Probing Single Polymer Chain Mechanics Using Atomic Force

Chapter 11

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Probing Single Polymer Chain Mechanics Using Atomic Force Microscopy Pamela Y. Meadows, Jason E.Bemis,SabahAl-Maawali, and GilbertC.Walker Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260

Abstract Polymer and protein adsorption play important roles in processes such as the fouling of ships to determining the biocompatibility of surfaces. By understanding the mechanics involved in polymer-surface interactions, new insight can be obtained into designing surfaces that resist biofouling. With the atomic forcemicroscope's(AFM) unique ability to measure small magnitudes of force (< 20pN) as a function of tip-sample separation, it has become an essential tool for studying ligand-receptor adhesion forces, polymer elasticity, and the folding kinetics of many biological systems. In the review presented here, we will investigate the elastic properties of polystyrene-b-poly-2-vinylpyridine (PS-P2VP) chains from spun-cast films, characterize the polydispersity of poly(dimethylsiloxane) (PDMS) surfaces, and estimate the stability of an adhesion promoting protein (fibronectin, FN) as a function of protein surface density. 1

2

3

148

© 2005 American Chemical Society

Batteas et al.; Applications of Scanned Probe Microscopy to Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 2005.

149

Introduction Single Polymer Chain Elongation by Atomic Force Microscopy 1

Studies of PS-P2VP adhesion to an A F M probe were examined and modeled. Adhesion models between two surfaces such as Johnson, Kendall, and Roberts theory (JKR) could not be used since the macroscopic models fail to describe the adhesion of surfaces linked by a single or multiple polymer chains. Figure 1 shows a typical force plot obtained for PS60800-P2VP46900 (the numbers after the block name indicate the molecular weight of each individual block in units of Daltons). As the tip contacts the surface, one or more polymer chains can physisorb to the tip. Once the AFM piezo retracts from the surface (A), the polymer chains become elongated as can be seen in Β and C of Figure 1. Here, the AFM probe experiences elastic tension due to the attached polymer chain, giving rise to the increase in force. At point C, the polymer chain breaks free from the tip, resulting in a return to zero tip deflection (D). The length (58 nm) and force (180 pN) at point C characterize the behavior of the extended polymer chain; data between points A through C are fit by theoretical models (dotted and solid lines).


4

0.05,—,

-0.2

,

LL

10

.

,

,

,

20 30 40 50 60 Tip-sample separation [nm]

,—,

70

Figure 1: A force plot obtained for the extension of PS60800-P2VP46900 with tip illustration ofpolymer dynamics occurring during forced extension. The solid line is a WLCfitto the data giving parameters of 5.75 Â (persistence length), 0.90 (extension ratio), and α χ of 1.52. The dotted line represents a FJC fit with 5.86 À obtained for the Kuhn length, 0.96 for the extension ratio, and αχ of 1.45. (Reproduced with permission from reference 1. Copyright 1999) 2

2


150 5

Two principal models used to explain the entropie elasticity of polymer stretching events are the freely jointed chain (FJC) and the wormlike chain (WLC) models. In the FJC model, the force-distance dependence is described by Equation 1 where L*(R) is the inverse Langevin function, L*(R) = β, with the Langevin function L(R) = coth(P) - 1/β.


F =

(1)

V

Here F represents the tension between two points in units of nN, k is the Boltzmann constant (aJ/K), Τ is the temperature in units of Kelvin, and A is the Kuhn length in units of nm. R represents the unitless extension ratio and can be defined as the fraction of the polymer's contour length that is extended. In the WLC model, the force-distance behavior is described by Equation 2 where q is the persistence length in nm. k

(2)

F =| — 4 ; 4(l — /?)

4

Figure 1 demonstrates a fit of the polymer elastic response to both the FJC model (dotted line) and the WLC model (solid line). The major difference in the fitting of the data by these two models occurs in the low force, low extension region (25 to 45 nm). However, due to the noise in the data and as Table 1 demonstrates with the χ values, neither model can be assigned as the better fit. The analysis of the distribution using these models can be seen in Table 1. 2

Table 1: Fitted Parameters for the WLC and FJC Models

WLC Polvmer

PS7800PVP10000 PS13800PVP47000 PS52400PVP28100 PS60100PVP46900

median persistence length. Â 3.0 ± 2 . 6

FJC

0.70 ± 0 . 1 5

median Kuhn leneth. Â 3.6 ± 2 . 7

0.74 ± 0 . 1 7

2.4 ± 2 . 1

0.41 ± 0.26

3.0 ± 4.0

0.49 ± 0 . 3 5

2.9 ± 11.3

0.40 ± 0 . 1 8

4.0 ± 1 1 . 6

0.42 ± 0 . 1 8

4.5 ± 14.0

0.72 ± 0.44

5.8 ± 10.5

0.70 ± 0 . 4 4

mean y

2

mean χ

2

Evidence of Single Molecule Measurements


151 It is now important to determine whether the single rupture force plots seen in Figure 1 represent the extension of a single polymer chain or the extension of multiple chains. Using Equation 3, it is possible to estimate the chain diameter that is being elongated with the AFM tip.

Here D represents the chain diameter, q is the persistence length obtained from a WLC fit, k is the Boltzmann constant, Τ is temperature, and Ε represents the Young modulus which has a value of 3 GPa for polystyrene. Analysis shows the molecular diameter to be 2.5 ± 0.5 Â which suggests that either a single chain or chains in series are being extended. We can eliminate the extension of chains in series as a probable event by looking at the polymer contour length obtained from the AFM measurments. The mean length of polymer extension obtained with AFM is plotted versus the chain length (estimated from the covalent radii of carbon, the carbon-carbon bond angle, and the number of monomers in the chain) in Figure 2 (solid line). As the chain length increases, the probability of entanglement increases, and therefore, the length to which the AFM probe can extend the polymer from the surface is smaller as well. Also in Figure 2, an estimate of the contour length of 140 'nm]


(3)

120 c ο » 100

Φ Φ «•—

ο χ:

80

Βc Φ

60

c φ

40

ε

20 0

50

100 150 200 250 length of chain [nm]

300

Figure 2: A plot of four block copolymers ofPS-P2VP of varying molecular weights. The solid line is a plot of the rupture length obtained from AFM measurements versus the chain length. The upper dashed line is the chain contour length between the tip and surface estimated from the extension ratios from the WLCfit.(Reproduced with permission from reference 1. Copyright 1999)


152 the chain between the tip and surface is plotted versus the chain length (dashed line). The contour length estimation was made using the extension ratio obtained from the WLC fits. Since the estimated contour length is significantly less than the length estimated from the molecular weight, we can exclude the case that chains in series are being extended from the surface by the A F M tip. Further evidence for single molecule measurements comes from the persistence length of 3 to 4 Â. Data obtained from X-ray and neutron scattering have obtained values on this same order, providing further evidence that the single rupture force plots involve the extension of a single polymer chain.


6

Multiple Elastic Responses Can Indicate Single Molecule Measurements Figure 3 illustrates a less frequent case where multiple elastic ruptures are observed when the tip retracts from the polymer covered surface. The origin of these ruptures could arise from multiple chains breaking free from the tip or multiple attachments of a single polymer chain rupturing from the A F M probe. To determine whether the multiple ruptures correspond to a single molecule or 0.05

20

40 60 80 100 120 140 160 Tip-sample separation [nm]

Figure 3: Force plot of PS60800-P2VP46900 displaying multiple elastic responses. A) The multichain, multipersistence length WLC model (solid line) with the dashed lines representing the individual chain responses gives the following values for persistence length ( from left to right): 1.9, 12, 22, 63, 21, and 4.7 A. The χ is 1.09. B) The single chain, single persistence length WLC model gives a persistence length of0.44nm with α χ of 1.96. (Reproduced with permission from reference 1. Copyright 1999) 2

2


153 multiple polymer chains, the data were fit by several models. In Figure 3A a multichain, multipersistence length model was used while the data in Β was modeled by a single chain with a single persistence length. As noted in the caption, the multichain model yielded higher persistence lengths. The data were also fit to a multichain, single persistence length model (not shown), giving a persistence length of 5.7 Â and a χ of 2.54 which is greater than the single molecule, single persistence length model. Because of the correct persistence lengths and molecular diameters obtained with the single chain model compared to the multichain models, it can be concluded that the multiple ruptures observed in Figure 3 are more likely to arise from multiple polymer attachments of a single chain to the A F M tip rather than the extension of multiple polymer chains.


2

Polydispersity of Grafted Poly(dimethylsiloxane) Surfaces Using Single-Molecule Atomic Force Microscopy 2

Synthesis of polymers through polycondensation or free radical mechanisms produce molecules of various molecular weights and hence lengths. " The polydispersity index (PI) is used to describe the chain length distribution of the polymer solution and can be expressed by Equation 4. 7

PI = M IM w

Here M

w

9

(4)

n

is the weight average molecular weight (g/mol) where M

n

is the

number average molecular weight. If the solution is monodisperse, the polydispersity index will have a value of 1. Gel permeation chromatography (GPC), light scattering, and vapor pressure osmometry have been used to quantify the polydispersity of polymer solutions, but few methods exist that quantify the molecular distribution at surfaces. Here, we use an A F M to study poly(dimethylsiloxane) (PDMS) and its molecular distribution on hydroxyl terminated silicon surfaces. Molecular weights of 3000 and 15000-20000 were studied with contour lengths of 11 and 50-80 nm respectively. Figure 4 and Table 2 show the distribution of polymer chain lengths obtained with varying volume ratios of PDMS and CH2CI2 as obtained by A F M extension measurements and the WLC model. Data obtained from GPC can also be seen in Figure 4. The shift of the distribution toward higher contour lengths with increasing peak widths as the PDMS:CH Cl2 volume ratios increase indicates a preferential adsorption of longer chains at higher volume ratios. At the most dilute PDMS:CH C1 ratio, the A F M data correlate well with analysis performed using GPC. 7,9

2

2

2



154

Figure 4: AFM distributions of the contour length obtained for different PDMS.CH2CI2 volume ratios along with the results from GPC. (Reproduced with permission from reference 2. Copyright 2001.)

Table 2: Peak Heights and Widths at Different PDMS:CH C1 Volume Ratios using Gaussian fits 2

2

PDMS:CH CI Volume Ratios

Peak Positions at Highest Probabilities (nm)

Peak Widths (nm)

PI

0.005 0.04 0.11 0.16

40.0 52.7 69.9 101.0

63.2 85.4 119.7 152.7

1.56 1.56 1.47 1.4

2

2

The observance of preferential adsorption of higher molecular weight polymers at higher concentrations is consistent with other studies that analyzed the remaining unreacted solution. " This observation is illustrated qualitatively in Figure 5 using Flory-Huggins theory where the entropy of mixing is plotted versus the polymer chain length. Longer chains are more likely to react at the surface since their entropy of mixing per mass is lower than shorter chains. From the A F M results for the contour lengths, an estimation of the polymer molecular weight can be made using Equation 5 where the molecular weight of one siloxane monomer is 74 and 0.28 nm is the length of one monomer. 7

9

7



155

Figure 5: A plot of the entropy of mixing as a function of polymer chain length using Flory-Huggins theory. The lines indicate peak positions of the AFM results for contour lengths of PDMS at different PDMS:CH Cl ratios. (Reproduced with permission from reference 2. Copyright 2001.) 7

2

2

l

-

M. = 1

(5)

0.28

The polydispersity index can then be calculated using Equation 4 after calculating the weight average molecular weight and number average molecular weight using Equations 6 and 7.

η=^Σ '

Μ

Μ

(6)

Σ*

Probing Single Polymer Chain Mechanics Using Atomic Force

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