Study on the association behavior of a hydrophobically modified polyacrylamide in aqueous solution based on host-guest inclusion

Study on the association behavior of a hydrophobically modified polyacrylamide in aqueous solution based on host-guest inclusion

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Accepted Manuscript Study on the association behavior of a hydrophobically modified polyacrylamide in aqueous solution based on host-guest inclusion

Wanli Kang, Zhou Zhu, Hongbin Yang, Shujie Tian, Pengxiang Wang, Xiangfeng Zhang, Zeeshan Ali Lashari PII: DOI: Reference:

S0167-7322(18)34391-5 https://doi.org/10.1016/j.molliq.2018.11.063 MOLLIQ 9973

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

26 August 2018 4 November 2018 14 November 2018

Please cite this article as: Wanli Kang, Zhou Zhu, Hongbin Yang, Shujie Tian, Pengxiang Wang, Xiangfeng Zhang, Zeeshan Ali Lashari , Study on the association behavior of a hydrophobically modified polyacrylamide in aqueous solution based on host-guest inclusion. Molliq (2018), https://doi.org/10.1016/j.molliq.2018.11.063

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ACCEPTED MANUSCRIPT Study on the association behavior of a hydrophobically modified polyacrylamide in aqueous solution based on host-guest inclusion a,

Wanli Kang *, Zhou Zhu , Hongbin Yang a, Shujie Tian b, Pengxiang Wang a, Xiangfeng Zhang a, Zeeshan Ali Lashari a a

a

School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, PR China b

School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, PR China *Corresponding authors: Wanli Kang (Email: [email protected]; Tel.: +86-13589332193)

Abstract

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A quantitative method to study the association behavior of the hydrophobically modified

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polyacrylamide (HMPAM) in aqueous solution was proposed based on host-guest inclusion. Scanning

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electron microscopy (SEM), dynamic light scattering (DLS), rheometer and fluorescence probe were also used to investigate its association behavior for comparative study. The hydrophobic association

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contribution rate (HACR) of HMPAM can be quantitatively calculated by means of β-cyclodextrin

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inclusion. The critical association concentration (CAC) of Poly (AM-co-AMPS-co-DS) (PAAD) terpolymer obtained by the HACRs was about 924 mg/L, which was almost consistent with that (882

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mg/L) obtained by the method of fluorescence probe. SEM images showed that larger supra-molecular

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aggregates formed as HMPAM concentrations were higher than CAC. Moreover, the effects of temperature and salt on the association behavior were also characterized by the HACRs, and the results

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were also confirmed by the methods of rheology, DLS and fluorescence probe. Thus, HACR is another

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way to study the association behavior of HMPAM in aqueous solutions. Keywords: hydrophobically modified polyacrylamide; association behavior; host-guest inclusion; enhance oil recovery

1

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1. Introduction During a chemical flooding to enhance oil recovery (EOR), mobility control is generally required to divert the injected fluids to the poorly swept layer[1]. These tasks are usually implemented by adding water-soluble polymers into the aqueous phase to increase the displacing phase viscosity[2].

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Among them, partially hydrolyzed polyacrylamide (HPAM) is a common water-soluble polymer for

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EOR due to its low cost, good water solubility and excellent thickening capacity[3]. However, HPAM

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as a mobility control agent can hardly meet the requirements in oil and gas field development due to the harsh reservoir conditions such as high salinity brine with divalent ions and high temperature[4]. To

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further expand the application of chemical flooding to more challenging conditions, hydrophobically

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modified polyacrylamide has attracted widespread interest in the last decade [5-8]. HMPAM are water-soluble polymers that contain some hydrophobic units and functional groups

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in the molecule backbone[9, 10]. Taylor and Nasr-El-Din[11] pointed out that acrylamide was

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commonly used to prepare HMPAM through copolymerization with free radical reaction. In aqueous solution, the presence of those hydrophobic units in the molecule promotes the associations of

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intra-molecular and inter-molecular at a certain concentration range, resulting in a sharp increase in

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solution viscosity[12, 13]. In addition, the introduction of functional groups gives these polymers more excellent properties, i.e., temperature resistance and salinity tolerance[14, 15]. Those aspects are of great technological interest, especially for EOR[16, 17]. According to what have been mentioned above, the viscosity is an important factor in the performance of those HMPAMs used for EOR. Several researchers [9, 18, 19] had observed that the association behavior of HMPAM in aqueous solution could affect its thickening ability. Generally, the association behavior of HMPAM was studied by dynamic light scattering, scanning electron 2

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microscopy and atomic force microscope, etc.[20-22]. The changes of the association behavior for HMPAM under different reservoir conditions (temperature, salinity and pH value, etc.) could be qualitatively analyzed by these methods. However, the quantitatively study of the association behavior is still a problem. Although some methods are capable of quantitatively analyzing the association

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behavior of the HMPAMs[23-25], these methods usually require specialized equipment. In addition,

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some materials used in the tests (e.g., pyrene as a probe) are toxic, and testing processes are relatively

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cumbersome. In order to study the association behavior more effectively, a simple, safe and reliable quantitative method is necessary.

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Cyclodextrin (CD) has a torus-shaped ring structure linked by 1, 4-α-glucosidic bonds[26].

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According to the number of glucose units, there are mainly three types of CDs named α-CD, β-CD, and γ-CD with 6, 7 and 8 glucose units, respectively[27]. Each CD molecule is composed of a hydrophobic

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inner core and a hydrophilic outer shell[28]. Due to the specific structure, CD can selectively

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incorporate hydrophobic groups of suitable size into their cavities to form inclusion complexes through hydrophobic interactions between the inner core of CD and the hydrophobic groups[29, 30]. Some

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studies[31, 32] have shown that the size of CD cavity has an impact on the interactions. The cavity

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diameters of α-CD, β-CD, and γ-CD are 4.7~5.3 Å, 6.0~6.5 Å, and 7.5~8.3 Å, respectively[33]. For HMPAM, the hydrophobic units generally contain long alkyl chains or benzene groups. For long alkyl chains such as C18 group, its cross-section diameter is 3.1 Å[33], which can enter the cavity of α-CD, β-CD, or γ-CD. However, it may not enter the cavity of α-CD for benzene group with a cross-section diameter of 5.8 Å[34]. Due to the larger cross-section diameter of γ-CD, host-guest inclusion complexes could not be formed. Therefore, β-CD is commonly used as a host inclusion material because it has an appropriate cavity size. 3

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In this work, an HMPAM as the research object was prepared by micellar polymerization. The rigid structure of benzene and the flexible structure of the long-chain alkyl group allowed the polymer to have excellent thermal-stability and strong hydrophobic association. The introduction of sulfonic acid functional group also gave the polymer an excellent salt tolerance. In our previous study[35], it

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was reported that the intensity of hydrophobic association was characterized by the method of β-CD

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inclusion. With the deepening of research, it was feasible to study the association behavior of HMPAM

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based on host-guest inclusion. The purpose of this work is to introduce a quantitative method for studying the association behavior of HMPAM in aqueous solutions. It provides theoretical and

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methodological guidance for the application of HMPAM in chemical EOR.

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2. Experimental 2.1 Materials

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Acrylamide (AM) was purchased from Kemiou Chemical Reagent Co., Ltd. (Tianjin, China) and

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used without further purification. 2-acrylamido-2-methylpropanesulfonic acid (AMPS), 2, 2'-azobis (2-methylpropionamidine) dihydrochloride (AIBA), sodium hydroxide (NaOH), sodium dodecyl

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sulfate (SDS), ethanol, β-cyclodextrin (β-CD) and sodium chloride (NaCl) were purchased from the

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Aladdin Chemical Reagent Factory (Shanghai, China) as analytical pure products. 4-dodecylstyrene (DS) was synthesized according to the method described in the literature[36, 37]. 2.2 Synthesis of co-polymers Poly (AM-co-AMPS-co-DS) (PAAD) terpolymer was prepared by micellar polymerization. AM (7.69 g, 108.26 mmol), AMPS (2.54 g, 12.26 mmol), SDS (7.95 g, 27.60 mmol) and DS (0.50 g, 1.84 mmol) were dissolved in deionized water, and then the prepared solution was filled in a three-necked flask with mechanical stirrer. Thereafter, the pH value of the solution was adjusted to 7 by using 10 M 4

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NaOH solution. The mass concentration of all monomers was set at 25%. The solution was purged with nitrogen for 1 hour to remove oxygen and the temperature of water bath was set to 45℃. AIBA (4.29 mg) was introduced into the mixture when the temperature reached 45℃. In a nitrogen atmosphere, the polymerization reaction was carried on at this temperature for 4 hours. The obtained co-polymer was

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purified by dissolution in deionized water and precipitation with ethanol. The purification procedure

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was repeated several times. Finally, the dried co-polymer product was granulated to obtain PAAD

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powder. Another modified polyacrylamide without hydrophobic units, poly (AM-co-AMPS) (PAAM), was also prepared in our lab for comparative study[38]. The chemical structures of two co-polymers

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were shown in Fig.1. Composition and parameters of the co-polymers were shown in Tab.1. From

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Tab.1, it can be seen that each monomer was well involved in the copolymerization reaction. The weight-average molecular mass (MW) of PAAD and PAAM were very close. However, there were

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differences in the z-average root-mean-square radius of gyration () and the second virial

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coefficient (A2) of those polymers. The of PAAD was greater than that of PAAM because of hydrophobic association among polymer molecules. The smaller A2 showed that PAAD had a worse

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solubility than that of PAAM (without hydrophobic unit). The structure of PAAD was characterized by

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FT-IR and 1HNMR in the supplement material.

* z

y

*

x O

O

O O

R S

x O

NH

NH2

* y

*

O NH2 O O

NH

S O

O

PAAM

PAAD

R=

Fig.1 Chemical structures of the co-polymers 5

ACCEPTED MANUSCRIPT Tab.1 Composition and parameters of the co-polymers Feed molar ratio a

Sample

Actual molar ratio b

MW c

c

A2 c

(g/mol)

(nm)

(cm3mol/g2)

88.5:10:1.5

88.44:9.98:1.47

2.62×106

134.8

1.27×10-5

PAAM

90:10

88.92:10.08 [35]

2.97×106

106.2

1.56×10-3

a

Determined by orthogonal experiment ( see Tab.S1).

b

Determined by elemental analysis ( see Tab.S2).

c

Determined by laser light scattering ( see Tab.S3).

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PAAD

2.3 Preparation of co-polymer solution and inclusion solution

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The co-polymer solution was prepared by the dried polymer powder dissolved in aqueous solution

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with the help of mechanical stirring (300 revolutions per minute) at 25℃ for 4 hours. The inclusion

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solutions were prepared by adding β-CD into the co-polymer solution until β-CD dissolved completely. The prepared solutions were placed at room temperature.

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2.4 Apparent viscosity

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The apparent viscosity of the solution was measured by using a DV-II+PRO Viscometer

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(Brookfield, USA). During the test, the rotational speed of the rotor was constant at 6 revolutions per minute and test temperature was 25℃.

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2.5 Hydrophobic association contribution rate Hydrophobic association contribution rate (HACR) was determined based on the apparent

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viscosity of the solution. The initial apparent viscosity of the co-polymer solution (without β-CD) was recorded as ηi. The apparent viscosity of the inclusion solution was recorded as ηs when it was stable as β-CD concentration increased. The HACR of the solution could be calculated by using Equation 1. This method can also be seen in our previous study[35].

HACR 

i   s 100% i

(1)

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2.6 Average hydrodynamic diameter The average hydrodynamic diameter (Dh) of the co-polymer in solutions was determined by the method of dynamic light scattering (DLS) using a laser particle analyzer (Nano ZS90, Malvern Instrument, UK). Test results could be automatically obtained through DTS (Nano) software of

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Malvern Instrument and follow the CONTIN method[39]. Test temperature was constant at 25℃.

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2.7 Scanning electron microscopy

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Scanning electron microscopy (SEM) images were acquired by using a Hitachi S-4800 type cold field emission scanning electron microscopy (Hitachi, Japan). The samples were processed by freeze

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vacuum drying, and different resolution images could be scanned at an acceleration voltage of 5 kV.

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2.8 Fluorescence probe

Fluorescence spectrum measurements were performed using an F-7000 fluorescence

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spectrophotometer (Hitachi, Japan), and the scanning range is from 350 nm to 450 nm. As a fluorescent

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probe, pyrene may determine the polarity of the micro-environment around the pyrene probe by the ratio between the fluorescence intensities of peak I1 (371 nm) and peak I3 (383 nm)[18]. The pyrene

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concentration in the experiment was 10-6 mol/L.

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2.9 Cohesive energy

The cohesion energy of the co-polymer solution were measured at different temperatures using an Anton Paar MCR301 stress-controlled rheometer equipped with a vertebral plate system with a frequency of 1 Hz and a strain of γ = 0.01 % ~ 100 %. The cohesive energy of the system could be determined by using Equation 2.

1 C.E.  G' Ay 2 2

(2)

Where C.E. was the cohesive energy, Pa; G' was the storage modulus value corresponding to the 7

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linear viscoelastic region, Pa; and Ay was the limited value corresponding to the linear viscoelastic region, %. 3. Results and discussion 3.1 Determination of HACR based on host-guest inclusion

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According to Fig.2a, the apparent viscosity of PAAD solutions decreased as the β-CD

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concentration increased. The apparent viscosity of 1500 mg/L PAAD solution reduced from 342 mPa·s

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to 28.1 mPa·s when the β-CD concentration increased from 0 to 800 mg/L. Moreover, when the apparent viscosity of the inclusion solution was unchanged, for 500 mg/L, 1000 mg/L and 1500 mg/L

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PAAD solutions, the inclusion concentrations of β-CD were about 200mg/L, 400mg/L and 600 mg/L,

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respectively. The differences were related to the inclusion degrees of β-CD, and this trend was consistent with what was described in the literature[33]. Karlson et al.[40] estimates the binding

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constant of 11.2 mM-1 for the complexation of the hydrophobically modified polymer containing

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C14 hydrophobic groups with β-CD at 25℃. This result may be used as a reference because the HMPAM has similar hydrophobic groups. From the SEM images of Fig.2b, it can be seen that the

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size of the aggregate changed significantly when the host-guest inclusion system formed. Based

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on host-guest inclusion, the calculation formula of HACR was shown in the Fig.2b. From Fig.2b, it can be seen that the apparent viscosity of the solution gradually decreased and eventually stabilized with the increasing of β-CD concentration. We also found that ηs did not change even if the concentration of β-CD was excessive. However, the apparent viscosity of PAAM solution did not obviously change with the increase of β-CD concentration (see Fig.2c). These results indicated that the hydrophobic inclusion of PAAD was caused by β-CD. For HMPAM, effect of molecular weight on viscosity is another factor. When the polymer concentration is above its critical 8

ACCEPTED MANUSCRIPT association concentration (CAC), the effect of the molecular weight is not significant. Combined with the results of Fig.2b and Fig.2c, it was found that the apparent viscosity of PAAM (no hydrophobic unit) with high molecular weight was higher than that of PAAD with low molecular weight (see Tab.1) after inclusion of β-CD at the same polymer concentration of 1500 mg/L.

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However, the apparent viscosity of PAAD in aqueous solution was much higher than that of

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PAAM at the same polymer concentration because of its hydrophobic association. It was indicated

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that for the HMPAM, the molecular weight was not a major factor affecting the apparent viscosity

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polymer solution after inclusion of β-CD.

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of the associated polymer solution, but the molecular weight affected the apparent viscosity of the

Fig.2 The apparent viscosity of the co-polymer solution as a function of β-CD concentration (deionized water, T = 25℃) 3.2 Determination of CAC based on host-guest inclusion Fig.3 showed that the HACRs increased from 32% to 85% when PAAD concentrations ranged 9

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from 500 mg/L to 1500 mg/L. When PAAD concentration was 1500 mg/L, the HACR was 85%, indicating that its apparent viscosity was mainly dependent on the hydrophobic association of hydrophobic groups. The hydrophobic interactions among hydrophobic groups cause the formation of hydrophobic

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association in terms of intra-molecular and inter-molecular interaction, which can transform under

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different circumstances[41, 42]. It can be seen from Fig.3 that the HACRs increased sharply when

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PAAD concentrations were less than 1000 mg/L. Moreover, the HACRs tended to be constant when its concentrations were higher than 1000 mg/L. This indicated that there was a noticeable change in the

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curve, which was related to the changes in association behavior. To accurately confirm the critical

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association concentration (CAC) of PAAD solution, a method was proposed as follows: firstly, when PAAD concentrations were below or above 1000 mg/L, the data points on the curve were linearly fitted

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to obtain the fitting formulas and the correlation coefficients (R2); secondly, two fit lines had an

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intersection, which corresponded to its concentration- at the CAC. As a result, the CAC obtained by the method of inclusion was about 924 mg/L. As seen from SEM images in Fig.4, the hydrophobic

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association of PAAD molecules formed supra-molecular aggregates at different polymer concentrations.

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However, larger supra-molecular aggregates formed with the increase of PAAD concentrations because of the change from intra-molecular association to inter-molecular association. The results of SEM illustrates the effect of PAAD concentration on its association behavior. From Fig.5, it can be seen that more and more hydrophobic micro-domains formed by hydrophobic interactions and a huge amount of pyrene dissolved into the hydrophobic micro-domains as PAAD concentration increased. When PAAD concentration was higher than a certain value, the ratios of I3/I1 increased significantly, and the corresponding concentration (882 mg/L) was its CAC. 10

ACCEPTED MANUSCRIPT Compared with the results from Fig.3, it was found that there was no significant difference in the CAC obtained by two different methods, indicating that the method of inclusion for confirming the CAC was

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feasible.

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Fig.3 HACR as a function of PAAD concentration (deionized water, T = 25℃)

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Fig.4 SEM images of PAAD solutions with different concentration (deionized water)

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(a), (d) 500 mg/L PAAD. (b), (e) 1000 mg/L PAAD. (c), (f) 1500 mg/L PAAD

(deionized water, T = 25℃)

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Fig.5 I3/I1 variation as a function of PAAD concentration

3.3 The effect of salt on association behavior The hydrophobic association affects solution properties of HMPAM in aqueous solution. In general, the concentration of HMPAM should be higher than the CAC so as to obtain more excellent properties. In order to illustrate the effects of salt and temperature on the association behavior better, PAAD concentration was set at 1500 mg/L (above the CAC). As shown in Fig.6, the HACRs of PAAD solutions increased as NaCl concentration increased. 12

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However, the HACRs were reduced sharply when NaCl concentrations were above 2000 mg/L. This indicated that the hydrophobic association could be enhanced with a small amount of salt, while the hydrophobic association was weakened at high salt concentration. In addition, fluorescent probe tests were also performed to illustrate the effect of salt on the association behavior of PAAD. Fig.6 showed

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that the ratios of I3/I1 increased as NaCl concentration increased. However, the ratios of I3/I1 were

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reduced sharply when NaCl concentrations were above 2000 mg/L. The results obtained by the method

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of fluorescence were consistent with those obtained by the method of inclusion.

DLS measurements were performed to determine the average hydrodynamic diameter (Dh) of

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co-polymer solution under different NaCl concentrations. Based on Fig.7, the Dh of PAAD solution

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increased firstly and then decreased as NaCl concentration increased. The Dh of PAAM solution decreased smoothly during the process of adding NaCl. The results indicated that a small amount of

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salt could increase the Dh of PAAD solution and its Dh decreased under high salt conditions. As

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combined with the results of DLS of both co-polymers, salt had a different effect on the D h due to the presence of hydrophobic association.

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A schematic diagram of the effect of salt on association behavior was shown in Fig.8. The

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hydrophobic interactions among hydrophobic groups could form the intra-molecular or inter-molecular hydrophobic association, and the inter-molecular hydrophobic association became dominant (above its CAC). In the deionized water, the electrostatic repulsion among the sulfonic acid groups (SO3-) in PAAD side chains caused more stretched the conformation of the polymer molecules. Under low salt conditions, the hydration film formed around the sulfonic acid groups could resist the attack of the salt ions because of the strong hydration of the sulfonic acid group. Simultaneously, a small amount of salt could raise the polarity of the solution, which favored the enhancement of hydrophobic association[43]. 13

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This contributed to the formation of a stronger network structure through inter-molecular hydrophobic associations. However, by further increasing the salt concentrations, the electrostatic repulsion in polymer chains was sharply shielded by the salt effect that caused the polymer chains to coil[44, 45]. Moreover, the amount of water molecules used to dissolve the polymer might reduce at the presence of

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salt ions , which made individual polymer molecules coil and thus reduced the possibility of

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inter-molecular hydrophobic association[46]. This led to a change in the association behavior of PAAD

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in the solution. Combining the results of fluorescence probe, DLS and HACR, We concluded that salt

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concentration had different effects on the association behavior of PAAD in aqueous solution.

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Fig.6 HACR and I3/I1 as a function of NaCl concentration (T = 25℃)

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Fig.7 Dh as a function of NaCl concentration (T = 25℃)

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Fig.8 Schematic diagram of the effect of salt on association behavior 3.4 The effect of temperature on association behavior

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From Fig.9, it can be found that the HACRs of PAAD solution decreased with the increasing of

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temperature. When the temperature exceeded 45℃, the HACRs were significantly reduced. When the temperature increased from 25℃ to 65℃, the HACRs decreased from 85% to 43%. This indicated that

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the effect of temperature on the HACR was significant. The reasons included the following two aspects:

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firstly, the interaction among hydrophobic groups was an entropy-driven process of endothermic[47], in other words, the increase in temperature was conducive to the enhancement of hydrophobic association; secondly, as the temperature increased, the thermal motion of the hydrophobic groups increased and the hydrophobic association was weakened due to the disassociation of hydrophobic groups. Thus, the change of HACRs of PAAD solutions was not significant under the effects of the two factors when the temperature was below 45℃. However, when it was above 45℃, the disassociation of hydrophobic groups became dominant, leading to a significant decrease of the HACR. 15

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Cohesive energy (C.E.) was used to verify the accuracy of the results obtained by the method of inclusion. For HMPAM, C.E. is the self-cohesive force between HMPAM molecules, and C.E. also provides the characterization of the elastic strength of the system. The larger the C.E. is, the higher the intensity of the structure is. The C.E. indicates how much energy is required to destroy the structure of

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the system.

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As shown in Fig.10, storage modulus values (G') and loss modulus values (G'') did not vary at low

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amplitude. The higher the temperature was, the smaller G' and G'' were. When the strain reached the limit value (Ay), G' began to decrease due to the damage of the system structure. When the temperature

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was lower than 45℃, G' was always higher than the G'', indicating that PAAD solution showed an

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elastic fluid characteristic. However, when the temperature was higher than 45℃, G' was less than G'', indicating that PAAD solution showed a viscous fluid characteristic. The transition from the elastic

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fluid to the viscous fluid was related to changes in association behavior under the influence of

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temperature. According to the results in Fig.10, G' (the storage modulus value corresponding to the linear viscoelastic region) and Ay (the limited value corresponding to the linear viscoelastic region)

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could be obtained. The C.E. could be calculated by Equation 2 and the results were shown in Tab.2. Tab.2 The parameters of C.E.

Temperature (℃)

G' (Pa)

Ay (%)

C.E. (Pa)

25

1.85

39.81

1.47×10-1

35

1.48

31.62

7.40×10-2

45

0.83

25.12

2.62×10-2

55

6.18×10-2

19.95

1.23×10-3

65

1.21×10-2

15.85

1.51×10-4

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ACCEPTED MANUSCRIPT From Tab.2, it can be seen that the C.E. of 1500 mg/L PAAD solution decreased from 1.47×10-1 Pa to 1.51×10-4 Pa when the temperature increased from 25℃ to 65℃. For the HMPAM with a specific structure, the C.E. of PAAD solution decreased with the increase of temperature. This indicated that there was a significant negative correlation between the temperature and the association among the

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molecules. In other words, the association among the molecules was inclined to be weaker with the

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increase of temperature. The conclusions obtained by the rheological method and the inclusion method

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were consistent.

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Fig.9 HACR and C.E. as a function of temperature (deionized water)

Fig.10 Amplitude scanning curves of PAAD solution with different temperature (Frequency = 1 Hz, deionized water)

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4. Conclusions The HACR of PAAD solution could be quantitatively determined by β-CD inclusion. The quantitative method based on the HACR can be used to confirm the CAC of PAAD solution and investigate the effects of salt and temperature on the association behavior of PAAD in aqueous solution.

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The quantitative method has the advantages of no required expensive instrument, simple operation,

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convenient testing, and low cost. It must be pointed out that the method is based on the premise that

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β-CD can form the inclusion complex with HMPAM. However, in order to improve the thickening property of HMPAM used for EOR, hydrophobic groups with strong hydrophobicity are used to

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enhance the hydrophobic association in the design of the molecular structure of HMPAMs, which has

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created favorable conditions for the inclusion of β-CD on guest molecules. Thus, this method offers another simple way to study the association behavior of HMPAMs in aqueous solution.

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Acknowledgments

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The work was supported by the National Natural Science Foundation of China (51774309), Shandong Provincial Natural Science Foundation, China (ZR2017LEE001), Key Research and

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Development Plan of Shandong Province (2018GGX102010), the Fundamental Research Funds for the

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Central Universities (18CX02166A), Scientific Research Fund for Introducing Scholars of China University of Petroleum (YJ201601088).

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ACCEPTED MANUSCRIPT Highlights

1. A quantitative method to study the association behavior of the HMPAM was proposed.

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2. Different conventional methods were used to verify the accuracy of this method.

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3. A novel method to determine the CAC of the HMPAM was introduced.

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4. The effect of salt on the association behavior of the HMPAM was revealed.

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5. The effect of temperature on the association behavior of the HMPAM was revealed.

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