Influence of Solvent Quality on the Force Response of Individual Poly

Sep 13, 2017 - Best fit of the force–extension profiles with the FJC model reveals that the Kuhn length varies systematically with solvent quality. ...
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Influence of Solvent Quality on the Force Response of Individual Poly(styrene) Polymer Chains Milad Radiom,† Plinio Maroni, and Michal Borkovec* Department of Inorganic and Analytical Chemistry, University of Geneva, Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland S Supporting Information *

ABSTRACT: Single molecule mechanics of poly(styrene) polymer chains is investigated in different organic solvents with atomic force microscopy (AFM). The acquired force−extension profiles can be well fitted with a modified freely jointed chain (FJC) model. The model describes the force−extension profiles in terms of an apparent Kuhn length and an elasticity constant. The elasticity constant is found to be the same for all different solvents investigated. Best fit of the force−extension profiles with the FJC model reveals that the Kuhn length varies systematically with solvent quality. In fact, one can establish a good correlation between the Kuhn length and the Flory−Huggins interaction parameter. The increase in the Kuhn length with increasing solvent quality reflects the larger extent of swelling of the polymer in good solvents.

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For this reason, we performed accurate measurements of force−extension profiles of poly(styrene) in different organic solvents with the AFM featuring a high force resolution of about 0.01 nN. Since the presently measured forces reach 1.0 nN, these conditions extend the measurement range and accuracy beyond previous reports substantially. Therefore, we can extract new information from our experiments and are able to pinpoint the variation of the force response with solvent quality for the first time. The scheme of the experiment is depicted in Figure 1a. The poly(styrene) used has a molecular mass of 280 kg/mol and a polydispersity index of 2.3. The substrate is coated with the polymer by placing a drop of polymer solution of a concentration of 10 mg/L in toluene for 20 min on its top. The coated substrate is then rinsed with toluene, dried, and mounted in the fluid cell of the AFM (Cypher, Oxford Instruments). The organic solvent in question was filled into the cell, which was then sealed to prevent solvent evaporation. The interaction between the AFM-tip and substrate is probed with repeated approach-retraction cycles with a velocity of 200 nm/s. Force−distance profiles were acquired with a sampling rate of 2 kHz, and were subsequently converted to force− extension profiles by subtraction of the tip deflection.21 Typical traces measured in octane are shown in Figure 1b. On approach, the cantilever feels basically no force, except at short separations due to the interaction with the substrate. On retraction, however, polymer chains are occasionally picked up, and their stretching is signaled by a spike-like force response. As

robing the force response of single polymer molecules became an active research area, especially during the past decade. Within these efforts, DNA was probably investigated in greatest detail with atomic force microscopy (AFM) as well as optical and magnetic tweezers, as these force profiles reveal substantial complexity due to their dependence on its twisting and zipping states.1 The force response of muscle proteins (e.g., titin, tenascin) was mostly studied by AFM and was found to be determined by a sequence of conformational transitions within individual protein domains.2−5 The force response of simpler polymers, particularly polyelectrolytes and polysaccharides, was equally analyzed and quantified with various models.6−11 Force response of individual neutral polymers was studied to a far lesser extent.12−16 One exception is the detailed studies of the force−extension behavior of poly(ethylene glycol) with the AFM.16−18 These studies reveal that the force response of poly(ethylene glycol) is different in apolar solvents and in water. The response is found to depend on the size of the solvent molecules and, in water, it is governed by conformational transitions between a planar and helical structure of the chain. Pang et al.19 reported similar differences of the force− extension behavior in poly(acrylamides) between apolar solvents and water and attributed those to the presence of hydrogen bonds. Force−extension relationships were also studied with the AFM for various poly(acrylamides), poly(vinyl alcohol), and poly(styrene).13−15,20 Wang et al.14 studied three different polymers in an organic solvent, but these authors could not find any significant differences in the force−extension behavior of the polymers. However, we are not aware of other comparisons of force−extension relationships of simple polymer molecules in different organic solvents, especially concerning the effects of solvent quality. © XXXX American Chemical Society

Received: August 25, 2017 Accepted: September 11, 2017

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up by the AFM tip. The consistency of the present analysis is confirmed by the collapse of the different force curves on a single master curve and the fact that the same Kuhn length is obtained in spite of the substantial variation of the contour length. We carried out the same experiments with different substrates (i.e., silica, mica, gold) and different tips (i.e., quartz and epoxy-functionalized). The congruence of the force− extension profiles measured with different substrates and tips and with polymers of different length confirms that the present experiments reflect the stretching response of single polymer molecules. The present value of the Kuhn length agrees well with the findings by Wang et al.14 These authors have also analyzed the stretching response of poly(styrene) in octane with the AFM and fitted their data with the freely rotating chain (FRC) model. They find that the length of the rotating unit is 0.154 nm. This FRC model gives an equivalent force response as the presently used FJC model, provided the Kuhn length is identified with twice the length of the rotating unit. Similar experiments were carried out in eight additional organic solvents. In most solvents the detachment forces exceeded 1.0 nN. For toluene and xylene, however, these forces were lower, and they were around 0.8 nN. We suspect that these solvents weaken the polymer−substrate interactions. Similar least-squares fits of the force profiles with detachment forces exceeding 1.0 nN confirm that the elasticity constant is the same within experimental error, with a mean value K = 21 ± 1 nN. We have therefore fixed this parameter to the respective mean value and refitted all profiles with this constraint with almost the same accuracy. Our value of K = 21 nN of the elasticity constant agrees reasonably well with the theoretical value of 29 nN, which was calculated for propane by ab initio quantum chemistry methods.22 Selected results together with the respective best fits with the modified FJC model are shown in Figure 2. One observes that

Figure 1. Probing the extension mechanics of single poly(styrene) polymer molecules in octane by AFM. (a) Scheme of the experiment. (b) Representative approach and retraction force−extension profiles. (c) Force profiles plotted vs relative extension, together with the best fit with modified FJC model. Experiments with silica, gold, and mica substrates were performed with quartz tips. Silica* denotes traces obtained with a silica substrate and an epoxy-functionalized tip. The resulting fitting parameters are Kuhn length S = 0.38 ± 0.02 nm and elasticity constant K = 21 ± 1 nN. The residuals are shown in (d).

the cantilever is being lifted further, the polymer detaches, and the cantilever jumps back. Further outward from that point, the cantilever does not feel any force. The probability to observe single molecule stretching events was around 0.1%. The maximum detachment force was about 1.5 nN in octane, and this value is similar to the ones observed earlier for comparable adsorption conditions of poly(vinyl amine) or polypeptides.22 Further details on the present experiments are given in the Supporting Information. The stretching part of the force profile is analyzed by leastsquares fit with the modified freely jointed chain (FJC) model. This model predicts that the applied force F is related to the extension x of the chain by11,23 ⎛ SF ⎞ kT x F = coth⎜ ⎟ − + ⎝ ⎠ L kT SF K

(1)

where L is the contour length, S is the apparent Kuhn length, k is the Boltzmann constant, T is the absolute temperature, and K is the elasticity constant. The first two terms reflect the nonlinear extension relation of the FJC model, and the last term is the elastic term. This relation assumes that these two springs to act in series, and yields virtually identical results to the one proposed earlier, which is based on a force-dependent contour length.24 The FJC model was shown to provide the proper limiting behavior for force−extension relationships at high forces, as being probed by the AFM. While the worm-like chain (WLC) model should be applicable at lower forces, this regime cannot be accurately probed in our experiments.25,26 The modified FJC model predicts that the force is a universal function of the relative extension x/L and, thus, the force profiles of polymers of different lengths should collapse on a unique master curve. Such a master curve is shown in Figure 1c and the best-fit residuals in Figure 1d. One observes that the model provides an excellent description of the data. Best fits yield an apparent Kuhn length S = 0.38 ± 0.02 nm and an elasticity constant of K = 21 ± 1 nN with octane as solvent. The fitted contour length L of poly(styrene) vary between 30− 180 nm, as chains of different contour length are being picked

Figure 2. Force profiles in different solvents plotted versus the relative extension (solid color) together with the best fits with the modified FJC model (solid black). These models use a common elastic term (dashed line) with an elasticity constant of 21 nN. The different apparent Kuhn lengths S are indicated in the figure as well.

the force response differs substantially in the low force regime, but that at higher forces their slope converges to similar values. This slope reflects the elasticity constant K, which suggests that this constant is independent of the type of the solvent. Figure 2 demonstrates that the apparent Kuhn length varies systematically with the solvent, and decreases from a value of 0.43 nm for toluene, 0.38 nm in octane, to a value of 0.27 nm in ethanol. Indeed, this variation suggests to be related to the solvent quality, since toluene is a good solvent for poly(styrene), while 1053

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reported for other polymers.9 One can rationalize these differences by noting that the Kuhn length depends on the length scale being probed. With increasing extension of the polymer chain, the long wavelength fluctuations are progressively eliminated, which leads to a softening of the polymer chain and a decrease of the effective Kuhn length.33 In conclusion, we have accurately measured the force− extension relationship of single poly(styrene) molecules in different organic solvents with the AFM. The observed force response can be well quantified with a modified FJC model. We find that the Kuhn length increases systematically with increasing solvent quality. While this trend is expected, the present study is the first one to confirm such variations with measurements of the force−extension relationships of individual polymer molecules. This trend is preserved even for the apparent Kuhn length of highly extended polymers, whose values are much smaller than the ones of unperturbed chains.

ethanol is a rather poor one. Figures S1−S4 summarize the experimental data for all solvents. The anticipated trend in the apparent Kuhn length with the solvent quality can be confirmed by considering the dependence on the Flory−Huggins χ interaction parameter. This parameter is commonly used to characterize solvent quality, and can be estimated from the relation27−29 χ = 0.34 +

VS (δS − δ P)2 RT

(2)

where VS is the molar volume of the solvent, R is the gas constant, and δS and δP are the solubility parameters for the solvent and the polymer, respectively. The solubility parameters are tabulated (Table S1).28 The ones for the solvents were obtained from heats of vaporization, while the one was for the polymer from solubility studies, chromatography, or by other methods. Figure 3 illustrates the relation between the measured

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.7b00652. Details on experimental methods, Figures S1−S4, and Table S1 (PDF).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Figure 3. Apparent Kuhn length obtained from fitting the force− extension profiles versus the Flory−Huggins interaction parameter χ. The latter parameter is a measure of solvent quality. The solid line is a linear regression line.

Milad Radiom: 0000-0002-6339-9288 Michal Borkovec: 0000-0002-1114-4865 Author Contributions

† School of Chemical Science and Engineering, KTH Royal Institute of Technology, Drottning Kristinas väg 51, Stockholm 10044, Sweden.

apparent Kuhn length and the Flory−Huggins interaction parameter together with a linear regression line. Indeed, one observes that the Kuhn length decreases with decreasing solvent quality. A statistical test reveals on a highly significant level that the slope of the regression line is negative. This trend is anticipated since the polymer is expected to be swollen in a good solvent while more collapsed in a poor solvent. The Kuhn length should be thus largest in a good solvent, while smallest in a poor one.30 The values for isopropanol lie somewhat below the trend line, which could be caused by contributions of hydrogenbonding. The values for xylene lie above the line, for which specific interactions between xylene and poly(styrene) could be responsible. For octane and cyclohexane, one observes similar Kuhn lengths in spite of the somewhat different interaction parameters. In spite of these minor variations, this correlation is most encouraging and represents the main result of this letter. The smallest Kuhn length observed are similar to the twice the projected bond length of 0.25 nm, as one would expect from the FRC model.25 The apparent Kuhn lengths reported here are substantially smaller than the ones for poly(styrene) obtained from neutron scattering experiments carried out in θ solvents.31,32 These measurements suggest a value for the persistence length around 1 nm. This value corresponds to a Kuhn length of about 2 nm, which is roughly a factor of 5 larger than the presently measured value in cyclohexane. Similar discrepancies were

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support of this research was provided by the National Center of Competence in Research (NCCR) for Bio-Inspired Materials and University of Geneva.

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