thinning behavior at

445

every NP concentration and temperature tested in this study. It was observed that the addition of

446

unmodified silica NPs and modified silica NPs (with both silanes and OAA) improved the

447

thickening behavior of the HPAM solution. However, silica NPs modified with DDDA, SAA,

448

SAB, and OAB resulted in reduction in the viscosity of the HPAM solution. The XG

449

nanopolymers sols, on the other hand, exhibited shear-thinning behavior over the entire range of

450

shear rate tested as well as enhanced viscosity with increased modified/unmodified NP

451

concentration. The increase in viscosity is most likely due to the formation of three-dimensional

452

structures between the silica NPs and the XG polymeric chains. Both HPAM and XG

453

nanopolymer sols of the modified silica NPs showed more temperature tolerance than the

454

unmodified silica NPs. As expected, HPAM solutions and nanopolymer sols were more sensitive

455

to salinity and temperature changes than the XG sols. The results of neural network modeling

456

confirmed that the developed BR-MLP model outperformed the other models. BR-MLP model

457

prediction displayed an average absolute relative error of 2.46% and R2 of 0.9996. The proposed

458

model can predict the viscosity of the nanopolymer sols at different temperatures, shear rates,

459

types of polymers, and type and concentration of the modified/unmodified NPs with high

460

accuracy.

461

462 463

ACKNOWLEDGMENT


Page 26 of 30

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Energy & Fuels

464

Laura M Corredor-Rojas expresses her gratitude to Ecopetrol S.A for the awarded scholarship to

465

pursue her graduate studies. Special thanks to Amitabha Majumdar for his great help in the

466

experimental work.

467 468 469

NOMENCLATURE SiO2-DDDA

Silica modified with 1-12 dodecanedioic acid

SiO2-MPS

Silica modified with 3-(methacryloyloxy)propyl] trimethoxy silane

SiO2-OAA

Silica modified with oleic acid-Method A

SiO2-OAB

Silica modified with oleic acid-Method B

SiO2-OTES

Silica modified with octyl triethoxy silane

SiO2-SAA

Silica modified with stearic acid-Method A

SiO2-SAB

Silica modified with stearic acid-Method B

470 471 472

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539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584

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Rheological Behavior of Surface Modified Silica Nanoparticles

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